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Xerox University Microfilms300 North Z eeb RoadAnn Arbor, Michigan 48106

73-23,943

JAYROE, J r . , R obert Rhea, 1940-UNSUPERVISED SPATIAL CLUSTERING WITH SPECTRAL DISCRIMINATION.

The U n iv e rs ity o f Oklahoma, P h .D ., 1973 P h y s ic s , g e n e ra l

University Microfilms, A XEROX Company, Ann Arbor, Michigan

THIS DISSERTATION HAS BEEN MICROFILMED EXACTLY AS RECEIVED.

THE UNIVERSITY OF OKLAHOMA

GRADUATE COLLEGE

UNSUPERVISED SPATIAL CLUSTERING WITH SPECTRAL DISCRIMINATION

A DISSERTATION

SUBMITTED TO THE GRADUATE FACULTY

in p a r t i a l f u l f i l lm e n t o f th e requ irem en ts fo r th e

degree of

DOCTOR OF PHILOSOPHY

BY

ROBERT R. JAYROE, JR.

N om an, Oklahoma

1972


APPROVED BY

iT i f n '

DISSERTATION COMMITTEE

ACKNOWLEDGMENT

This work i s subm itted to th e G raduate College of th e U n iv e rs ity of

Oklahoma in p a r t i a l f u l f i l lm e n t o f th e requirem ents fo r th e degree of

D octor o f P h ilosophy .

The au th o r w ishes to ex p ress h is s in c e re s t g ra t i tu d e and ap p rec ia

t io n to h is Major P ro fe s so r , Dr. R. G. Fow ler, of th e Department of

P hysics and Astronomy a t th e U n iv e rs ity of Oklahoma fo r p rov id ing

a s s is ta n c e , m orale and guidance th roughout th e e n t i r e graduate

cu rricu lum ..

The au th o r a lso w ishes to ex p ress a s in c e re ap p re c ia tio n to

Dr. F. R. K rause o f th e N a tio n a l A eronau tics and Space A dm in istra tio n ,

George C. M arshall Space F l ig h t C en te r, Aero-Astrodynamics L aborato ry ,

H u n ts v il le , Alabama, and th e T ra in in g Branch o f M arshall Space F lig h t

C enter fo r p rov id in g th e o p p o rtu n ity of co n tin u in g ed u ca tion , working

ex p erien ce and perform ing in te r e s t in g re s e a rc h .

In a d d i t io n , th e au th o r w ishes to exp ress h is g ra ti tu d e to

Mr. M elvin R. P h i l l ip s o f th e ITT R esearch I n s t i t u t e , who performed

th e program ing fo r in te r f a c in g th e c l a s s i f i c a t i o n programs w ith th e

v a r io u s in p u t-o u tp u t d ev ices and fo r in te g ra t in g th e se programs in to the

E arth R esources P ro cesso r Computer Program developed under h is c o n tra c t ,

NAS8-26797.

iii

The au th o r w ishes to acknowledge D r. H arry W. Smedes o f th e

U nited S ta te s G eo lo g ica l Survey , D enver, C o lorado , f o r h is many

in t e r e s t in g d is c u s s io n s and co o p e ra tio n and f o r sup p ly in g th e raw

d a ta , ground t r u t h , and e v a lu a tio n o f r e s u l t s f o r th e Y ellow stone

P ark t e s t s i t e .

The au th o r a ls o w ishes to acknowledge Dr. David Landgrebe and

Mr. T erry P h i l l ip s o f Purdue U n iv e rs i ty f o r su p p ly in g th e d a ta and

ground t r u t h fo r th e Purdue F l ig h t L ine Cl t e s t s i t e .

T his work was perform ed a t th e George C. M arsh a ll Space F l ig h t

C en te r, H u n ts v i l le , Alabama, and i s in su p p o rt o f th e Alabama E a rth

R esources Technology S a t e l l i t e 1 in v e s t ig a t io n and M arsh a ll Space

F l ig h t C e n te r’s Skylab E arth R esources E xperim en ta l Package

I n v e s t ig a t io n 560M.

IV

TABLE OE CONTENTS

Page

LIST OF TABLES.......................................................................................................................... v i

LIST OF F IG U R E S ................................................................................................................... v i i

C hapter

I . INTRODUCTION .................................................................................................. 1

I I . SYNOPSIS ON FEATURE EXTRACTION .......................................................... 3

I I I . UNSUPERVISED FEATURE EXTRACTION............................................................13

IV. RESULTS .............................................................................................................28

V. CONCLUSIONS........................................................................................................ 72

LIST OF REFERENCES................................................................................................................. 76

APPENDIX A PROGRAM DESCRIPTION..................................................................................78

APPENDIX B COMPUTER PROGRAM L IS T IN G S .....................................................................82

APPENDIX C CHANNEL DEPENDENCE CONSIDERATIONS ............................................. 104

V

LIST OF TABLES

Table Page

1. Channel and W avelength Correspondence ................................................... 29

2. Ground T ru th In fo rm atio n .................................................................................. 32

3. M erging P rocedu re fo r F i r s t 40 C l u s t e r s ..................................................34

4. Merging P rocedure fo r C lu s te rs 4 1 - 7 9 ................................................... 35

5. Merging P rocedure fo r C lu s te rs 2 5 - 5 2 ................................................... 37

6. M u ltip le C lu s te r F ie ld s ................................................................................. 38

7. F e a tu re Symbol and D e s c r ip t i o n ........................................................................40

8. User I n te r p r e ta t i o n o f R e s u l t s ....................................................................... 41

9. Merging P rocedu re fo r Y ellow stone D a t a ......................................................57

10. I n te r p r e ta t i o n o f Y ellow stone R e c r u i t s ......................................................58

V i

LIST OF FIGURES

Figure Page

1. Data C o lle c tio n P la tfo rm Showing Sensor O utputs and

A ssocia ted F ea tu re V ecto rs . . . . . . . . . . . .................. 6

2 . Program Logic F lo w ........................................................................................14

3. F lig h t Line Cl - A e r ia l Pho to , C lu s te r S e le c tio n and

I n i t i a l C la s s i f ic a t io n ................................................................................ 31

4 . F in a l Cl C la s s i f ic a t io n Map - S ec tio n 1 ............................................ 42

5. F in a l Cl C la s s i f ic a t io n Map - S ec tio n 2 ............................................ 43

6. F in a l Cl C la s s i f i c a t io n Map - S ec tio n 3 ............................................ 44




10. F in a l Cl C la s s i f i c a t io n Map - S ec tio n 7 ..................................... . 48

11. F in a l Cl C la s s i f i c a t io n Map - S ec tio n 8 ............................................ 49

12. F in a l Cl C la s s i f ic a t io n Map - S ec tio n 9 .............................................50

13. F in a l Cl C la s s i f i c a t io n Map - S ec tion 1 0 .............................................51

14. F in a l Cl C la s s i f i c a t io n Map - S ec tio n 1 1 .............................................52

15. F in a l Cl C la s s i f i c a t io n Map - S ec tion 12 . . ............................... 53

16. Y ellow stone P ark - Video R e p rin t, C lu s te r S e le c tio n ,

I n i t i a l C la s s i f ic a t io n and Secondary C lu s te r S e le c tio n . . . 55

17. F in a l Y ellow stone Park C la s s i f ic a t io n Map - S ec tio n 1 . . . . 60

vii

LIST OF FIGURES (co n tin u ed )

F ig u re Page

18. F in a l Y ellow stone P ark C la s s i f i c a t io n Map - S ec tio n 2 . • . .61

19. F in a l Y ellow stone P ark C la s s i f i c a t io n Map - S ec tio n 3 . • . .62

20. F in a l Y ellow stone Park C la s s i f i c a t io n Map - S ec tio n 4 . • . .63



23. F in a l Y ellow stone Park C la s s i f i c a t io n Map - S ec tio n 7 . • . . 66

24. F in a l Y ellow stone P ark C la s s i f i c a t io n Map — S ec tio n 8 . • . .67

25. F in a l Y ellow stone Park C la s s i f i c a t io n Map - S ec tio n 9 . ■ . .68

26. F in a l Y ellow stone P ark C la s s i f i c a t io n Map - S ec tio n 10. • . .69

27. F in a l Y ellow stone Park C la s s i f i c a t io n Map - S ec tio n 11. • . .70

28. F in a l Y ellow stone Park C la s s i f i c a t io n Map - S ec tio n 12. • . .71

29. Channels 1 and 2 Mean V alues . . . . . 106

30.

31. Channels 1 and 2 V ariances ................... o 110

32. Channel 1 V ariances and C ovariances w ith Channel 2 • • ' . I l l

33.

34. Channel 1 V ariances and C ovariances w ith Channel 3 . . . . 113

V l l l


CHAPTER I

INTRODUCTION

The o b je c tiv e o f t h i s r e s e a rc h i s th e co n v ers io n o f rem o te ly sensed

d a ta in to u s e fu l in fo rm a tio n re g a rd in g th e lo c a t io n and d i s t r i b u t i o n o f

v a r io u s c la s s e s o f i d e n t i f i a b l e .ea rth o b s e rv a tio n f e a tu r e s . The rem o te ly

sensed d a ta i s c o l le c te d from a p la tfo rm , which may be an a i r p la n e , a

s h ip , a b a llo o n o r a s a t e l l i t e . The se n so rs used g e n e ra lly c o l l e c t

e le c tro m a g n e tic r a d ia t io n in s p e c if ie d w avelength i n t e r v a l s (m u lt i-

s p e c t r a l and therm al s c a n n e rs , o th e r ty p e s o f ra d io m e te rs , and m u ltiband

p h o to g rap h y ), echo r e tu rn s ( s id e lo o k in g a e r i a l ra d a r and so n ar) and

m agnetic f i e l d in fo rm a tio n (m agnetom eter), to name a few. The c o l le c te d

d a ta may be an a lo g , d i g i t a l o r a ph o to g rap h ic im age; and th e d a ta i s

fo rm a tted such th a t a one to one correspondence i s p re se rv e d betw een

th e ground scene and th e d a ta , a s in an a e r i a l ph o to g rap h . The d a ta

i s th en analyzed to d e te rm in e what f e a tu r e s can be e x tra c te d from th e

d a ta and to determ ine th e lo c a t io n and th e d i s t r i b u t i o n o f th e se

f e a tu r e s . Examples of f e a tu r e s could be crop ty p e s , d is e a se d c ro p s ,

bo d ies o f w a te r , w a te r p o l lu t io n and lan d ty p e s . M u ltitu d e s o f o th e r

ty p es o f f e a tu r e s e x i s t . As p r e s e n t ly u se d , th e r e a re th r e e m ain ty p es

o f f e a tu r e e x t r a c t io n m ethods, w hich w i l l be deno ted by human photo

1

2

i n t e r p r e t a t i o n , su p e rv ise d com puter f e a tu r e e x t r a c t io n , and u n superv ised

com puter f e a tu r e e x t r a c t io n . The f i r s t two f e a tu r e e x t r a c t io n methods

in v o lv e human su p e rv is io n and judgm ent a f t e r th e f a c t , w hereas th e

t h i r d method does n o t pe rm it any change o f c r i t e r io n from datum to

datum . The u n su p erv ised com puter f e a tu r e e x t r a c t io n method i s based

e n t i r e ly on a lo g ic a l s e t o f m a th em atica l r u le s designed to e x t r a c t th e

f e a tu r e s p re s e n te d in th e rem o te ly sensed d a ta . T his r e p o r t d is c u s s e s

th e th re e m ost commonly used ty p e s o f f e a tu r e e x t ra c t io n methods and

p re s e n ts a r e c e n t ly developed com puter program fo r u n superv ised f e a tu r e

e x t r a c t io n .

CHAPTER II

SYNOPSIS ON FEATURE EXTRACTION

The most u n iv e rs a l method of f e a tu r e e x tra c tio n i s th e c l a s s i c a l

a r t of photo in t e r p r e ta t io n . This a r t i s p r im a rily a p rocess of v is u a l

in s p e c t io n and s u b je c t iv e a n a ly s is by a tra in e d human o b se rv e r, and i t

h as been g r e a t ly enhanced by a v a r ie ty o f in s trum en ts and machines

( s te r e o v ie w e rs , m ic ro d en s ito m e te rs , a u to p lo t te r s , f a ls e co lo r image

enhancem ent, e t c . ) . The hum an's r o le in t h i s ta s k i s to su b je c tiv e ly

combine v is u a l ly a c q u ire d in p u ts r e l a t i n g to s p a t i a l p ro p e r t ie s , c o lo r ,

te x tu r e and tem poral phenomena to id e n t i f y and c la s s i fy o b je c ts in th e

1 2 3ground scen e . ’ ’ In perform ing th i s ta sk th e human ex e rc ise s a

s o p h is t ic a te d a b i l i t y to combine v a r io u s types of d a ta and draw

co n c lu sio n s as to in fo rm a tio n s u b t l e t i e s p re s e n t. As an example of t h i s

s o p h is t ic a t io n , co n s id e r th e land u se c l a s s i f i c a t i o n s , "p as tu re" and

"improved p a s tu r e ." Improved p a s tu re i s p a s tu re th a t i s surrounded by a

fe n c e , b u t from an a e r i a l pho tograph , fen ces a re o f te n d i f f i c u l t to

o b serv e . Grazing an im als , however, develop th e h a b it of walking along

th e fen ce s and th e photo in t e r p r e te r m erely has to look fo r a brown path

su rround ing a green f i e l d . The most obvious and se r io u s inadequacy of

photo i n t e r p r e ta t io n i s th e amount o f manpower and tim e needed to

an a ly ze la r g e volumes o f d a ta r e s u l t in g from rem ote sensing oh a la rg e

a re a s c a le .

3

4

Because o f t h i s inadequacy, more and more em phasis i s be ing p laced

on develop ing computer techn iq u es fo r an a ly z in g la rg e volumes o f

rem o te ly sensed d a ta . P re sen t computer tech n iq u es a re designed to

e x p lo it th e s p e c t r a l in fo rm atio n of imagery o r o f s p e c t r a l scanners f o r

e x tra c t in g in fo rm a tio n . One approach to t h i s te ch n iq u e i s to use a d a ta

bank. The u se o f a d a ta bank assumes th a t an o b je c t o r an a re a of

s u f f i c i e n t dim ensions in th e ground scene to be considered homogeneous

p o sse sse s a unique s p e c t r a l s ig n a tu re . The s p e c tr a l s ig n a tu re s a re

produced by re c o rd in g th e re tu rn e d energy (combined r e f le c te d and

r a d ia te d e lec tro m ag n e tic energy) in each o f a number o f narrow and

d is c r e t e w avelength in t e r v a l s . The d a ta bank would co n ta in p re s to re d o r

e m p ir ic a lly d e riv e d s t a t i s t i c s on th e s ig n a tu re s o f known o b je c ts o r i t

would c o n ta in th e a b i l i t y to model and a n a ly t ic a l ly c a lc u la te what a

g iven s ig n a tu re should be.

The d i f f i c u l t y w ith t h i s techn ique i s th a t th e re i s a p p re c ia b le

v a r i a b i l i t y in th e s ig n a tu r e s , which i s due to n a tu ra l tem poral changes

as w e ll as man-made changes. In p r a c t ic e , t h i s v a r i a b i l i t y i s ev id en t

even fo r re p e a te d o b se rv a tio n s in which g re a t c a re i s taken to m a in ta in

c o n s ta n t sun a n g le , view ing a n g le , cloud co v er, am bient tem p era tu re and

h um id ity , in s tru m en t c a l ib r a t io n , e tc . T his v a r i a b i l i t y can be

a t t r ib u t e d to a la rg e degree to a la c k o f m icro sco p ic homogeneity

between g ro s s ly id e n t ic a l o b je c ts o r sp e c ie s in two d i f f e r e n t ground

scen es . For exam ple, no two le av es of d ise a se d corn w i l l appear e x a c tly

th e same, and no two rows of corn w i l l be a rray ed e x a c tly th e same o r be

surrounded by th e same c o lo r o f ground exposed between th e s t a lk s . Thus,4

th e problem o f s ig n a tu re com parison le a d s to modeling th e o ry .

D

A nother s e r io u s drawback to t h i s te ch n iq u e i s th e amount o f computer

memory re q u ire d to s to r e a l l p o s s ib le s ig n a tu re s and t h e i r v a r i a t io n s ,

and a p r o h ib i t iv e amount o f computer tim e re q u ire d to compare an

unknown s p e c t r a l s ig n a tu re w ith a l l p o s s ib le s ig n a tu re s s to re d in th e

d a ta bank, u n le ss a ta b le look up p rocedu re can be u se d .^

The n ex t approach to be d e sc r ib e d i s p robab ly th e most p o p u la r and

w idely used com puter f e a tu r e e x t r a c t io n te c h n iq u e . This approach has

been developed e x te n s iv e ly a t Purdue U n iv e rs i ty ,^ and many r e la te d

te c h n iq u e s '^ and improvements have been d e riv e d from t h i s approach .

This te ch n iq u e w i l l be c a l le d th e su p erv ised c l a s s i f i c a t i o n tech n iq u e

s in c e i t r e q u ir e s human su p e rv is io n f o r th e s e le c t io n o f t r a in in g a re a s ,

which u l t im a te ly de te rm in e th e number and types o f f e a tu r e s to be

e x t r a c te d , as w e ll as th e accuracy o f c l a s s i f i c a t i o n .

In o rd e r to d e s c r ib e t h i s te c h n iq u e , i t w i l l be n e c e ssa ry f i r s t to

d e s c r ib e th e d a ta c o l le c t io n and fo rm a ttin g , as w e ll as to develop th e

m athem atical n o ta t io n fo r o p e ra tin g on th e d a ta . A m u l t i s p e c t r a l scanner

i s g e n e ra lly used fo r th e d a ta c o l le c t io n . The scan n er i s a monochromator

w ith a d e te c to r a r ra y fo r re c o rd in g th e r e f le c te d and e m itted r a d ia t io n

from th e ground in d i f f e r e n t w avelength in t e r v a l s . The monochromator i s

mounted in an a i r c r a f t and th e r o ta t in g m irro r scans th e ground scene as

th e a i rp la n e f l i e s , p roducing an analog s ig n a l as shown in F ig u re 1. I f

th e d e te c to r a r ra y c o n ta in s n d e te c to r s , th en n s im u ltaneous s ig n a ls o r

channe ls o f d a ta a re reco rd ed f o r th e same ground scen e . The analog

d a ta i s th en d ig i t i z e d and reco rded on m agnetic ta p e to produce an n -

d im ensional d i g i t a l image of th e ground scen e . Let th e a lg e b ra ic v a lu e

of th e d i g i t a l number d e riv e d from th e analog s ig n a l be denoted by j^x^^

TRACES ON MULTICHANNEL O SC ILLO SC O P E

X : D e te c to r Center WovelengthX : X ,

Channel n Ampl i tude

i * -

h iX = Xi

Channel 2 Amplitude

Channel i Ampl i tude

X : X o

y = y on-D IM E N S IO N A L F E A T U R E VECTOR TAKEN FROM SIGNAL TRACE FOR A RESOLUTION ELEM ENT A T ( x ^ , /<, }

Amplitude 11 kError Bars Indicate Uncertainty in Feature Vector Signoture Due to Instrument Variabi l i ty, l l luroinotion, Polar iza t ion, Atmospheric E f fec ts , etc.

CUTAMAY VIEW OF A IR C R A F T SHOWING INSTRUMENTATION

Monochromator and D e tec to r Array

Tope RecorderOscilloscope

iEntrance Slit

RotatingMirror

I/ I Stat ionaryI I Mirrorf I

Iy, Ground Scene

Coordinate and. Scanning Direction

Ground Scene With Three Different Ref lectance and Emittonce Regions

Resolution Element Field of View at ( x * , y^)

-• X •* / **■ -V / ^ X •** ** **

X , Ground Scene Coordinate and Fl ight Direction

FIG. 1. DATA C O L L E C T I O N P L A T F O R M SHOWING SENSOR O U T P U T S A N D A S S O C I A T E D F E A T U R E V E C T O R S

7

w here k = l th e channel number o r w avelength in te r v a l ;

1=1, 2 , 3 ......... .. A, th e scan l i n e number o r x c o o rd in a te o f th e ground

scen e ; and j = l , 2 , . . . . , m, th e sam ple number fo r scan i o r th e y

c o o rd in a te o f th e ground scen e .

Thus, th e d a ta s e t c o l le c te d co n ta in s n channels o f d a ta , S, scan

l i n e s , and m d i g i t a l sam ples p e r scan p e r channel w ith an am plitude

g iv en by . Each ground scene c o o rd in a te , i and j , o f th e d ig i t a l

image i s no rm ally c a l le d a r e s o lu t io n elem ent and each r e s o lu t io n

elem ent i s th e re f o r e d e sc rib e d by an n -d im ensional v e c to r c a l le d a

f e a tu r e v e c to r , The components o f th e f e a tu re v e c to r a re =

t i * i j ' 2 * i j ' '" 'n % i j ] '

The nex t s te p i s to produce a boundary map^^ so th a t i t may be

compared w ith an a e r i a l pho tograph tak en of th e ground scene a t the

same tim e th a t th e m u l t i s p e c t r a l scanner d a ta was c o l le c te d . The

boundary map and a e r i a l pho tograph a re shown in Chapter 4 and a method

fo r p roducing a boundary map w i l l be d iscu ssed in th e nex t s e c tio n . The

photograph a llo w s an o b se rv e r to s e l e c t , f o r example, a rea s which appear

to be crops and th en to lo c a te th e scan l i n e and column number of th e

d a ta co rresp o n d in g to th o se crops from th e boundary map. The d a ta may15

th en be accessed fo r a n a ly s is and used as a t r a in in g a re a .

For i d e n t i f i c a t i o n o f crop s p e c ie s , ground t r u t h in fo rm atio n i s

r e q u ir e d , u n le s s a d a ta bank i s a v a i la b le . The ground t r u th in fo rm a tio n

cou ld be c o l le c te d by an o b se rv e r v i s i t i n g each f i e l d o r o b ta in in g th e

in fo rm a tio n from a fa rm er as to th e crop ty p e . I t i s in t e r e s t in g to n o te

th a t t h i s ty p e o f in fo rm a tio n c o l le c t io n has o c c a s io n a lly been erroneous

and p re s e n t c l a s s i f i c a t i o n te ch n iq u es have been s u f f i c i e n t ly a c c u ra te

8

to p o in t o u t th e se e r r o r s . With t h i s in fo rm a tio n , th e f i e l d s in th e

a e r i a l photograph can be la b e le d acco rd in g to crop ty p e . • T ra in in g

a re a s a r e th en s e le c te d from th e boundary map co rrespond ing to

p a r t i c u l a r known f i e l d s in th e a e r i a l pho tograph . The d e s ire d

s t a t i s t i c s a re c a lc u la te d from th e d a ta in th e t r a in in g a re a and a

s t a t i s t i c a l d e c is io n r u le i s used fo r c l a s s i f y in g th e rem ain ing d a ta

in th e d i g i t a l image. A com puter map o f th e ground scene i s th e n

p r in te d o u t showing th e lo c a t io n o f a l l r e s o lu t io n elem ents th a t w ere

c l a s s i f i e d acco rd ing to th e s t a t i s t i c a l d e c is io n r u le as be long ing o r

b e in g s im ila r to th e p a r t i c u l a r t r a in in g a re a s s e le c te d . The computer

map can be compared w ith th e ground t r u t h in fo rm a tio n in th e a e r i a l

photograph f o r accu racy . A ccu rac ies o f 80 to 90 p e rc e n t a re n o t ;

uncommon.

One o f th e most w idely used d e c is io n r u le s i s th e maximum

lik e l ih o o d r a t i o te c h n iq u e . The developm ent o f t h i s te ch n iq u e depends

upon two ty p e s o f d e c is io n e r r o r s th a t can be made in th e c l a s s i f i c a t i o n .

The f i r s t ty p e of e r r o r i s n o t a s s ig n in g a f e a tu r e v e c to r as b e long ing

to a c la s s when i t a c tu a l ly d o es . The second ty p e o f e r ro r i s a s s ig n in g

a f e a tu r e v e c to r to a c la s s when in a c t u a l i t y i t does n o t belong .

W eights a re u s u a lly a ss ig n ed to b o th ty p e s o f e r r o r s depending on how

c o s t ly th e e r r o r i s in making th e wrong d e c is io n . These w e ig h ts ,

a r e r e f e r r e d to as c o s t f a c to r s and a r e a s s o c ia te d w ith c l a s s i fy in g a

f e a tu r e v e c to r , x , b e lo n g in g to c la s s i in to c la s s j .

U ltim a te ly , th e d e c is io n p ro ced u re m ust be a b le to in d ic a te a f i n a l

cho ice f o r each p o in t in th e n -d im en sio n a l f e a tu r e sp ace . The f e a tu r e

sp a c e , R, must be d iv id e d in to m m u tu a lly e x c lu s iv e re g io n s , R^, R g , . . .^ ^ .

9L et th e p r o b a b i l i ty d e n s ity fu n c tio n fo r sam ples from c la s s i be

f^ (x ) and th e a p r i o r i p ro b a b il i ty of occu rrence o f c la s s i be P^. The

p r o b a b i l i ty o f m is c la s s ify in g a sample from c la s s i in to c la s s j i s

P ( j | i ) = f f (x )dx , (1)

" j

and th e c o n d itio n a l expected c o s t i f th e sample i s from c la s s i i s

m mC. = E L . . P ( j | i ) = E L . . / f . ( x ) d x . (2)

j= l j= l

One u s e fu l c r i t e r io n th a t i s o f te n used i s th e average co s t which i s

g iven by

m m mC = E P.C. = E f E L . . P . f . ( x ) d x , (3)

i = l ^ ^ j = l Rj i = l ^ ^

and th e reg io n s R^ R^ a re chosen to m inim ize th e average c o s t . Them

average co s t i s minimized i f th e in teg ran d E L . .P . f . ( x ' ' i s a minimum,i= l ^ ^

which i s e q u iv a le n t to d ec id in g th a t a sample x i s from c la s s j i f

m mE L . . P . f . ( x ) £ E L P . f . ( x ) fo r a l l k={=j (4)i= l ^ ^ i= l 1 1m

By s u b tra c t in g E L . . P . f . ( x ) from bo th s id e s , th e d e c is io n r u le i s i= l ^ ^

o b ta in e d , x i s in c la s s j i f

. ,3,£,(x) (Lj, -

Since th e c o s t f a c to r s L^^ and th e a p r i o r i p r o b a b i l i t i e s P^ a re

c o n s ta n ts , th e d e c is io n r u le th a t m inim izes th e average r i s k i s th e

r a t i o o f two c o n d itio n a l p ro b a b il i ty d e n s i t ie s o r l ik e lih o o d r a t i o s w ith

a th re sh o ld v a lu e . The c o s t f a c to r s and a p r i o r i p r o b a b i l i t i e s a re used

10

only in de term in ing th e th re s h o ld v a lu e . W ith a sim ple ch o ice o f c o s t

. f a c t o r s , = 0 f o r c o r r e c t c l a s s i f i c a t i o n , = 1 w ith i^ j fo r

m is c la s s i f ic a t io n and eq u a l a p r i o r i p r o b a b i l i t i e s , th e d e c is io n r u le

reduces to d ec id in g th a t x i s in c la s s j i f

f j ( x ) > f^Xx) f o r a l l k=fj ‘ (6)

T his i s g e n e ra lly r e f e r r e d to as th e maximum lik e l ih o o d d e c is io n r u le .

In a c tu a l p r a c t ic e th e c o s t f a c t o r s , a p r i o r i p r o b a b i l i t i e s , and

th e p r o b a b i l i ty d i s t r i b u t io n s a re n o t known, b u t must be e s tim a te d from

members o f each t r a in in g a re a . The v a r io u s c l a s s i f i c a t i o n tech n iq u es

th a t have been developed a re e s s e n t i a l l y d i f f e r e n t methods f o r e s tim a tin g

th e p r o b a b i l i ty d i s t r i b u t io n s .

In most cases a m u l t iv a r ia te G aussian d i s t r i b u t io n i s assumed fo r

th e t r a in in g a re a d a ta ; and th e v e c to r means, M^, and co v arian ce m a tr ic e s ,

V^, a re c a lc u la te d from th e d a ta in each t r a in in g a re a . Because th e

G aussian d i s t r i b u t io n i s e x p o n e n tia l , th e lo g a rith m o f th e d e c is io n r u le

i s u sed . Thus, d ec id e th a t x belongs to c la s s j fo r a l l k^ j i f

l og^ | V. | + ( x - S . ) V ‘ ^(x-M .) < log^lVj^l + ( x - M ^ ) \ '^ ( î - M j^ ) , (7)

where |v^[ and ^ a re th e d e te rm in an t and in v e rse o f th e co v arian ce

m a trix and T deno tes th e tra n s p o se o p e ra tio n o f a m a tr ix .

The advantage o f th e su p e rv ised tech n iq u e i s th a t w ith a v a i la b le

ground t r u t h , known a re a s o f p a r t i c u l a r i n t e r e s t can be used to lo c a te

s im ila r a re a s elsew here in th e d a ta . The d isad v an tag e o f th e su p erv ised

te ch n iq u e i s th e manual s e le c t io n o f t r a in in g a re a s from th e d a ta , w hich,

when a p p lie d to la rg e d a ta volum es, can become as te d io u s and as tim e

consuming as th e a r t o f photo i n t e r p r e t a t i o n . T his i s e s p e c ia l ly t r u e of

h ig h a l t i t u d e m u l t is p e c tr a l a e r i a l photography.

11

In re c e n t y e a r s , th e amount of rem o te ly sensed d a ta c o l le c te d on

e a r th o b se rv a tio n s has been phenom enal, as ev idenced by p u b lic a t io n s in

th e l i t e r a t u r e . T h e f u tu r e o u tlo o k in d ic a te s th a t t h i s d a ta

c o l le c t io n w i l l co n tin u e to grow, as shown by E arth R esources Technology

S a t e l l i t e s 1 and 2 , th e Skylab E a rth R esources Experim ent Package and

th e Space S h u tt le S o r t ie L ab o ra to ry . Because th e volume of d a ta

expected appears to be g e t t in g ou t o f hand , much em phasis i s being

p laced on th e developm ent o f un su p erv ised tech n iq u es f o r f e a tu r e

e x t r a c t io n . These computer tech n iq u es a re designed to e x t r a c t f e a tu r e s

from rem otely sensed d a ta w ith o u t e i th e r th e a s s is ta n c e and su p e rv is io n

o f an o b se rv e r o r th e p r io r b e n e f i t of ground t r u t h in fo rm a tio n .

R eferences 18 and 19 g iv e a re c e n t rev iew of th e s t a t e - o f - t h e - a r t of

th e se te c h n iq u e s . The p re s e n t d isad v an tag es o f th e unsuperv ised

tech n iq u es a re th a t a h ig h degree of c l a s s i f i c a t i o n accuracy i s o f te n

d i f f i c u l t to o b ta in and che computer tim e i s r e l a t i v e ly e x te n s iv e .

Thus, th e s p e c i f i c problem to a t ta c k i s th e developm ent o f an

unsuperv ised f e a tu r e e x t r a c t io n program th a t c l a s s i f i e s w ith a h igh

degree of accu racy . The com puter tim e re q u ire d can th en be more

e f f i c i e n t l y u t i l i z e d by o p tim iz in g th e com puter program lo g ic ,

program ing in an e f f i c i e n t machine language, and by u sing s p e c ia l

purpose com puters. The advantage of th e u n su p erv ised te ch n iq u e i s th a t

no p r io r ground t r u t h in fo rm a tio n i s re q u ire d b e fo re th e d a ta a n a ly s is .

The r e s u l t s o b ta in ed w ith th e u n su p erv ised tech n iq u e a re designed to

show th e lo c a t io n and d i s t r i b u t io n of th e e x tra c te d f e a tu r e s , b u t no

id e n t i f i c a t i o n of th e f e a tu r e s i s p o s s ib le w ith o u t ground t r u t h

in fo rm a tio n . Thus, th e r e s u l t s o f th e u n su p erv ised tech n iq u e can be

12

used f o r d i r e c t in g ground t r u t h p a t r o l s and th e lo c a t io n and amount of

ground t r u t h needed can be a c c u ra te ly determ ined b e fo re any ground

t r u t h i s c o l le c te d . The adequa te d e te rm in a tio n o f where and how much

ground t r u t h to c o l l e c t i s an im p o rtan t economic c o n s id e ra tio n when d a ta

i s c o l le c te d on a g lo b a l o r even a re g io n a l b a s i s . I f d a ta i s c o l le c te d

on a s e a so n a l i n t e r v a l , f o r exam ple, f u tu r e ground t r u t h c o l le c t io n can

be m inim ized by m o n ito rin g th e f e a tu r e s ig n a tu re s as a fu n c tio n of

seaso n . I f some o f th e s e s ig n a tu re s change s ig n i f i c a n t ly from p a s t

= ra-3u lts , th e c l a s s i f i c a t i o n map can be used to d i r e c t ground t r u t h

p a t r o l s to update on ly th o se f e a tu r e i d e n t i f i c a t i o n s which have changed.

In o rd e r to m a in ta in c u r re n t in fo rm a tio n on c u r re n t accom plishm ents

in rem ote s e n s in g , th e "P roceed ings o f th e I n te r n a t io n a l Symposia on

Remote Sensing of th e E nvironm ent," p u b lish e d by th e W illow Run

L a b o ra to r ie s , U n iv e rs ity o f M ichigan , and th e "Annual E a rth R esources

A i r c r a f t Program S ta tu s Review ," p u b lish e d by NASA, a re h ig h ly

recommended along w ith th e l i t e r a t u r e survey l i s t e d in R eference 17.

The n e x t C hapter d is c u s s e s a proposed u n superv ised computer

program fo r f e a tu r e e x t r a c t io n .

CHAPTER I I I

UNSUPERVISED FEATURE EXTRACTION

F ea tu re e x t r a c t io n from rem ote ly sensed d a ta i s a v e ry complex

p ro c e s s . For t h i s re a so n , no com prehensive model o r e x p l i c i t e x te rn a l

c r i t e r i a e x i s t fo r d e f in in g and e x t r a c t in g a l l f e a tu r e s . The s e le c t io n

o f t r a in in g a re a s f o r f e a tu r e e x t r a c t io n in tro d u c e s th e b ia s o f human

o b se rv a tio n and p reconceived judgm ent in to th e c l a s s i f i c a t i o n c r i t e r i a .

For exam ple, an o b serv er may s e le c t a t r a in in g a re a c o n ta in in g corn in

o rd e r to a ttem p t to c l a s s i f y corn in a l l o th e r p o r tio n s o f th e ground

scen e , w h ile th e d a ta from th a t t r a in in g a re a may on ly be cap ab le of

c la s s i fy in g a l l s p a rs e ly grow ing, sm all g reen p la n ts surrounded by b a re

s o i l .

The ph ilosophy behind th e developm ent o f t h i s c l a s s i f i c a t i o n

program i s to accep t t e n ta t i v e ly an in t e r n a l c r i t e r i o n ; th a t i s , th e

d a ta i t s e l f should n a tu r a l ly su g g es t th e f e a tu r e s to be e x tra c te d and

su b seq u en tly id e n t i f i e d .

A flow c h a r t of su c c e s s iv e s ta g e s o f th e computer program i s shown

in F ig u re 2.

The f i r s t s ta g e o f th e program i s to produce a boundary map o f th e

d a ta by s e p a ra tin g th e d a ta in to homogeneous and inhomogeneous a re a s .

T his i s accom plished by com puting th e average f e a tu r e v e c to r s p e c t r a l

13

14

ISTAGE ONE

INPUT RAW DATA

CALCULATESTATISTICS

OUTPUTBOUNDARYTAPE

Î

RAW DATA TAPE

STA G E TWO

INPUTBOUNDARYTAPE

USE PXP ARRAYTO LOCATE 2

INITIAL CLUSTERS

OUTPUT TAPECONTAINING MAPOF BOUNDARYAND CLUSTERLOCATIONS

STAG E TH R EE

INPUT TAPES CONTAINING LOCATIONS OF CLUSTERS AND RAW DATA

CALCULATE STATISTICS AND DO SPECTRAL MERGING

SAVE STATISTICS OF FINAL CLASSES

S T A G E FOUR

INPUT BOUNDARY AND RAW DATA TAPES AND STATISTICS FOR CLASSIF ICATION

CLASSIFY DATA AND UPDATE BOUNDARY TAPE TO CONTAIN BOUNDARIES AND CLASSES

OUTPUT BOUNDARY AND CLASSIFICATION TAPE

DECREASE PXP ARRAY TO QXQ AND INPUT BOUNDARY AND CLASSIFICATION TAPE

ISCLASSIFICATION OF GROUND SCENE

COMPLETE?

I- - - - - - - -YES

OUTPUT FINAL RESULTS

FIG. 2. P R O G R A M L O G I C F L O W

15

d is ta n c e p e r channel o r d im ension in th e d i r e c t io n o f the x and y

ground scene c o o rd in a te s . The fo rm ulas fo r th i s c a lc u la tio n a re

g iven by

n 1 / r-, n/ 2 and s =y

(8)

where i and j a re th e scan l i n e and scan l i n e column number, r e s p e c t iv e ly ,

o f th e d a ta in th e d i g i t a l image and th e summation i s over n channels o f

d a ta .

These s p e c t r a l d is ta n c e s a re c a lc u la te d fo r each r e s o lu t io n elem ent

and s to re d in a j o i n t p r o b a b i l i ty d i s t r i b u t io n , P (s^ , s ^ ) . The average

f e a tu r e v e c to r d is ta n c e p e r dim ension i s computed to determ ine a m easure

o f change p re s e n t in th e d a ta from one r e s o lu t io n element to th e nex t

and a lso to keep th e numbers o ccu rrin g in th e c a lc u la t io n in th e same

ra n g e , r e g a rd le s s o f th e number o f dim ensions used. The a rea s o f th e

d a ta where th e s p e c t r a l change, in e i th e r th e x o r y ground scene

c o o rd in a te d i r e c t io n , i s equal to o r le s s th an th e average s p e c t r a l

change w i l l be c l a s s i f i e d as a homogeneous re s o lu t io n elem ent; o th e rw ise ,

th e r e s o lu t io n elem ent w i l l be c l a s s i f i e d as a boundary. The average

d is ta n c e s o f th e average f e a tu r e v e c to r s p e c tr a l d is ta n c e p e r channel a re

computed u s in g th e form ulas

4 ' 4 '“=x'“=y’

Sy - 1 ! Sy P(s^^Sy) d s /S y , and (10)

Vy ■ ":%Sy P(Sx.Sy) ds ds . (ID

16

These c a lc u la t io n s a re used f o r d e f in in g a d e c is io n boundary in th e

j o i n t p r o b a b i l i ty d i s t r i b u t io n as to what com bination of x and y

s p e c t r a l d is ta n c e s a re c l a s s i f i e d as belo n g in g to a homogeneous

r e s o lu t io n elem ent o r a boundary r e s o lu t io n e lem en t. The d e c is io n

boundary i s in th e shape of an e l l i p s e which may have p r in c ip a l axes

in d i r e c t io n s o th e r th an s and s , The d i r e c t io n and m agnitude o fX y

20th e p r in c ip a l axes a re c a lc u la te d from th e e ig e n v e c to rs and

e ig en v a lu es a s s o c ia te d w ith th e m a tr ix

X ®x®y

I Vy

(12)

The eq u a tio n of th e e l l i p s e in th e p r in c ip a l axes c o o rd in a te system

I S

. ' 2

= 1, (13)

w here s ' and- s ' a re th e d is ta n c e s s and s r o ta te d in to th e p r in c ip a l X y X y

axes c o o rd in a te system by th e e ig en v ec to r tra n s fo rm a tio n , s ' ^ andX y

a re th e e ig en v a lu es o r h a l f le n g th s o f th e p r in c ip a l axes squared .

. ' 2

(14)

i s th en ro ta te d back in to th e s , s c o o rd in a te system by th e in v e rs ex ’ y

17

e ig e n v e c to r tra n s fo rm a tio n to o b ta in th e eq u a tio n o f th e e l l i p s e on th e

d e c is io n boundary in th e s ^ , c o o rd in a te system . The e q u a tio n o f th e

e l l i p s e i s g iven by

as^ + bs^ + cs s = 1 , (15)X y X y

where a , b , c a re de term ined from r o ta t in g (1 4 ). The d e c is io n i s to

c l a s s i f y a r e s o lu t io n elem ent as b e ing homogeneous i f

as^ + bs^ + cs s < 1 . (16)X y X y —

A d i g i t a l image o f a boundary map i s reco rd ed on m agnetic ta p e fo r use

in th e second s ta g e o f p ro c e s s in g . The m agnetic ta p e map u t i l i z e s -1

to d e s c r ib e a boundary elem ent and zero fo r a homogeneous e lem en t.

The second s ta g e i s concerned w ith th e s e le c t io n and s p a t i a l

m erging o f unknown c a n d id a te f e a tu r e s based upon th e hom ogeneity o f th e

ground sc e n e , as d isp la y e d by th e boundary map reco rd ed on th e m agnetic

ta p e . Because th e b o u n d arie s on th e map a re n o t c lo sed and have open

gaps in some c a s e s , th e problem i s to s e le c t homogeneous a re a s w ith a

m a th em atica l lo g ic th a t w i l l p rev en t th e s e a re a s from c o n ta in in g a

m ix tu re o f d i f f e r e n t f e a tu r e s . This i s accom plished by u s in g a f ix e d

shape p X p r e s o lu t io n elem ent a r ra y which moves th rough th e boundary

map on ly in th e x o r y ground scene c o o rd in a te d i r e c t io n . I n i t i a l l y , a

homogeneous a re a in th e boundary map i s found which i s la rg e enough fo r

th e a r r a y to f i t i n to . The a re a covered by th e a r ra y i s d e s ig n a te d as

belo n g in g to c l u s t e r 1. The a r ra y i s allow ed to move in t h i s a re a u n t i l

a boundary i s encoun tered and th en th e d i r e c t io n of movement must be

changed. A ll r e s o lu t io n elem ents f a l l i n g w ith in th e movement o f th e

f ix e d a r r a y a re s a id to belong to c l u s t e r 1 , and th e ze ro s p re v io u s ly

o c c u rr in g on th e boundary map in th e s e lo c a t io n s a re changed to +1. A fte r

18

th e a r ra y can no lo n g e r move and en g u lf new r e s o lu t io n e lem en ts , an o th e r

lo c a t io n i s found w hich w i l l c o n ta in th e p x p a r ra y . A ll r e s o lu t io n

élém ents f i t t i n g in to t h i s a r ra y w i l l be d e s ig n a te d as be long ing to

c lu s t e r 2 . The p ro cess i s re p e a te d u n t i l a l l o f th e boundary map d a ta

has been exh au sted . C lu s te rs which p h y s ic a l ly touch on th e boundary map

a re merged and c a l le d th e same c l u s t e r . This i s c a l le d s p a t i a l m erging,

which w i l l be c o n tra s te d w ith s p e c t r a l m erging l a t e r . A fte r s p a t i a l

m erging , th e c lu s t e r s a re renumbered so th a t th e c lu s t e r numbers w i l l

have a con tinuous range from 1 ...........,N. The o u tp u t of t h i s second s ta g e

i s an o th e r map co n ta in in g th e numbers - 1 , 0 , 1 , 2 , . . . . , N, w ith -1

in d ic a t in g boundary r e s o lu t io n e lem en ts , 0 in d ic a t in g homogeneous

r e s o lu t io n elem ents n o t encountered by th e moving f ix e d shape a r r a y , and

1 , 2 , . . . . , N in d ic a t in g r e s o lu t io n elem ents be long ing to c lu s t e r s 1 , 2 ,

. . . . , N, r e s p e c t iv e ly . The f ix e d shape a r r a y , i f chosen la rg e enough,

w i l l n o t p erm it th e m ixing o f f e a tu r e s because th e open gaps in th e

b o u n d arie s w i l l be so sm all compared to th e a r ra y s iz e th a t th e a r ra y

w i l l n o t be a b le to p ass th rough th e boundary. On m u l t is p e c tr a l scanner

d a ta taken a t an a l t i t u d e o f 2600 f e e t , a 10 x 10 a r ra y i s s u f f i c i e n t to

keep d i f f e r e n t f e a tu r e s s e p a ra te . T h is a ls o p ro v id es a minimum sample

s iz e o f 100, which i s a very adequa te sam ple on which to base s t a t i s t i c a l

c a lc u la t io n s . T y p ic a lly , most m u l t is p e c tr a l d a ta i s c o l le c te d a t h ig h e r

a l t i t u d e s so th a t a 10 x 10 a r ra y w i l l , in g e n e ra l , be s u f f i c i e n t to

p rev en t th e m ixing of f e a tu r e s . The m agnetic ta p e c o n ta in in g th e

bo u n d arie s and lo c a t io n s o f c lu s t e r s and th e m agnetic ta p e c o n ta in in g th e

raw d a ta a r e th e in p u ts to th e th i r d s ta g e o f p ro c e s s in g .

19

The t h i r d s ta g e o f p ro cess in g i s concerned w ith s p e c t r a l m erging

o f th e s e le c te d unknown c an d id a te f e a tu r e s . The boundary and c lu s te r

map ta p e g iv es th e lo c a tio n s of th e raw d a ta on th e raw d a ta tap e

belong ing to each c l u s t e r . The mean f e a tu r e v e c to rs and co v ariance

m a tr ic e s , c , a re c a lc u la te d fo r each c lu s t e r u sing th e form ulas

1

km^jl " k ^ i£ m^U " ^k^£^ ^m^£^ ’

where x i s th e a lg e b ra ic v a lu e of th e i*"^ sample in th e k o r m^^ channel

of th e c lu s t e r c o n ta in in g sam ples. The mean v a lu e o f th e samples

in th e k^^ channel o f th e c lu s t e r i s g iven by ^x^, w h ile th e

co v arian ce between channels k and m of th e c lu s t e r i s g iven by

, c „ . These c a lc u la t io n s a re used to d e f in e d e c is io n boundaries w ith km Jo

which to p h y s ic a l ly surround th e d a ta belong ing to a c lu s te r in

n -d im en sio n a l sp ace . The most g e n e ra l c lo sed su rfa c e th a t can be used

to surround th e n -d im en sio n a l d a ta i s an n -d im ensional h y p e re l l ip s e .

The c e n tro id of th e c lu s te r e l l i p s e i s g iven by th e f e a tu r e v e c to r mean

v a lu e s w h ile th e p r in c ip a l axes d i r e c t io n and m agnitude can be

determ ined by th e e ig e n v e c to r tra n s fo rm a tio n as was d iscu ssed when

E quations (12) th ro u g h (14) were in tro d u ced .

In a s t a t i s t i c a l sen se , th e e ig en v ec to r tra n s fo rm a tio n on th e

co v arian ce m a trix lo c a te s th e d i r e c t io n o f o rth o g o n a l p r in c ip a l axes fo r

21which th e v a r ia n c e s a re minimized and maximized . The v a r ia n c e s a re

th e d ia g o n a l elem ents o f th e covarian ce m a trix and th e o f f d iag o n a l

20

e lem en ts, c o v a ria n c e s , a re made zero by th e tra n s fo rm a tio n . Thus, th e

eq u a tio n o f an n -d im en sio n a l e l l i p s e in reduced form i s o b ta in ed fo r

each c l u s t e r , and, in g e n e ra l, each c lu s t e r w i l l have a d i f f e r e n t

co o rd in a te system . The n ex t s te p i s to d e r iv e a d e c is io n r u le fo r

de term in ing how many c lu s t e r s a c tu a l ly re p re s e n t th e same f e a tu r e .

This d e c is io n i s now based e n t i r e ly upon s p e c t r a l in fo rm a tio n r a th e r

th an th e s p a t i a l in fo rm a tio n which was used in E quations (12) th rough

(1 4 ). The d e c is io n r u le i s th a t two c lu s te r s re p re s e n t th e same f e a tu r e

i f th e c e n tro id s o f b o th c lu s t e r s a re co n ta in ed in b o th c l u s t e r s ’

e l l i p s e s . A lthough th i s s p e c t r a l merging p ro ced u re was d e riv e d from

22p h y s ic a l i n t u i t i o n , a theorem was lo c a te d w hich adds m athem atical

p re c is io n . The theorem s t a t e s th a t th e o rth o g o n a l tra n s fo rm a tio n

which m inim izes th e mean square d is ta n c e between a s e t o f v e c to rs from

th e c l u s t e r , s u b je c t to th e c o n s tr a in t th a t th e volume of th e space

i s in v a r ia n t under tra n s fo rm a tio n , i s a r o t a t i o n , E^, fo llow ed by a

d iag o n a l tra n s fo rm a tio n , The rows of th e m a tr ix E^ a re th e e ig en

v e c to rs of th e co v arian ce m a tr ix , c^ , of th e s e t o f v e c to r s , and th e

elem ents o f a re th o se g iven in E quation (1 9 ), where ^^c^ i s th e

s tan d a rd d e v ia tio n o f th e c o e f f i c ie n t s o f th e s e t o f v e c to rs in th e

d i r e c t io n o f th e e ig e n v e c to r o f c^ .

The d iag o n a l e lem ents o f th e d iag o n a l tra n s fo rm a tio n , a re given

by

n 1

- 7 7 T • (W )j j &

21

The r a t i o n a le beh ind th i s theorem , as p re se n te d in R eference 2 3, m e r i ts

some d is c u s s io n as ap p lied to s p e c t r a l m erging. This d is c u s s io n w i l l

a lso apply to s p e c t r a l c l a s s i f i c a t i o n , which i s to be d esc rib e d l a t e r .

I t i s d e s i r a b le to have a m easure o f s im i l a r i t y between two c l u s t e r s ,

S“^ , f o r d e c id in g w hether o r n o t two c lu s t e r s a re to be merged. L et

V be th e mean fe a tu r e v e c to r o f one c l u s t e r , w ith components g iven

by e q u a tio n (1 7 ) , and l e t be th e e n t i r e s e t o f f e a tu r e v e c to rs con

ta in e d in th e o th e r c lu s t e r s w ith th e s u b s c r ip t on deno ting th e m*- v e c to r

o f th e s e t . The s im i la r i ty may be reg a rd ed as a mean square s p e c t r a l d i s

ta n c e and shou ld d e sc r ib e th e c lo se n e ss o f v to th e e n t i r e s e t o f f e a tu r e

v e c to r s , ( x ^ . A ccording to th e p h ilo sophy o f R eference 23 , th e d e f in i t i o n o f

" d is ta n c e " does no t n e c e s s a r i ly mean E uclidean d is ta n c e , bu t may mean .

" c lo se n e ss" in some a r b i t r a r y , a b s t r a c t p ro p e rty o f th e s e t {x^} which

has y e t to be determ ined . The use o f an undeterm ined d is ta n c e measure

does n o t a l t e r th e d e f in i t io n o f s im i l a r i t y , bu t p ro v id es an o rd e rin g

which s im i la r i ty la c k s . M ath em atica lly , th e s im i la r i ty S ^ (v ,{ x ^} ) of

a f e a tu r e v e c to r v and a s e t of f e a tu r e v e c to rs {x^} exem plify ing a

c l u s t e r can be w r i t t e n as

MS ^ (v , {x^}) = ^ Z d^(v , x^>, (20)

m=l

where th e d is ta n c e m easure, d^( ) , has n o t y e t been s p e c if ie d . The

in v e rse of S i s used because th e sm a lle r th e d is ta n c e , th e more s im i la r i ty .

One p o s s ib le way to choose th e d is ta n c e m easure i s to u t i l i z e th e

knowledge th a t th e s e t {x } d e sc r ib e s one f e a tu r e , and', th e r e f o r e , th em

members of th e s e t should a l l be very s im i la r o r c lo s e . F urtherm ore ,

th e members o f th e s e t could be made even more s im i la r by u s in g f e a tu r e

22

w eig h tin g c o e f f i c i e n t s , and m in im izing th e av erag e i n t e r c l u s t e r

d is ta n c e o f a l l th e members o f th e s e t . Thus, th e e q u a tio n to .b e

m inim ized i s

D? =Mg Mg nZ Z I = minimum.

p^= l mj^=l k= l ^(21)

thw here k r e p re s e n ts th e k component o f th e f e a tu r e v e c to r and m and p^

r e p re s e n t th e m^^ and p^^ f e a tu r e v e c to r o f th e s e t Ü c o n ta in in g

members.

In o rd e r to m inim ize E quation (2 1 ) , some c o n s t r a in t must be p la ced

on th e f e a tu r e w e ig h tin g c o e f f i c i e n t s . S e v e ra l a l t e r n a t iv e s a re

p o s s ib le , b u t th e m ost ap p ea lin g c o n s t r a in t i s

n(22)

I f th e f e a tu r e w eig h tin g c o e f f i c ie n t s a re co n s id e re d to be th e

d im ensions o f a hypercube , th e n E quation (22) i s a c o n s ta n t volume

c o n s t r a in t . In o rd e r to m inim ize E quation (21) needs to be w r i t t e n

in a more co n v en ien t form .

— Mj n

2m=l “ Jl ^bp2= l

2M, nz

----------------------2M, n,w ! ( .x g - .x . )= Z -2

th

(23)

w here i s th e v a r ia n c e o f th e k*"" d im ension o f th e f e a tu r e v e c to r s in

s e t a . Using th e c o n s t r a in t and an undeterm ined m u l t i p l i e r , th e

m inim izing e q u a tio n becomes

23

= 0 f o r j = l , 2 , ......... ..... (24)

which may be r e w r i t te n as

k k^ i/ T

k * l(25)

U sing th e c o n s tr a in t fo r de te rm in in g X g iv e s

kk^&

nn

p=i

V n

k°A(26)

The f e a tu r e w eig h tin g c o e f f i c ie n t s in d ic a te th a t i f th e v a r ia n c e in a

p a r t i c u l a r dim ension i s sm a ll, th en th e v a lu e o f th e f e a tu r e can be

a n t ic ip a te d w ith a h ig h degree o f accu racy and should be h e a v i ly w eighed.

On th e o th e r hand , i f th e v a r ia n c e i s l a r g e , th en l i t t l e w eigh t shou ld be

a t ta c h e d to th a t f e a tu r e .

E quation (26) i s th e d ia g o n a l tra n s fo rm a tio n d isc u sse d in th e

theorem encom passing E quation (19) and i s i d e n t i c a l to E quation (1 9 ). As

th e theorem s t a t e s , t h i s d is ta n c e m easure can be a d d i t io n a l ly m inim ized

by app ly ing th e e ig e n v e c to r tr a n s fo rm a tio n . I t fo llo w s by E quations (18)

and (21) th a t th e s im i la r i ty c r i t e r i o n , E quation (2 0 ), fo r d ec id in g

w hether to merge two c lu s t e r s k and Ü i s g iven by

- p V “

n(27)

24

where v, i s th e mean f e a tu r e v e c to r o r c e n tro id fo r c lu s t e r k , and {x } k

a re th e f e a tu r e v e c to rs belong ing to c lu s te r &.

S u b s t i tu t in g E quation (19) fo r g ives

. V 2

PP

V n

p=i p p V(28)

The d e c is io n fo r m erging two c lu s t e r s w i l l now depend on th e th re sh o ld

v a lu e g iven to t ’ e a s r s of s im i la r i ty fo r bo th c l u s t e r s . A th re sh o ld

v a lu e can be d(^ c a lc u la t in g th e average s im i la r i ty w ith in a

c l u s t e r , which i s g iven by

% . l

n ^p^m. " p*&)E ------— ------—

p=l p p V+ n

n Vn2n. (29)

(30)

Using E quation (29) as a th re s h o ld v a lu e fo r E quation (28) g iv e s th e

d e c is io n r u l e , merge c lu s t e r s k and Si i f

p= i pp^&

N otice th a t E quation (30) i s th e eq u a tio n o f a h y p e re l l ip s e in th e

p r in c ip a l axes c o o rd in a te s , which was e a r l i e r d e riv ed by p h y s ic a l

i n t u i t i o n . N o tice a lso th a t th e th re s h o ld v a lu e n i s independent o f

c lu s t e r and depends on ly on th e dim ension of th e f e a tu r e sp ace . 'T hus,

i f an e l l i p t i c a l boundary d e c is io n ru le i s used in th e p r in c ip a l a x is

c o o rd in a te system , th e theorem can be extended to say th a t th e d iag o n a l

tra n s fo rm a tio n i s n o t needed and on ly th e e ig en v ec to r tra n s fo rm a tio n i s

25

needed s in c e th e th re sh o ld can always be w r i t t e n as some c o n s ta n t tim es

A fte r th e i n i t i a l M s e t o f c lu s t e r s has been merged in to a f i n a l N

s e t o f c l u s t e r s , w ith N ^ M, th e e ig e n v e c to r r o ta t io n m a trix and th e

eq u a tio n fo r th e h y p e re l l ip s e in p r in c ip a l axes c o o rd in a te s a re s to re d

in memory fo r each f i n a l c l u s t e r . The c lu s t e r s a re now c a l le d c la s s e s

s in c e each c la s s re p re s e n ts a s t a t i s t i c a l l y d i f f e r e n t f e a tu r e p re se n te d

by th e d a ta . The re g io n s in f e a tu r e space R^, R^ co rrespond ing

to each c la s s a re d i s t i n c t s in c e no more m erging i s p o s s ib le . This

f e a tu r e e x t r a c t io n in fo rm a tio n i s now ready f o r use in th e l a s t s ta g e of

p ro c e ss in g .

The f i n a l s ta g e o f p ro c e ss in g i s concerned w ith c la s s i fy in g th e

d a ta in th e d i g i t a l image o f th e ground scene and showing th e lo c a t io n

and d i s t r i b u t io n o f th e f e a tu r e s . The in p u ts to t h i s s ta g e o f p ro c e ss in g

a re th e raw d a ta ta p e , th e s t a t i s t i c s f o r each c la s s and th e boundary

ta p e . The d e c is io n r u le f o r .c l a s s i f y in g a r e s o lu t io n elem ent f e a tu r e

v e c to r V in to c la s s i i s g iven by

p=i PP a

which i s th e same as E quation (30) excep t f o r th e f a c to r o f two. The

f a c to r o f two i s j u s t i f i e d based on th e fo llo w in g argum ents. F i r s t , th e

d e c is io n r u le f o r c la s s i fy in g a r e s o lu t io n elem ent can be more le n ie n t

than th e d e c is io n r u le f o r m erging two c l u s t e r s . The e r r o r s of

m ism erging a re more pronounced in th e c l a s s i f i c a t i o n th a n th e

m is c la s s i f ic a t io n o f in d iv id u a l r e s o lu t io n e lem en ts. Secondly , th e

26

e x p re ss io n on th e l e f t hand s id e o f th e in e q u a l i ty in E quation (31) i s

id e n t ic a l to th e argument in th e ex p o n e n tia l o f a d i s j o i n t m u l t iv a r ia te

G aussian d i s t r i b u t io n . Thus, a r e s o lu t io n elem ent i s n o t c l a s s i f i e d as

belo n g in g to a c la s s i f th e n -d im en sio n a l e x p o n e n tia l n - f o ld s . F u r th e r

j u s t i f i c a t i o n fo r u s in g E quations (30) and (31) and th e th re sh o ld

v a lu e s o f n and 2n r e s p e c t iv e ly i s th a t th e term s co n ta in ed in th e

summation a re c h i-sq u a re d i s t r i b u te d , and a c h i-s q u a re d i s t r i b u t io n has

a m ean-value n and v a r ia n c e 2n, where n i s th e number o f d eg rees of

, 23freedom .

The d a ta o b ta in ed from th e raw d a ta ta p e i s c l a s s i f i e d acco rd ing

to th e d e c is io n r u le in E quation (31) and th e r e s u l t o f th e c l a s s i f i

c a t io n i s updated on th e boundary ta p e map. For exam ple, i f a r e s o lu t io n

elem ent belongs to c l a s s 3 , a 3 i s p la ced on th e boundary ta p e a t th e

lo c a t io n o f th e r e s o lu t io n e lem en t. I f a r e s o lu t io n elem ent i s no t

c l a s s i f i e d as be long ing to any c l a s s , no change i s made on che boundary

ta p e . I f a r e s o lu t io n elem ent can be c l a s s i f i e d as be lo n g in g to s e v e ra l

c l a s s e s , th e r e s o lu t io n elem ent i s p laced in th e c la s s which makes th e

l e f t hand s id e o f E quation (31) a minimum. The boundary ta p e i s now

c a l le d a c l a s s i f i c a t i o n ta p e and c o n ta in s th e numbers - 1 , re p re s e n t in g

an u n c la s s i f ie d boundary r e s o lu t io n e lem en t, 0 , re p re s e n t in g an

u n c la s s i f ie d homogeneous r e s o lu t io n e lem en t, and 1 , 2 , . . . . , N r e p re s e n t in g

r e s o lu t io n elem ents p la ced in c la s s e s 1 , 2 , . . . . , N r e s p e c t iv e ly .

I f th e i n i t i a l s i z e o f th e p x p a r ra y fo r c lu s t e r s e le c t io n i s too

la r g e , an incom plete c l a s s i f i c a t i o n o f th e ground scene w i l l r e s u l t . The

com puter program has th e c a p a b i l i ty fo r u s in g th e c l a s s i f i c a t i o n map as

a boundary map, t r e a t in g th e c l a s s i f i e d r e s o lu t io n e lem ents as a lso

27

b eing b o u n d a rie s , d e c re a s in g th e p x p a r ra y to a q x q a r r a y , and

s e le c t in g a d d i t io n a l c l u s t e r s . A ll p rev io u s in fo rm a tio n o b ta in ed on th e

c la s s e s i s u p d a ted , i f a p p ro p r ia te , and th e c l a s s i f i c a t i o n map i s

r e c l a s s i f i e d u s in g th e o ld unchanged in fo rm a tio n and th e new updated

in fo rm a tio n . T h is p ro ced u re can be re p e a te d a s many tim es as d e s ir e d ,

bu t two c l a s s i f i c a t i o n p asse s a re g e n e ra lly s u f f i c i e n t .

Because o f th e la rg e amounts o f d a ta in v o lv e d , th e o u tp u t o f th e

c l a s s i f i c a t i o n map i s nom inally pu t on m ic ro film r a th e r th an s tan d a rd

com puter paper p r in to u t . T his i s ev idenced by th e f a c t th a t th e

c l a s s i f i c a t i o n map from a 70mm a e r i a l ph o to g rap h , u s in g s tan d a rd

computer p r in t o u t , can e a s i l y cover a 400 sq u are fo o t w a ll .

R e su lts a re shown in th e n ex t C hap ter. The poor q u a l i ty o f th e

f ig u re s d e s c r ib in g th e d a ta and com puter r e s u l t s is due to th e

re d u c t io n in s c a le and number o f copying p ro c e sse s re q u ire d fo r th e

p re s e n tin g o f th e in fo rm a tio n .

CHAPTER IV

RESULTS

C la s s i f i c a t io n maps were o b ta in ed from th e a n a ly s is o f two d a ta

s e t s , P u rd u e 's F l ig h t L ine Cl and th e Y ellow stone P ark t e s t s i t e s . The

advantage o f working w ith th e se two s e ts o f d a ta i s th a t th ey have been

e x te n s iv e ly analyzed by o th e r in v e s t ig a to r s u s in g d i f f e r e n t f e a tu r e

e x t r a c t io n te c h n iq u e s . The r e s u l t s o f th e s e in v e s t ig a t io n s a r e m ain ly

a v a i la b le in R eferences 6 , 11, and 12 fo r com parison.

Both d a ta s e ts were acqu ired w ith th e same m u l t i s p e c t r a l scanner

and c o n ta in 12 channels o f d a ta . A ll 12 channels were used in th e

c l a s s i f i c a t i o n , and th e w avelength in t e r v a l s co rrespond ing to each

channel a re l i s t e d in T able 1. The d a ta s e t s c o n ta in 222 tw elve

d im ensional f e a tu r e v e c to rs per scan , and 901 scans from each s e t were

an a ly zed . The d a ta i s a lso u n c a l ib ra te d and th e re fo re on ly c o n ta in s

r e l a t i v e num bers. The s im i la r i ty o f th e two d a ta s e t s d r a s t i c a l l y comes

to an end w ith th e above d e s c r ip t io n .

F l ig h t l i n e Cl i s a v ery f l a t a g r i c u l tu r a l scene approx im ate ly

6 .5 k ilo m e te rs long and 1 .6 k ilo m e te rs w ide, and th e r e s o lu t io n o f th e

d a ta i s app rox im ate ly 6 m e te rs . The ground scene m ostly c o n ta in s

r e c ta n g u la r p a t te r n s o f crop acreag e which appear homogeneous.

28

29

TABLE 1 . ŒAMEL AND WAVELENGTH CORRESPONDENCE

CHANNEL WAVELENGTH INTERVALNUMBER IN MICROMETERS

1 .4 - .44

2 .44 - .46

3 .46 - .48

4 .48 - .50

5 .50 - .52

6 .52 - .55

7 .55 - .58

8 .58 - .62

9 .62 - .66

10 .66 - .72

11 .72 - .80

12 .80 - 1 .0

30

Y ellow stone P a rk , however, i s a w ild e rn e ss a re a approx im ate ly

16 k ilo m e te rs long and 3 .2 k ilo m e te rs w ide w ith a r e s o lu t io n of

approx im ate ly 15 m e te rs . The W ilderness a re a c o n ta in s v e ry i r r e g u la r

shaped p a t te rn s and i s q u i te inhomogeneous in some lo c a t io n s . This

d a ta s e t a lso p o sse sse s a c o n s id e ra b le dynamic ran g e in th e ty p e of

t e r r a i n and amount o f f e a tu re s p re s e n t . For exam ple, th e re a re

m ountains and canyons, and th e v e g e ta t io n coverage ranges from dense

f o r e s t to s c a t te r e d t r e e s , meadows, and f i n a l ly to b a re ro c k s . The

geo lo g ic in fo rm atio n ranges from a sand and g ra v e l b a se , abundan tly

sp r in k le d w ith E lk droppings in th e meadow a re a s , to rock s covered

w ith moss and l ic h e n , and f i n a l l y to la rg e b o u ld e rs .

Cl F lig h t Line

F ig u re 3 co n ta in s an a e r i a l photograph of th e ground scene on th e

l e f t , a boundary map in th e c e n te r w ith th e lo c a t io n s o f th e i n i t i a l

c l u s t e r s , and a c l a s s i f i c a t i o n map o f th e ground scene u s in g s t a t i s t i c s

from th e se c lu s t e r s . The a e r i a l photograph a lso c o n ta in s a l i s t o f

symbols th a t id e n t i f i e s th e co n te n ts o f th e ground scene . The l i s t o f

symbols and th e i r i d e n t i f i c a t i o n a re g iven in T ab le 2. Exam ination of

th e r e s u l t s o b ta in ed from th e m u l t is p e c tr a l scanner d a ta re v e a ls a

problem th a t does no t occur in m ultiband p h o tog raph ic d a ta . The a i r

c r a f t a c q u ir in g th e scanner d a ta was n o t q u ite a b le to f ly a s t r a i g h t

l i n e and had o c c a s io n a l yaw problem s. The scan n er d a ta i s r o l l

com pensated, however, as i s th e case w ith most sc a n n e rs .

The computer maps shown in F ig u re 3 dem onstra te th e f i r s t two ou t

o f th re e in te rm e d ia te o u tp u ts th a t can be o b ta in ed from th e computer

program and a re c o n s id e ra b ly sc a le d down to show th a t th e p a t te r n in th e

31

lu

ID.A.- R

" g

FIGURES. FLIGHT UNE ClA ER IA L PH O TO G R A PH , C LU STER SE L E C T IO N , AND INITIAL CLASSIFICATION

32

TABLE 2 . GROUND TRUTH INFORMATION

SYMBOL DESCRIPTION

A ALFALFA

C CORN

H HAY

0 OATS

P PASTURE

R RYE

S SOYBEANS

T TIMOTHY

W WHEAT

B.S. BARE SOIL

D.A. DIVERTED ACRES

R.C. RED CLOVER

33

d a ta has a d e f in i t e resem blance to th a t o f th e a e r i a l pho tograph . H ence,

i t i s n o t p o s s ib le o r n e c e ssa ry a t th i s s ta g e to be a b l e 't o read th e

symbols on th e com puter maps.

The boundary map c o n ta in s 79 d i f f e r e n t c l u s t e r lo c a t io n s a f t e r

s p a t i a l m erging. A 10 x 10 a r ra y was used to s e le c t th e se c l u s t e r s .

The f i r s t c lu s t e r i s a t th e top o f th e map j u s t to th e r ig h t o f th e ro a d ,

w h ile th e second c l u s t e r i s to th e r ig h t and j u s t below c l u s t e r 1 .

C lu s te r 3 i s th e top l e f t c lu s t e r in a co rn f i e l d , w h ile c lu s t e r 4 i s

th e f i r s t c l u s t e r in th e soy f i e l d below th e wheat f i e l d to th e l e f t of

th e ro ad . C lu s te r 5 i s th e f i r s t c l u s t e r d i r e c t l y below c lu s t e r s 1 and

2 and i s a lso lo c a te d in a soy f i e l d . C lu s te r 6 i s in th e same soy

f i e l d as c lu s t e r 4 and i s j u s t below c l u s t e r 4 , w h ile c lu s t e r 8 i s j u s t

to th e r ig h t o f c lu s t e r 6. The r e s t of th e c lu s te r s fo llo w u s in g th e

same computer p a t te r n lo g ic . Only 43 s in g le c h a ra c te r o u tp u t symbols

a re a v a i la b le to name th e 79 c lu s t e r s and, th e r e f o r e , th e symbol usage

i s re c y c le d s t a r t i n g w ith c lu s t e r 44. T ab les 3 and 4 g ive th e o r ig in a l

c l u s t e r num bers, ground t r u t h in fo rm a tio n , a d e s c r ip t io n o f th e s p e c t r a l

m erging p ro cess and th e f i n a l c l a s s number. Remember th a t when s e v e ra l

c lu s t e r s a re s p e c t r a l ly merged, th e number g iven to th e merged c lu s te r

i s th e sm a lle s t c lu s t e r number o f th e c lu s t e r s invo lved in th e m erging,

and some o f th e rem ain ing c lu s t e r s n o t invo lved in th e m erging may have

t h e i r c l u s t e r numbers changed in o rd e r alw ays to keep th e numbering o f

th e c lu s t e r s in a c o n se c u tiv e o rd e r . T his i s i l l u s t r a t e d in th e s p e c t r a l

m u l t ip le m erging columns o f T ab les 3 and 4 . I f no ground t r u t h i s

a v a i la b le fo r a c l u s t e r , th e l e t t e r U i s used to in d ic a te th a t i t i s

u n id e n t i f ie d . E xam ination of T ab le 3 m u l t ip le merge number 1 r e v e a ls

34

TABLE 3. MERGING PROCEDURE FOR FIRST 40 CLUSTERS

CLUSTER IDENTI- SPECTRAL MULTIPLE MERGE NUMBERFINALCLASS

NUMBER FICATION 1 2 3 4 NUMBER

1 U 1 1 1 1 12 U 1 1 1 1 13 C 2 2 2 2 24 S 3 3 3 3 35 S 4 4 4 4 46 S 3 3 3 3 37 S 4 4 4 4 48 S 3 3 3 3 39 S 4 4 4 4 410 S 5 5 5 5 5

11 DA-BS 6 6 6 6 612 C 7 7 7 7 713 C 7 7 7 7 714 C 7 7 7 7 715 u 8 8 8 8 816 s 9 8 8 8 817 s 3 3 3 3 318 BS 6 6 6 6 619 s 10 9 3 3 320 U 8 8 8 8 821 C 11 8 8 8 822 c 12 8 8 8 823 c 8, 9, 11, 12 8 8 8 824 c 10 9 9 925 s 7 7 7 726 s 4 4 4 427 s 7 7 7 728 w 11 10 10 1029 s 3, 9 3 3 330 c 11 11 1131 0 12 12 1232 0 12 12 1233 c 13 13 1334 w 10 10 1035 w 10 10 1036 0 12 12 1237 u 14 14 1438 w 10 10 1039 c 15 3 340 w 10 10 10

35

TABLE 4. MERGING PROCEDURE FOR CLUSTERS 4 1 - 7 9

CLUSTERNUMBER

IDENTIFICATION

SPECTRAL MULTIPLE MERGE NUMBERFINALCLASSNUMBER

41 C 14 14 1^ 14 1442 U 15 14 14 14 1443 s , c 3 3 3 3 344 u 14, 15 14 14 14 1445 0 15 15 15 1546 w 10 10 10 1047 s 16 16 16 1648 u 16 16 16 1649 DA-R 17 17 17 1750 DA-R 18 17 17 1751 P-0 19 18 18 1852 DA-R 1 7 , 18 17 17 1753 DA-R 17 17 1754 DA-R 17 17 1755 0 19 19 1956 0 19 19 1957 C 8 8 858 C 20 20 2059 C 8 8 860 S 21 21 2161 S 22 21 2162 S 21 , 22 21 2163 S 21 2164 S 21 2165 C 7 766 S 22 2267 S 7 768 S 5 569 S 5 570 S 5 571 S 3 372 S 5 573 S 23 2374 u 1 175 s 22 2276 s 23 2377 s 24 2478 u 3 379 u 3 3

36

th a t th e s t a t i s t i c s o f c lu s t e r s 1 and 2 w ere merged to g e th e r and th e

r e s u l t was c a l le d c lu s t e r 1. C lu s te r 3 d id no t merge w ith c lu s t e r 1 ,

bu t was renamed c l u s t e r 2 so th a t co n secu tiv e numbering would be

p re se rv e d . C lu s te r 4 was renamed c lu s t e r 3 because i t would n o t merge

w ith c lu s t e r s 1 and 2 , and c lu s t e r 5 was renamed c lu s t e r 4 because i t

would n o t merge w ith c lu s t e r s 1 , 2 o r 3. C lu s te r 6 would merge w ith

c l u s t e r 3 and th e s t a t i s t i c s o f c lu s t e r 3 were updated to in c lu d e th e

s t a t i s t i c s o f c l u s t e r 6. F in a l ly , c lu s t e r 23 was a b le to merge w ith

c lu s t e r s 8 , 9 , 11 , 12 and th e s t a t i s t i c s o f c lu s t e r 8 were updated to

in c lu d e th e s t a t i s t i c s o f c lu s t e r s 9 , 11, 12 and 23. The renam ing of

th e c lu s t e r s r e s u l t in g from t h i s m u lt ip le merging i s shown in m u lt ip le

merge column number 2 , and th i s column c o n tin u es u n t i l an o th e r m u ltip le

merge i s en co u n te red . The c l a s s i f i c a t i o n map r e s u l t in g from th e merging

and f i r s t c l a s s i f i c a t i o n pass i s shown on th e r ig h t hand s id e o f F ig u re 3.

T his map c o n ta in s 24 c la s s e s , o r f e a tu r e s , as in d ic a te d by th i s h ig h e s t

number in Table 4 under th e column e n t i t l e d , "F in a l C lass Number."

Because th e c l a s s i f i c a t i o n was in co m p le te , a d d i t io n a l c lu s te r s were

s e le c te d by a 6 x 6 a r ra y s t a r t i n g w ith c lu s t e r number 25, and u s in g th e

c l a s s i f i c a t i o n map as in p u t f o r th e c l u s t e r s e le c t io n r a th e r than th e

boundary map. The merging p roced u re i s l i s t e d in Table 5 under th e

column " F in a l C lass Number" s in c e no m u lt ip le merges were encoun tered .

The com puter program only a llow s f o r 43 c la s s e s and th e re fo re re fu se d to

acc ep t any a d d i t io n a l d a ta a f t e r c lu s t e r 48 , as in d ic a te d in T able 5.

T able 6 l i s t s th e i n i t i a l c lu s t e r numbers o f a l l c lu s te r s th a t a re lo c a te d

in th e same f i e l d f o r bo th c l a s s i f i c a t i o n p a s se s . T his p ro v id es an

a d d i t io n a l check to determ ine w hether th e m erging was conducted p ro p e rly

37

TABLE 5. MERGING PROCEDURE FOR CLUSTERS 25 = 52

CLUSTERNUMBER IDENTIFICATION

FINALCLASSNUMBER

25 WATER 2526 C 2627 C 2628 DA-RC 2729 S 2830 S 2931 DA-RC 3032 DA-RC 3133 P 3234 DA-RC 3335 C 3436 DA-RC 3537 DA-RC 3038 P 3639 C 3740 C 3741 C 3842 H-RC 3043 H-RC 3044 C 3945 0 4046 0 4147 0 4248 U 4349 RC50 RC51 052 RC

38

TABLE 6. MULTIPLE CLUSTER FIELDS

CLASSIFICATION PASS 1-10x10 ARRAY INITIAL

CLUSTER NUMBERS IDENTIFICATION

CLASSIFICATION PASS 2-6x6 ARRAY INITIAL

CLUSTER NUMBERS IDENTIFICATION

1,2 U 26,27 C

4 , 6 , 8 S 3 1 ,3 2 ,3 4 ,3 6 ,3 7 DA-RC

5 , 7 , 9 S 39,40 C

1 2 ,1 3 ,1 4 C 42,43 H-RC

17,19 S 4 5 ,4 6 ,4 7 ,5 1 0

2 1 ,2 2 ,2 3 ,2 4 C

25,27 S

31,32 0

3 4 ,3 5 ,3 8 ,4 0 w

4 9 ,5 0 ,5 2 ,5 3 ,5 4 DA-R

55,56 0

57 ,5 8 ,5 9 C

60 ,63 ,64 S

6 6 ,7 3 ,7 5 ,7 6 S

67,77 S

6 8 ,6 9 ,7 0 ,7 1 ,7 2 S

39

and to a s s i s t in lo c a t in g th e f i r s t c l a s s i f i c a t i o n p ass c lu s t e r s shown

in F ig u re 3 i f d e s ir e d . The reason th a t one f i e l d may have s e v e ra l

c l u s t e r s i s th a t boundary p o in ts w ith in a f i e l d may n o t p erm it s p a t i a l

m erging o f th e se c l u s t e r s . S p e c tra l m erging i s used to overcome th i s

problem .

T ab le 7 l i s t s th e f i n a l c la s s number, com puter symbol p r in to u t and

a b r i e f d e s c r ip t io n o f th e c la s s o r f e a tu r e based upon th e a v a i la b le

ground t r u t h .

A u s e r may now d e s i r e to in t e r p r e t th e r e s u l t s f o r h is s p e c if ic

n eeds, which may be crop i d e n t i f i c a t i o n , fo r example. T able 8 was

p rep a red fo r t h i s example and fo r exam ining th e f i n a l r e s u l t s . C lasses

1 , 7 , D and / a re n o t l i s t e d in th e ta b le because a s p e c i f i c crop name

o r f e a tu r e could n o t be a t ta c h e d . N o tice th a t c la s s e s 7 , D, and / occur

a t th e edges o f th e com puter map.

F ig u re s 4 th rough 15 a re th e f i n a l c l a s s i f i c a t i o n r e s u l t s fo r

f l i g h t l i n e C l, and F ig u re s 4 th rough 9 co rrespond to th e l e f t s id e of

th e a e r i a l pho tograph , w h ile F ig u re s 10 th rough 15 correspond to th e

r ig h t s id e .

In F ig u re 4 w ate r i s re p re se n te d by th e l e t t e r 0 and wheat by th e

number z e ro . The ze ro s have a s l i g h t ly re c ta n g u la r shape as compared to

th e l e t t e r 0. F ig u re s 7 th rough 9 s t a r t to show s e v e ra l a re a s th a t were

n o t c l a s s i f i e d . This i s because th e maximum o f 43 c la s s e s was o b ta in ed

in th e a re a o f F ig u res 7 and 13 and th e rem ain ing u n c la s s i f ie d r e s o lu t io n

elem ents were s ig n i f i c a n t l y d i f f e r e n t from th e 43 p re v io u s ly o b ta in ed

f e a tu r e s .

40

TABLE 7. FEATURE SYMBOL AND DESCRIPTION

CLASSNUMBER

COMPUTERSYMBOL BRIEF DESCRIPTION AND COMMENTS

-1 • UNCLASSIFIED BOUNDARY RESOLUTION ELEMENT0 UNCLASSIFIED NON-BOUNDARY RESOLUTION ELEMENT1 1 UNIDENTIFIED - CLASSIFIED AS CORN IN REFERENCE 62 2 CORN3 3 MIXTURE - 84% SOY, 8% COEN AND 8% UNIDENTIFIED4 4 SOY BEANS5 5 SOY BEANS6 6 BARE SOIL7 7 MIXTURE - 51% SOY AND 49% CORN8 8 MIXTURE -73% CORN AND 27% SOY9 9 CORN

10 0 WHEAT11 A CORN12 B OATS13 C COEN14 D UNDECIDED - PROBABLY CORN15 E OATS16 F PROBABLY ALL SOY -89% SOY AND 11% UNIDENTIFIED17 G DIVERTED ACRES AND RYE18 H PASTURE AND OATS19 ■ 1 OATS20 J COR]H21 K SOY BEANS22 L SOY BEANS23 M SOY BEANS24 N SOY BEANS25 0 WATER26 P CORN27 Q DIVERTED ACRES AND RED CLOVER28 R SOY BEANS29 S SOY BEANS30 T DIVERTED ACRES AND RED CLOVER31 U DIVERTED ACRES AND RED CLOVER32 V PASTURE33 W DIVERTED ACRES AND RED CLOVER34 X CORN35 Y DIVERTED ACRES AND RED CLOVER36 Z PASTURE37 = CORN38 $ CORN39 9 CORN40 f OATS41 ( OATS42 * OATS43 / UNIDENTIFIED

41

TABLE 8 . USER INTERPRETATION OF RESULTS

CATEGORY COMPUTER MAP SYMBOL

CORN

SOY

BARE SOIL

WHEAT

OATS

DIVERTED ACRES

DIVERTED ACRES

PASTURE

WATER

RYE

RED CLOVER

2 ,8 ,9 ,A ,C ,J .P ,X ,= ,$ ,»

3 ,4 ,5 ,F ,K ,L ,M ,N ,R ,S

6

0

B , E ,H , I , ' , ( , *

G

Q,T,U,W,Y

V,Z

0

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54

A ccording to R eference 6 a m a jo r ity o f m i s c la s s i f ic a t io n and non

c l a s s i f i c a t i o n can be a t t r ib u t e d to weed grow th and low ly in g a re a s

w ith in d i f f e r e n t f i e l d s . This p ro b a b ly -a lso accoun ts fo r th e appearance

o f bo u n d arie s in th e f i e l d s p re se n te d in th e s e r e s u l t s . For exam ple,

F ig u re 10 c o n ta in s a h o r iz o n ta l ly p re se n te d w heat f i e l d n e a r th e bottom

w ith a m is c la s s i f ic a t io n o f o a ts in th e m idd le . T his m is c la s s i f ic a t io n

i s due to th e p re sen ce o f a low ly in g a re a . The bo u n d arie s in th e

d iv e r te d a c re s - re d c lo v e r f i e l d j u s t above t h i s w heat f i e l d a re due to

th e p resen ce o f a sm all sand dune.

I t may be o f i n t e r e s t to n o te th a t th e re a re u s u a lly more f e a tu re s

re p re s e n t in g a row crop such as corn and soy , and th a t th e non-row crop

f i e l d s such as wheat and o a ts a re more homogeneously c l a s s i f i e d per

f i e l d . This r e s u l t i s p robab ly due to th e sen so r having to average no t

o n ly over th e canopy s t r u c tu r e o f a row c ro p , bu t in a d d i t io n , averag ing

over a p e rce n tag e o f b a re s o i l o b se rv ab le between th e p la n ts . The type

of s o i l could a lso vary from lo c a t io n to lo c a t io n .

Y ellow stone Park

F ig u re 16 c o n ta in s a v ideo r e p r in t from channel 9 o f th e ground

scene on th e l e f t , a boundary map in th e c e n te r w ith th e lo c a t io n o f th e

i n i t i a l c l u s t e r s , and a f i r s t pass c l a s s i f i c a t i o n map w ith an a d d i t io n a l

s e le c t io n o f c l u s t e r s .

The Y ellow stone P ark d a ta was ana lyzed e x a c tly as th e Cl f l i g h t l i n e

d a ta . The v id eo r e p r in t c o n ta in s some ground t r u t h and lo c a t io n s of

t r a in in g a re a s used by o th e r in v e s t ig a to r s l i s t e d in R eferences 11 and

1 2 .

55

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FIGURE 16. YELLOWSTONE PARKVIDEO R E P R IN T , C LU STER SELEC TIO N , INITIAL CLASSIFIC A TIO N , AND SECONDARY C LU STER SELECTIO N

56

Table 9 g iv es th e merging p rocedu re f o r both c l a s s i f i c a t i o n p asse s

s in c e no m u lt ip le merges were en coun tered . No id e n t i f i c a t i o n i s g iven

f o r th e c lu s t e r s because th e c lu s t e r lo c a t io n s do n o t n e c e s s a r i ly c o in c id e

w ith th e t r a in in g a re a s , and i t i s e a s ie r to id e n t i f y th e f e a tu r e s a f t e r

th e f i n a l c l a s s i f i c a t i o n . The a n a ly s is o f t h i s d a ta s e t in d ic a te s th e ty p e

o f problem invo lved when a f a i r l y in a c c e s s ib le re g io n i s rem o te ly sensed .

I t i s d i f f i c u l t to e s tim a te what ty p es o f fe a tu re s can be e x tra c te d from

th e d a ta and i t may be econom ically to th e advantage o f th e in v e s t ig a to r

to c o l le c t th e ground t r u t h in fo rm a tio n based upon th e f e a tu r e e x t r a c t io n

map, r a th e r th an t r y in g to a n t ic ip a te th e needed d e ta i le d ground t r u t h .

Table 10 was p rep ared fo r in t e r p r e t i n g th e f i n a l r e s u l t s based on

in fo rm atio n d e riv e d from th e v ideo r e p r i n t . S ev era l meadow l i k e a re a s

w ere d is c e r n ib le , b u t were only g iven meadow numbers co rrespond ing to

t h e i r c la s s numbers because of la c k o f o th e r in fo rm a tio n . The g eo lo g ic

term s t i l l , t a l u s , kame, and v e g e ta te d ro ck ru b b le a re d e sc r ib e d in

R eferences 11 and 12, b u t a re re p e a te d h e re fo r convenience.

The c la s s t i l l c o n s is ts o f meadow a re a s u n d e r la in by g la c ia l t i l l .

They a re g ra s s la n d and sagebrush a re a s which were la rg e ly dormant a t th e

tim e of d a ta c o l le c t io n . M ineral s o i l i s exposed in about o n e - f i f t h of

th e a re a and c o n s is ts o f s i l t y to b ou lde ry d e b r is . Deer and e lk manure

a re lo c a l ly abundant in th e se a re a s .

The c la s s ta lu s in c lu d e s b lo c k f ie ld s , t a lu s , and ta lu s flow s o f

b a s a l t la v a f lo w s , v o lc a n ic t u f f , and g n e is s , formed by f r o s t - r i v in g and

s o l i f l u c t i o n from o u tc ro p s . They a re b locky and w e ll-d ra in e d d e p o s i t s ,

and t r e e s a re w idely spaced o r a b se n t. The b locks a re covered w ith

dark gray lic h e n s and range from a few c e n tim e te rs to about 1 m eter in

57

TABLE 9. MERGING PROCEDURE PGR YELLOWSTONE DATA

CLASSIFICATION PASS 1-10x10 ARRAY CLASSIFICATION PASS 2-6x6 ARRAY

INITIAL CLUSTER NUMBER

FINAL CLASS NUMBER

INITIAL CLUSTER NUMBER

FINAL CLASS NUMBER

1 1 11 11

2 2 12 11

3 2 13 11

4 3 14 11

5 3 15 11

6 2 16 11

7 4 17 11

8 4 18 11

9 3 19 11

10 4 20 12

11 4 21 13

12 5 22 14

13 4 23 14

14 6 24 15

15 6 25 15

16 4 26 16

17 4 27 16

18 4 28 16

19 4 29 16

20 7 30 17

21 8 31 18

22 9 32 19

23 10 33 19

24 10 34 20

25 10

58

TABLE 10. INTEEPEETATION OF YELLOWSTONE RESULTS

CLASS NUMBER SYMBOL BRIEF DESCRIPTION

1 1 MEADOW 1

2 2 MEADOW 2

3 3 mADOW 3

4 4 DENSE FOREST AND SHADOW

5 5 TILL

6 6 KAME

7 7 MEADOW 7

8 8 MEADOW 8

9 9 MEADOW 9

10 0 MEADOW 10

11 A TREES

12 B TREES

13 C TALUS

14 D TILL

15 E TILL

16 F TILL

17 G TILL

18 H TILL

19 I VEGETATED ROCK RUBBLE

20 J MEADOW 20

59

d ia m e te r . Most a re l a r g e r th an 10 c e n t im e te r s . The s lo p e s in th e se

a re a s range w id e ly , from 35 to 45 d eg rees a t th e head to 5 deg rees o r

le s s a t th e to e .

The c la s s kame i s v e ry s im ila r to t i l l excep t about o n e -fo u r th o f

th e a re a i s exposed m in e ra l s o i l .

The c la s s v e g e ta te d ro ck ru b b le c o n s is ts o f lo c a l ly d e riv e d an g u la r

ru b b le , f r o s t - r iv e n from b a s a l t la v a s , v o lc a n ic t u f f and b re c c ia , and

g n e is s . G rasses , l i c h e n s , everg reen s e e d l in g s , and mosses cover more

than th r e e - f o u r th s o f th e s u r fa c e u n d e r la in by th i s d e b r is . The rocks

range in d iam ete r from le s s than 1 c e n tim e te r to about 1 m eter and occur

on s lo p e s from zero to about 25 d eg ree s .

Three a d d i t io n a l ly known f e a tu r e s in th e ground scene d id n o t appear

in th e c l a s s i f i c a t i o n map because th e y were n o t co n ta in ed in a homo

geneous a re a la rg e enough to be s e le c te d b y a c l u s t e r . These f e a tu r e s

were w a te r , bedrock and bog. However, th e a re a s where th ey appear on

th e c l a s s i f i c a t i o n map can be lo c a te d w ith th e a id o f th e v ideo r e p r in t

and th ey appear as u n c la s s i f i e d a re a s . These c la s s e s could now be

id e n t i f i e d elsew here in th e d a ta by u s in g a su p erv ised tech n iq u e and

s e le c t in g th e se u n c la s s i f i e d r e s o lu t io n e lem ents as t r a in in g a re a s .

F ig u re s 17 th rough 28 co n ta in th e f i n a l c l a s s i f i c a t i o n r e s u l t s

fo r th e Y ellow stone Park t e s t s i t e and F ig u res 17 th rough 22 co rrespond

to th e l e f t s id e o f th e v id eo r e p r i n t , w h ile F ig u res 23 th rough 28

co rrespond to th e r ig h t s id e .

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1 3 fx 33 33AAA3-3 f\. rs. 3A3 3 3 AAAAAA AAAAAAAAAAAAAAAAAAA . . AA <• ■2 2 3 . . . — . 3 33 3AAAA <\fkf\fA333 3 3 3 3 3AAAAAAA2N|\iN2Nf>2Nf>3\AAAAAAAAAAAAAAAAAA ■ AA . r r r r2 2 2 >3 32 IN . 3 33 33AAA333 33333333 3AAA 2N. f\fvfV3Nf\f\2\2VAq A AAAAAAAAAAAAAAAAAAAA . r r r r2'W \3333 <\f\ 33333 33 333333333 333AAAA-, AA~4VU2MV AAAA AAAAAAAAAAAAAAAAAA r r r r rrj*. 3A3 3 3fV\2—3 3 2 333 333 3 33 3 3 33AAAA—r AAAAAAiv/nAAAAAAaA AA AAAAAAAAAAAAAi r r r r

rrrr^—r r r r r r r r f r r r r r r r r r r r r r . r. <*f'f*r'i"2»f»r» r r r r r r r .

r r r r r r r r r r r r r r r r ■rr rrr rr '

r r r r r r r . ■ • r r r r r r r r r r r . r r r r r r . r rmpr

r,<•2*1* r r r r r r <*rr»f'. r r r r .

r r r . ■ r r r r . r r f* r* n 2* !<• 2* 2* r» r 2*2» 2* f* r

r r r r r ~ i*2»2*r2"2*r2*2*. r r r ■ ■ »*2*2'2'f'2»2»2* . . . r r r r r r r r r

2 2 2 2 2 2 2 2A3 3 A2\WA JA2\2V 3rv AAA3 3 3 33 3 3 33333 33333AAAAV • Af\f\ AAAAAAAAAAAAAAAAAAAAAAAAA c m r11I 2 2 22A «- 2N2S2NAA2 3 3A3 3 3A fv3 3 333 3 33333333 A3333A A . ■ . o r p-AfV AA2\AA AAAAAAAAAAAAAAAAAA r r r r r r1 IA 2 2 2 J Arv3A>\2V2N3'M\A3A3 3 3 3 3 A3 3 3 333333 3 333 3A3333333 •- —— AA2\ 2\jAA A AA A AA A AA A AA A AAAA A AA A r r r r r r2 2 2 2rv2N2\2N 3AAT2\2\ A3 33 2 3333A2A333 3 3333 3 3 33 3 333A r&fs. r. AA 2\AAAAAAAAAAAAAAAAAAAA r r r r r r r r•113a \2\.2AA •■.»* AAA33A 3A 3A J 3A3 3A3 3 3 3 3 3 3A 3 3 A 2\2V . .J A 3AAAAAAAAAAAA AAA AAAA • r r r r r r r

2 2 3 1 AAA A AA . 2N. AAA . . ■ 3 33 33 3 333 3A 33 rvr. <N . . AAAAAA AAAAAAAAAA AAAAAA . r r r r r r -2 2 2 3 2 ATM AA *. — — <V_1 2 A 3AATA. ■ A 3 3 3 3 33 3 33 3AA3 AATJN r r p> AA 3 A AAAAA AAAAAAAAAAAAAAAT r r r r r r r -2 2 2 2 2 A 39 1 .— A-fWA3 9AA3A r r CN3VAA33 3 3 33 3 3 3 33 3 JA3>H% r —r3\ J 2 3 333 3AA AAAAAAA AAAAAAA r r r r r r r r r r '2 2 2 3 A <v /\rvAAAAA r r r Ar2AA33^3333 33 33 3 3 3AAA 2 3 3 3 3 TAAAAAAAAAAAAAAA r r r r r r r r r r r r’ 2 2 2 1 A -\AAA.\r A A «' : ..33AA3A3333333333333 f\AA3333AAAAAAAAAAAAAAAA r r r r r r r r r r r12 12 2 IWAAA2 2 —rvfVMA . . <\«3 3 3 33 3 3 3 3 3 333 7 3 3 3 3 3 3 . <vr\,-AA-AAAAJ 3AAAAAAAAAAAAAAAAA r r r r r r r r r r r2 2 .2 1 r\2*»2V2*\ 3 — rjv —f\A r A 3333333 2 33 333 3A3 3 3 JAArjVj ■' ■■ i\AAAA3AAA TAAAAAAAA AAAAA A.-r r r r r r r r r r r2 2 lA*. 2 fVA— --r3\2Vf\i-4i>,r <\ 3A33333 3 73A33 A3 3 3 3Af\2\AA. . f\. A3 3 AAAAAAAAAAAAAAAAAAA r r r r r r r r r r r rAAA I A3 —4^1 333333 3 33 3333 IN. Ou3A AA3 33AAA 3AAA AA A A AAAAAAA r r r r r r r r r r r r r .

«. — 3 3 3 3 3 3 3 3 .33333 3A A AA 3 3 A 3 AAAAAAAAAAAA . . . r r r r r rirr r r - - '_ r. — - 3 333333373333333 3 3A A AAAA3 3 3 3 3AAAAAAUAAAAAAA . . r r r r r r r r r r r .

i r n . . AW 3 2\2Vf-«\ — fVAA *N 33333332 233333333 AA2VMN 3 A3 333333 TAAAAAAAAAAAAAAA . r r r r r r r r r r r r rs* AA A *4 — NAAAA 3 3 3 3 3 3AA 33 3 333 3 7 3A f\ AA A3 7AA A33 3 3A AAAAAAAAAAAA r r r r r r r r r r r r r r

_ AAA 23333333 3.T 33333333 . - AA 3 3AA3 3 AAAAAAAAAAAAAA r r r r r r r r I* r r r r r r . AAAA'\ 2 .3.2 2A AAA3332 333333 3 3 23333 r3N2V2NJN 3 3A3 A 3 3AAAAAAAAAAAAA . r r r r r r r r r r r r r • • AAAA

.222 133222222 3AA33 3 33 3 3A <N (A3 333AA3 333 (N2\f\r,—T2\A3 3 3 3AA3 3 3AA AAAAAAAAAAA r r r r r r r r r r r r r r A A332333212223 3AA2 3 3 33:3 N A3 3 3 3 3A3 3 3 3 3 r\. . , W rvfv 3 3 3A3A3 3AA3 3AAAAAAAA A . r r r r r r r r r r r r r r r . — AAA

r r r r r r • r r r r r r r r r r • ■ *— rr rrrr

r r ■ ■ ■ r r r r r r r r r r r r r r

r r . r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r

• r r r r r r r r r r r r r r r ■ r r r r r r r r r r r r r r r r

A r r r r r r r r r r r r r r r r r a, r r r r r r r r r r r r r r r r r i-r r r r r r r r r r r r r r rrr r r r r r r r r r r r r r r r

. <*r ' . r r r r r r r r r r r . . r r r r r r r r r r r r r r . rr rrr r r r r r r r r r r r r

r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r . r r r r . r r r r r r r r r r r r . r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r . r r r r r r r r r r r r r r r r r . r r r r • r r r r r r r r r r r r

. r r r r r r r r r r r r

. r r r r r r r r r r r r r r r r r r r • rr«- r r r r r r r r r rr r r r r r r • (srrr r r r r r r r r rrrr

222322223223 22332233332122222 I 1232222232 <22322/ 22232)223322223223 2223221233222)3223 2223322232 I 12 23232 322331222)227.1 3221 2 : 2 1 2 3 323 ) 21 : 2112 2 2/222322222.* 222 122

A.T3AAAA1N 3 73333V333233 A <N33 3 3 3 3 3 .

3 A «N1N 3 3 33 3 3 32 3 <N2V 7(N(N AAA 3 7A 3 3 3 —

J n—rvr 3 f\2NA3 A (N>73 23 J TXrVtNj Ar»f\2N,-lN7 3 3 3 (A—<N2 2 2 vJArsrv/NArcsrs/SA A33 A ~

—<\3A2\2\rjNrs2\'N/VA3 3 3 3A/N2S —<\A AlNfvrrW A2 33 3 r\2N - .-VTV (NIMN A3 3 CNN

2AA ■. ■ . ~-C\rMNATv AAA <NTV:322232223322) 1 I2222A . ■ ■■ (NIN . 3(N337332321333223122) (NINT ——»f\rvrvfNr\<-rvAA3 3rs2*>

23 2222223321122)3 AA -e.<V\r — •»*t- AA <N22 \U 23 2 2 222 22 22 233 N, ................... . (MNAAA*(N1\ 23)1323221 1 2 A- - AAA•\fNC\t\ 1 2 2 2 3 3 2 2 \l\f\ 2«\f— fNw rVJNAA—<V —<xrrvfVtVJ 2 1 2 2 2 l«fV(\f\ - — - —(NfN, . . . — .3 Nf\lS f\•xIAVtv 3 3 2 3 2 Nl\ci\A. ■ ■ — — — p\jNJA- \r. — (N

3 2 13 \(\rvl* p.23 2 2 *Nr/\2\/\«*l\<-p—p—^3 2 \lNl\(VfVf\f\;-—.. — p. —#-p.P-f\r\p- AA * —

' 2 <“*N/SfM\nv —P..P - <NfN AA«4.p<fvr\^p.<\f\pp(N»p^^.p ■ I ippi. ■ f .fA V p/A A ^.

AAA 7 7AA7AAAAAAA AAA IN A7AAA A 3AAAAAAAAA . . r r r r r r r r r

(M»> (Nf\AA AA 3AA AAAAAAAAAAA . r r r r r r r mIN p\a a 7AAAA 77AAAAAAAAAAAAAA r r rrrr rr /* / p-r f AA AA 3 TAAAAAAAAAAAAAAA r r r r r r r r r r rs CAAA3 3AAAATAAAAAAAAAA r r r r r r r r r rr\ _<v AAAT TAAAAA* A AAAAAAAA r r r r r r r m

Nxv.- AAA33AAAAAA3A<-. AaAAAa r r r r r r r r r / f . r . A 3 TAAAAAAAAAAAAAAA ^ rrr rrrr r

AA 3 AAAAAAAAAAAAq AA . . r r r r r r r r r NiNf /mnAAaaaaAAAAAAAAaAAAA r r r r r r r r r r

N r\r\A AAA AAAAAAAAAAAAAA A «-rrrrrrrrr Np- «N aaaaaaaataaaaaAAAAa r r r r r r r r r r — p\ . AAAA IN AT3AAAAAAAAA r r r r r m rr ■..r. AA AT3N AT AAAAAAA r r r—«NT- «N/V A CVANAAT AAAAAAAA - rr ,• lAMN NIN rrA*;-AA 7 TA AAAAAAA - rn

— N2N p. /Np-r. «NAA3AAAAAAAA rr rr\r\ rrvp. . AAA AAAAAAAAAA r r r r

A rr rvAAAA AAAAAAAA r r r r<Nr\ ’*rv — iNAAAAAAAAAAAAr r r r r r r r r r r rA — '• pptv/nAAAaaaaaaa . r r r r r r r r r r r r. p. AAAAAAAAAAA r r r r r r r r r / rrp-.-r\ pp. <■. AAAAAAAAAA r r r r r r r r r r r«•«— IN/VA iNtSAUAAAAQAAAAA t-1-r m ' r r r r

.pp. —/\(Nr. AAAAAAAAAAAAAA r r r / r I r r mr^p-r A aaaaaaaaaAaAA r r t'r !• r I'r r r r rrp—r IN AAAAAAAAAA r r r r r r r r r r r ri. pppp iPpi p-r. —IN 2AAAAAAAAA r r r r r r r i ' r r r

p. - — — —IN AAAAAAAAA r r r r r r r r r r r.~~.r\AA « /\/pf\,-«p.rpAAAAAAA«*AAA r r r r r r r r r r r

" — AAA.." r* A AAAAAAAAAA r i r / r r r r r r •N/N AAA AA AAAA < i r r ( r r r— p. «V AAAr A A aAaA | ^ r r r r /'r /■

•Kl nil «I llltllilK AN A(.1I(AC.<1<2 a'lAAAAA

• r r r r r r r r

r r r r r r r r r r r r r

r r r r r r r r r r r r r r r r

r r r r r r r r r r

r r r r r r r r r

09

61

FIGURE 18. FINAL YELLOWSTONE PARK CLASSIFICATION MAPSECTION 2

62

FIGURE 19. FINAL YELLOWSTONE PARK CLASSIFICATION MAPSE C T IO N S

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r» »»T>T> T*T*T»V»%J f 1* •T«T> TST* • -

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t*>p •T»t» T»fr'»*T*T»WT»T»t»t»»»T»»*T*t»T» ' ' \ f

T*1>WBT»WT»W»WT» • ▼>tV •

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^T»rr*»T>T>T»WW»^T>T»l»TH>T>T»T»T>t*W»*»T> »T»r>T>T»T»T»T<r>TymVT>*>t» T«*T»flST»T*T*>*t» t T»T»T>T»T>T» *VIW*T»T»T*TI**V, "

TyT»T>T>T>tyT> ^r>T>T»T>f T>T*T>T>T>»*T>*>'t>T»^T»T>T>T»T>T* t »»»>T>T»r»T»T>T»T»t>r.*ïT»T>T»T>»* - *»*yT»Tyr>T» »»T»T»T>rf»TrT>T>nr*'*>T»T>’Y'j>» t '>

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FIGURE 22. FINAL YELLOWSTONE PARK CLASSIFICATION MAP

SECTION 6

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V.

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fJOOxrO -> •XJxlvrV»X>\JXjXjX»Nf'»x»X»SJXfXt\fv»Nrsj'JNfx»v>\r\ixixr'>* KiM \jsrxrxi\f*JMx»s.

c r / f c t »\»\r\rNj\»\J\iNi\jo\j>js»\js«s/'*\jx»>j\f>jM\r t 1 1 f r\r\»\r\f\f\*wi\)xr\fxr\f\i\.*xixfW\,xr\» rxjxiv.r t r c f c r * r- \rs/x»v'ixjxi'j\j\* i\j\«v\rx*\jxr\r»fv

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67

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FIGURE 24 . FINAL YELLOWSTONE PARK CLASSIFICATION MAPSECTION 8

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CHAPTER V

CONCLUSIONS

F e a tu re e x t r a c t io n can be in te r p r e te d as being an e x te n s io n to

photography. Photography i s capab le o f p re se n tin g p a t te rn s in c o lo rs

o r v a r io u s shad ings fo r in te r p r e ta t io n by an o b se rv e r , bu t o f te n enough

th e re a re some f e a tu r e s which appear s im i la r , bu t a re n o t , and v ic e

v e r s a . Computer f e a tu r e e x t r a c t io n adds th e c a p a b i l i ty to d is t in g u is h

s u b t le d if f e r e n c e s in m u lt ip le d i g i t a l d a ta images and to make a d e c is io n

concern ing th e s im i la r i ty o f th o se f e a tu r e s in q u e s tio n . This e x te n s io n

can be e x p lo ite d to i t s f u l l e s t l i m i t s , in some c a s e s , when a d a ta bank

can be used f o r a c tu a l i d e n t i f i c a t i o n o f th e f e a tu r e s .

The purpose o f t h i s work was to dem onstra te th e c a p a b i l i ty of

e x t r a c t in g f e a tu r e s from d i g i t a l d a ta images w ith o u t in v o lv in g an

o b se rv e r in th e d a ta p ro c e ss in g loop and to compress unmanageable

amounts o f d a ta in to manageable and u s e fu l in fo rm a tio n . An o b se rv e r

would s t i l l be needed to i n t e r p r e t th e r e s u l t s .

The su ccess of th e d a ta com pression i s s ig n i f i c a n t in th a t 12

channels of d a ta were com pressed in to 1 and th a t 200,022 re s o lu t io n

e lem ents were reduced to a maximum of 45 d i s t i n c t c a te g o r ie s .

The com puter programs p re se n te d in t h i s work were p u rpose ly

developed to be as g e n e ra l as p o s s ib le , and th e u lt im a te su ccess o f

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73

th e se computer program s f o r in fo rm a tio n e x t r a c t io n can on ly be

determ ined when th e program s a re t a i l o r e d and a p p lie d to so lv in g a

s p e c i f i c u se r o r u s e r ag e n c y 's n eed s . The p re s e n t u t i l i z a t i o n o f th e se

program s fo r f e a tu r e su rv e y in g , such as th e v e g e ta t io n and g e o lo g ic a l

c a te g o r iz a t io n s p re se n te d in th e t e x t , can be in te r p r e te d as be ing

s u c c e s s fu l s in c e th e com parison o f r e s u l t s w ith th o se p re v io u s ly

p u b lish e d in th e l i s t o f re fe re n c e s appears v ery fa v o ra b le .

The two keys to su ccess in u s in g th e u n su p erv ised fe a tu re

e x t r a c t io n program a re th e p ro d u c tio n o f a boundary map which c le a n ly

s e p a ra te s homogeneous a re a s belo n g in g to d i f f e r e n t f e a tu r e s and th e

ch o ice o f th e d e c is io n r u le fo r s p e c t r a l ly m erging s im i la r f e a tu r e s .

The over abundance o f b o u n d arie s in th e Y ellow stone d a ta in d ic a te s

th e need fo r improvement in th e m a th em atica l d e f in i t i o n o f a boundary o r

a t l e a s t a means f o r im proving th e th re sh o ld u s in g th e p re se n t boundary

d e f in i t i o n . I f r e p e t i t i v e coverage were a v a i la b le fo r a p a r t i c u la r t e s t

s i t e , th e optimum th re s h o ld fo r a boundary d e c is io n cou ld p robab ly be

de term ined . O th erw ise , th e e x p e rien ce gained from w orking w ith o th e r

ty p e s o f d a ta s e t s o r from p e ru s in g th e l i t e r a t u r e would have to p rov id e

th e im petus fo r d e te rm in in g a b e t t e r m athem atical d e f in i t i o n o f a

boundary. The two m ost im p o rtan t p ro p e r t ie s th a t need to be ta k en in to

c o n s id e ra tio n f o r t h i s d e f in i t i o n a re most p robab ly th e r e s o lu t io n and

some m easure o f roughness in th e p i c t o r i a l scene o f th e d i g i t a l d a ta

im age.

The use o f a p x p a r ra y fo r o b ta in in g i n i t i a l c l u s t e r s t a t i s t i c s

in a homogeneous a re a may have an advantage over th e manual s e le c t io n of

t r a in in g a re a s in th a t th e c l u s t e r a re a s can have a f a i r l y a r b i t r a r y

74

shape r a th e r th an be ing r e c ta n g u la r and th e d a ta s e le c te d from th e se

a re a s does n o t c o n ta in unusual d a ta p o in ts w hich could b ia s th e s t a t i s t i c a l

c a lc u la t io n s . The u se o f th e p x p a r ra y does have th e d e f in i t e

advantage th a t i t i s f a s t e r th an m anually s e le c t in g th e c o o rd in a te s of

th e t r a in in g a re a and e n te r in g th e se c o o rd in a te s in to th e com puter.

The use o f an e l l i p t i c a l d e c is io n r u le f o r merging and c l a s s i f i

c a t io n appears to be very a c c e p ta b le as ev idenced by th e f a c t th a t

p r a c t i c a l ly a l l o f th e r e s o lu t io n elem ents used fo r c a lc u la t in g th e

s t a t i s t i c s o f a f e a tu r e a re c l a s s i f i e d as be long ing to th a t f e a tu r e .

This f a c t i s even e v id e n t when s e v e ra l i n i t i a l c lu s te r s have been

merged to g e th e r to form a f i n a l c l a s s . A d d itio n a l su p p o rtin g ev idence

to t h i s co n c lu sio n i s th a t the i n i t i a l c l u s t e r s s e le c te d on th e second

pass th rough th e d a ta d id no t merge w ith any o f th e f i n a l c la s s e s

o b ta in ed from th e f i r s t pass through th e d a ta , and an alm ost u n n o tic e a b le

amount o f r e s o lu t io n elem ents had t h e i r o r ig in a l c l a s s i f i c a t i o n changed.

Most of th e e r r o r in c l a s s i f i c a t i o n occurs n e a r boundaries and n e a r th e

edges o f th e scan l i n e s . The f i r s t type o f e r r o r i s p robab ly due to th e

d a ta changing from one f e a tu re to an o th e r in th e v i c in i t y of a boundary

and in th e p ro cess p a ss in g through a d e c is io n re g io n of a t h i r d d i f f e r e n t

f e a tu r e . The m is c la s s i f ic a t io n n ea r th e edge of th e d a ta i s due to an

o p t i c a l e f f e c t c a l le d scan ang le e r r o r . The ang le a t which th e ground

scene i s viewed a t th e edge of a scan i s u s u a lly 30 to 40 d eg rees o f f

from th e lo c a l v e r t i c a l and, as a consequence, th e s ig n a l th a t i s

reco rd ed by th e sen so r r e f l e c t s an an g u la r dependence. I t i s re a so n a b le

to assume, how ever, t h a t th e u se o f an e l l i p t i c a l d e c is io n r u le could

ta k e in to accoun t th e an g u la r dependence. The an g u la r e f f e c t shou ld be

75

approx im ate ly l i n e a r dependent f o r th e d i f f e r e n t channels o f d a ta and

t h i s would amount to a le n g th s t r e tc h in g of th e p r in c ip a l axes o f th e

c l a s s i f i c a t i o n e l l i p s e s . I t i s apparen t th a t th e c l a s s i f i c a t i o n maps

p robab ly c o n ta in more d e ta i le d in fo rm atio n th an i s a c tu a l ly d e s ir e d . The

amount o f d e ta i le d in fo rm atio n p re se n t can be f u r th e r compressed by

v is u a l i n t e r p r e ta t io n and m anually merging th e d e s ire d f e a tu re s by

changing th e symbol o u tp u t on th e c l a s s i f i c a t i o n map.

When th e f e a tu r e s a re m anually m erged, c au tio n must be e x e rc ise d

in in te r p r e t in g a g iven f e a tu r e e x tra c te d from th e d a ta . For exam ple,

th e re a re s e v e ra l f e a tu r e s which re p re s e n t soy , co rn , and a m ix tu re of

corn and soy. A lthough th e re i s a te m p ta tio n to a t ta c h a s im ple

d e s c r ip t io n th a t i s commonly u sed , th e d e s c r ip t io n may be incom plete

w ith re s p e c t to th e in fo rm a tio n p re se n te d by th e d a ta and a lo g ic a l

manual m erging may n o t be p o s s ib le . D e ta ile d ground t r u t h would be

needed to p ro v id e th e q u a l i f ic a t io n s and a d je c t iv e s fo r a com plete

d e s c r ip t io n . For t h i s rea so n , i t may be im portan t to perform th e d a ta

a n a ly s is p r io r to p re ju d g in g th e in fo rm a tio n co n ten t o f th e d a ta r a th e r

th an u s in g th e ground t r u t h to a s s i s t in th e a n a ly s is of th e d a ta .

F in a l ly , i t m ust be em phasized th a t th e development o f th e

unsuperv ised f e a tu r e e x tra c t io n computer programs was d ir e c te d toward

o b ta in in g a com puter lo g ic th a t could e x t r a c t in fo rm a tio n from rem otely

sensed d a ta w ith a m oderate degree o f su c c e s s , which meant th a t computer

runn ing tim e n e c e s s a r i ly took a back s e a t . S ince th e developm ent work

has been com pleted , e f f o r t s can now be d ir e c te d toward o p tim iz in g th e

computer tim e and e f f ic ie n c y of th e program s.

BIBLIOGRAPHY

1. Lueder, D. R, A e r ia l P ho tog raph ic I n t e r p r e t a t i o n . New York:McGraw H i l l Book Company, I n c . , 1959.

2. Thompson, M. M. (E d i to r ) . Manual o f Photogram m etry. F a l l s Church,V irg in ia : American S o c ie ty of Photogram m etry, 1966.

3. Jen sen , N. O p tic a l and P ho tog raph ic R econnaissance System s.New York: John W iley and Sons, I n c . , 1968.

4 . Detchmendy, D. M., and P ace , W. H. "A Model fo r S p e c tra l S ig n a tu reV a r ia b i l i t y ." TRW IOC 4913 .7-71-193.

5 . E p p le r , W. G ., Helmke, C. A ., and Evans, R. H. "T able Look-UpApproach to P a t te rn R e c o g n itio n ." P ro c . Seventh I n t . Sym. on Remote Sensing o f th e Environm ent, 1971.

6. Remote M u lt is p e c tr a l Sensing in A g r ic u l tu re . Purdue U n iv e rs ityR esearch B u lle t in No. 844, 1968 and No. 873, 1970.

7. B auer, M. E . , Swain, P .H ., e t a l . "D e tec tio n of S outhern CornLeaf B lig h t by Remote Sensing T ech n iq u es ." P ro c . Seventh I n t .Sym. on Remote Sensing o f th e Environm ent, 1971.

8 . H o ffe r , R. M ., and G oodrich, F. E. " V a r ia tio n s in A utom aticC la s s i f i c a t io n over Extended Remote Sensing T est S i t e s . "P roc. Seventh I n t . Sym. on Remote Sensing of th e Environm ent, 1971.

9 . A nuta, P. E . , K r is to f , S. J . , e t a l . "C rop, S o il and G eo lo g ica lMapping from D ig it iz e d M u lt is p e c tr a l S a t e l l i t e P ho to g rap h y ." P roc. Seventh I n t . Sym. on Remote S ensing o f th e E nvironm ent, 1971.

10. S to n e r, E. R . , and H orvath , E. H. "The E f fe c t o f C u ltu ra l P ra c t ic e son M u ltis p e c tr a l Response from S u rface S o i l . " P roc . Seventh I n t . Sym. on Remote Sensing o f th e Environm ent, 1971.

11. Smedes, H. W., Lennerud, H. J . , e t a l . " D ig i ta l Computer Mappingby C lu s te r in g Techniques Using C olor F ilm as a T hree Band S e n so r." P roc. Seventh I n t . Sym. on Remote Sensing o f th e Env i r onment, 1971.

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12. Smedes, H. W., S pencer, M. M ., and Thomson, F. J . "P re p ro cessin gof M u lt is p e c tr a l D ata and S im u la tion o f ERTS D ata Channels to Map Computer T e r ra in Maps o f a Y ellow stone N a tio n a l Park T est S i t e . " P ro c . Seventh I n t . Sym. on Remote Sensing o f th e Environm ent, 1971.

13. Bond, A. D, D asara th y , B. V ., and A tk inson , R. J . "F ea tu reS e le c tio n and Superv ised N on-Param etric C la s s i f i c a t io n A pplied to E arth R esources M u lt is p e c tr a l Scanner D a ta ." NASA C o n tra c to r R ep o rt, C on trac t NAS8-21805, 1971.

14. Wacker, A. C ., and Landgrebe, D. A. "B oundaries in M u lt is p e c tr a lImagery by C lu s te r in g ." IEEE Symposium on A daptive P ro c e sse s , 1970.

15. R oth, C. B . , and Baumgardner, M. F. " C o rre la t io n S tu d ie s w ithGround T ru th and M u lt is p e c tr a l D ata: E f fe c t o f S ize ofT ra in in g F ie ld ." P ro c . Seventh I n t . Sym. on Remote Sensing o f Environm ent, 1971.

16. B endat, J . S . , and P ie r s o l , A. G. Measurement and A n alysis o fRandom D a ta . New York: John W iley and Sons, I n c . , 1966.

17. Remote Sensing o f E a rth R esou rces, A L i te r a tu r e Survey w ith In d e x e s .NASA SP-7036, 1970.

18. Nagy, G ., S h e lto n , G ., and T o laba , J . "P ro ced u ra l Q uestions inS ig n a tu re A n a ly s is ." P roc . Seventh I n t . Sym. on Remote Sensing o f th e Environm ent, 1971.

19. Nagy, G ., and T o laba, J . "N onsupervised Crop C la s s i f ic a t io nthrough A irborne M u lt is p e c tr a l O b se rv a tio n s ." IBM J . Res.D ev., 1971.

20. A yres, F. M a tr ic e s . New York; Schaum P u b lish in g C o ., 1962.

21 K en d a ll, M. G ., and S tu a r t , A. The Advanced Theory o f S t a t i s t i c s ,Vol. 3. New York: H afner P u b lish in g C o ., 1966.

22. S ebestyen , G. S. D ecision-M aking P ro cesses in P a t te rn R e co g n itio n .New York; The M acm illan C o., 1962.

23. K eeping, E. S. In tro d u c t io n to S t a t i s t i c a l In fe re n c e . P r in c e to n ,New J e rs e y : D. Van N ostrand C o ., I n c . , 1962.

24. P h i l l i p s , M. R. " C o rre la t io n S ig n a tu re s o f Wet S o ils and Snows."IIT R esearch I n s t i t u t e F in a l Report J6243 -6 , NASA C on trac t NAS8-26797, 1972.

APPENDIX A

PROGRAM DESCRIPTION

The computer program s which u t i l i z e th e eq u a tio n s in th e t e x t a re

w r i t t e n in th e form of su b ro u tin e s and have been in c lu d ed as an in t e g r a l

p a r t o f a much la rg e r com puter program c a l le d an E a rth R esources

P ro c e sso r . This p ro c e sso r c o n ta in s s e v e ra l p re p ro c e s s in g and d a ta

d is p la y ro u tin e s in a d d i t io n to th e c l a s s i f i c a t i o n program s and i s

documented and flow c h a r te d in d e t a i l in th e f i n a l r e p o r t o f c o n tra c t

NAS8-26797 by IIT R esearch I n s t i t u t e , 10 West 35 th S t r e e t , C hicago,24

I l l i n o i s . Hence, on ly a b r i e f d e s c r ip t io n o f th e s e su b ro u tin e s w i l l

be g iv en . A sm all e x e c u tiv e program can be w r i t t e n f o r c o n t ro l l in g th e

sequence of c a l l in g th e se s u b ro u tin e s by fo llo w in g th e lo g ic flow

p re v io u s ly d e sc rib e d in F ig u re 2 and d isc u sse d in C hapter I I I o f th e

t e x t .

S u b ro u tin e BWNDR3

S u b ro u tin e BWNDR3 i s th e f i r s t s ta g e o f p ro c e s s in g o r th e

boundary program and re a d s th e raw d a ta ta p e as in p u t . This su b ro u tin e

c o n ta in s E quations (8) th ro u g n (16) in th e t e x t and th e lo g ic f o r u s in g

th e s e e q u a tio n s . The boundary program a lso c o n ta in s two s u b ro u tin e s

which w i l l be d is c u s se d . S u b ro u tin e GET6 i s used f o r g e t t in g th e d a ta

o f f d i g i t a l ta p e and p u t t in g i t in to th e com puter. The c o n te n t o f t h i s

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su b ro u tin e has to be s p e c ia l iz e d to th e ty p e o f d i g i t a l ta p e form at

d e s ir e d . S u b ro u tin e JNTPB i s a j o i n t p r o b a b i l i ty d i s t r i b u t io n program ,

which w i l l be d isc u sse d n e x t .

S u b ro u tin e JNTPB

S ubrou tine JNTPB i s used f o r c a lc u la t in g th e j o i n t p r o b a b i l i ty

d i s t r i b u t io n o f s v e rsu s s in E quation (8) and th e d e c is io n r u le X y

as^ + bSy + c s^ s^ _< 1 , E quation (1 6 ). This program has a f ix e d s to ra g e

a l lo c a t io n , b u t th e shape of th e j o i n t d i s t r i b u t io n can be com plete ly

a r b i t r a r y because a se a rc h mode o f o p e ra tio n i s used r a th e r th an a ta b le

look-up p ro ced u re . This program w i l l a cc ep t d a ta o f any dynamic range

and o u tp u t a s c a t t e r d iagram bounded by th e minimum and maximum v a lu e s

o f th e d a ta . T his program c o n ta in s th re e su b ro u tin e s . S ub rou tine

DJCOBI i s an IBM l ib r a r y system su b ro u tin e fo r c a lc u la t in g th e e ig en

v a lu e s and e ig e n v e c to rs used in th e e l l i p s e e q u a tio n . S ub rou tine

LABELS i s used fo r la b e l in g th e axes o f th e s c a t t e r d iagram , w h ile

su b ro u tin e PLTBF6 i s s p e c ia l iz e d fo r use w ith th e S trom berg-C arlson 4020

p e r ip h e ra l equipment to o b ta in m icro film co p ies of th e boundary map.

S u b ro u tin e JNTPB a lso o u tp u ts th e boundary ta p e fo r u se in th e second

s ta g e o f p ro c e ss in g .

S u b ro u tin e CLASFY

S ubrou tine CLASFY c o n ta in s th e second, th i r d and fo u r th s ta g e s of

p ro c e ss in g v ia su b ro u tin e s TRUCK, SEQMRG, and CLASS, r e s p e c t iv e ly .

S u b ro u tin e CLASFY a ls o c o n tro ls th e number o f c l a s s i f i c a t i o n p asse s

d e s ire d and th e s iz e o f th e p x p c lu s t e r s e le c t io n a r ra y v ia s u b ro u tin e

TRUCK.

80

S u b ro u tin e TRUCK

The second s ta g e o f p ro cess in g i s su b ro u tin e TRUCK, which re a d s th e

boundary map ta p e as in p u t d a ta and lo c a te s th e homogeneous a re a s th a t

a re la rg e enough to c o n ta in a p x p a r r a y . T his su b ro u tin e a ls o

perform s th e s p a t i a l merging when two d i f f e r e n t c lu s te r s run to g e th e r .

The o u tp u t o f t h i s su b ro u tin e i s a boundary map ta p e c o n ta in in g th e

lo c a t io n o f th e i n i t i a l c l u s t e r s , which i s in p u t to th e th i r d s ta g e of

p ro c e s s in g . S u b rou tines LABELÀ and PLTBFA a re used fo r la b e lin g scan

and column numbers and o b ta in in g m ic ro film , r e s p e c t iv e ly , fo r th e v is u a l

d is p la y o f th e map o b ta in ed from su b ro u tin e TRUCK.

S ubrou tine SEQMRG

The th i r d s ta g e o f p ro cess in g i s su b ro u tin e SEQMRG and uses th e

boundary and c lu s te r lo c a tio n ta p e and th e raw d a ta ta p e as in p u t . The

boundary and c lu s t e r ta p s i s used to lo c a te and fe tc h raw d a ta belong ing

to each c l u s t e r . S t a t i s t i c s u t i l i z i n g E quations (17) through (30) a re

th en c a lc u la te d fo r each c lu s t e r and used fo r d ec id in g w hether to

s p e c t r a l ly merge c l u s t e r s . The c lu s t e r s a re read in s e q u e n t ia l ly , and

each new c lu s t e r has th e o p p o rtu n ity o f merging w ith any o r s e v e ra l of

th e p rev io u s c l u s t e r s . S u b rou tine SKRBIN i s an IBM system su b ro u tin e

and a llow s fo r sk ip p in g b in a ry re c o rd s on th e m agnetic ta p e . This

r o u t in e i s p r im a r ily used w ith th e c lu s t e r s e le c t io n s in c e th e c lu s te r s

may be lo c a te d anywhere on th e ta p e . S ub rou tine FETCOR i s used to f e tc h ,

c a lc u la te th e c e n tro id of each c lu s t e r and to c a lc u la te th e c ro ss channel

c o r r e la t io n s fo r each c l u s t e r . The means a re s u b tra c te d from th e

c o r r e la t io n s to form a co v arian ce m a tr ix in su b ro u tin e AMTRX, which

becomes an in p u t to th e e ig en v a lu e and e ig en v ec to r su b ro u tin e DJCOBI.

81

S ubrou tine ROTA i s a r o ta t io n m a trix c a lc u la t io n used to r o t a t e a

f e a tu r e v e c to r in to th e c o o rd in a te system o f a c l u s t e r . S ub rou tine

KCHECK i s used to check w hether th e c e n tro id s o f two c lu s te r s f a l l

w ith in each o th e r 's e l l ip s e s o r merge. I f two c lu s te r s w i l l merge,

th e s t a t i s t i c s of b o th c lu s t e r s a re combined and updated . The o u tp u t

o f SEQMRG i s a ta p e c o n ta in in g th e s t a t i s t i c s fo r th e f i n a l s e t of

c l a s s e s .

S ubrou tine FETCOR

In a d d itio n to fe tc h in g and c o r r e la t in g th e raw d a ta fo r each

c l u s t e r , su b ro u tin e FETCOR keeps t r a c k o f th e s t a r t i n g and sto p p in g

scan l in e s and columns o f th e c lu s te r s t h a t a re in th e com puter. This

in fo rm a tio n i s used w ith th e su b ro u tin e BSRECD, which i s an IBM system

l ib r a r y su b ro u tin e f o r back spacing re c o rd s . The u se o f t h i s su b ro u tin e

allow s f o r back spacing th e ta p e to f in d th e d a ta f o r th e n ex t c l u s t e r ,

r a th e r than rew inding th e e n t i r e ta p e and sea rch in g f o r th e n ex t

c l u s t e r 's d a ta .

S ub rou tine CLASS

The fo u r th s ta g e of p ro cess in g i s su b ro u tin e CLASS and u ses th e

ta p e c o n ta in in g th e s t a t i s t i c s fo r each c l a s s , th e boundary ta p e and

th e raw d a ta tape as in p u t . T his su b ro u tin e m ainly c o n ta in s E quation (31)

and th e p ro v is io n s f o r o u tp u t tin g th e c l a s s i f i c a t i o n map on s tan d a rd

computer p r in to u t o r m ic ro film . The c l a s s i f i c a t i o n map i s a lso ou tp u t

on tap e f o r use in su b ro u tin e CLASFY to o b ta in a d d i t io n a l c lu s te r s and

c l a s s i f i c a t i o n p a sse s .

APPENDIX B COMPUTER PROGRAM LISTINGS

SL'o ROU T T N f BV/NnR^r i j M F N S l O N X ( 1 2 » 2 5 6 ) » Y ( 1 ? » 2 5 6 ) » Mr H A N ( 1 2 ) »NN{ 2 5 6 ) » KS YM ( 4 9 ) , JSYM (

1 2 ^ 6 )n i ^^FNSI ON N W H I C H d ? )Na Mf L i S T / l N P U T 6 / N S r A N S > N 5 T A R T » N s P S » N C H » i ' J \ / A R » N S Y M , I S U M , N R T L G »

i M O D E f I T Y P F f M S F C » , N . 6 K I P , N B L K , I N C X » I N C Y , N S T X , N F T Y , N C R F N A M F L l S T / N C H ' J S F / N W M T r H F QU T V A L p Nc p ( N S r A N , N S r f t N S ) f Q U I V a L f Nt f ( N 5 T R T , N S T a RT) f Q U I V A L F N T F ( M r O L » N S P S )PQIJTVALFNCF ( NF HA N . N C H)I f A R n = 6 I P R I N T = 6 ï M T A P F = 1 0 Î 0 T A P F = 1 1R f a h C i r A R n , T N P l J T 6 )WRt T c ( t P R i N T » T N P U T 6 )R F A n ( i C A R n » N r H U S F )W R T T F ( l P R l N T , N r H U S F 1

1 F O R M A T ( I X , 7 1 4 )? f o r m a t ( I X , 12 11 )

rfao( rrARn,5 ) (.<syM( t ) , r = i , nsyM)6 F O R M A T ( 1 X , 6 0 A 1 )

MFLAG=0AV^=T5L!MA P O P = 0 , 0n x A V F = o , nD Y A V F z O . nD7 A V ' ^ = 0 , nN f a V=N!SCANI F ( N S K I P , F Q , 0) GO TO 9pn o 0 7 1 = 1 , N S K I PFALL S K R P I N ! T N T A P f , 1 , N OP )

0 7 C O N T I N U E OR C O N T I N UE

2 F O R MA T (1 HI )4 F0RMAT(5X,1I1II)

11 = 1K K = N 0 T R T - I

1 6 0 I F ( I I . f Q . N S F A N ) CO TO 510 1 1 = 1 1 + 1 NFLAC2=1 KK=KK+1! F ( I I . N F . 2 ) CO TO 9 0 0 0 0 1 7 0 J J = 1 , N C 0 Lc a l l g e t 6 ( X ( 1 , J J ) ,.n c o l , o , n c h a n , n s c a n o , i n t a p f , i e R R , n f l a g 2 , n s t R t ,

1 N p T L C , M O O F , N c R ' ^ , I T Y P F , M S F C )170 CONTINU"::9 0 0 C O M T I N U f

N F L A C 2 = 1no 0 0 0 J J = 1 , N C 0 Lc a l l G F T 6 ( Y ( 1 , J J ) , N r 0 L , 0 , N cH A N , N 5 C A N 0 , I i \ T A P r $ 1 F R R , N F L A C 2 , N S T R T ,

1 NPTLG,MOnF,NcRF,TTyPF,MSFC)'POO CON T I N UE

DO PRO J J = ? , N C O L

82

83

I J = J J - 1 X<i iM = 0 . 0 YC,I !M = 0 . 0 Z S U M c O . Ono 3 6 0 I C H A N = 1 , I S U M I r r H N = N W H I C H ( r C H A N )Xr , TFF = Y( T I CHN , J J )*-Y ( T ICHN , I J )Y n T F F = Y ( T I C H N , J J ) - X ( I I C H N , J J )XF!JM = XS!JM-} -Xni Fc: *xnTFF Y S U M = Y 5 U M + Y D T F F * Y n T F F ZSUM = Z 5 U . M + X n i F F * Y D T F F

3 6 0 r O N T T N U FX S U M = X S U M / A V Fy s u m = y s u m / a v e

Z S U M = Z S U M / A V F A P 0 P = A P 0 P + 1 . 0 a a = i . o / a p o pp p = 1 , 0 - A An X A V r = R q # n X AV'^ + A A^ YSUM OYAVF = R R * n Y A \ / F + A A^XSUM n Z A V R = P R * n Z A V F + A A * Z S U M XS U M ^ S Q R T ( X S U M )I F (XSUM , L T . F 3 . 4 ) GO TO 3 6 5

364 X.S'.IM = F 3 , 0 YFIJV! = F 3 , 0 GO TO 3 6 6

36 3 r O N T T N U FY S U M = S Q R T ( Y5UM)I F ( YSUY . L T . 3 3 . 4 ) GO TO 3 6 6 GO TO 3 6 4

3 6 6 C O N T I N U FCALL J N T P B ( YSUM, XSUM »Nf L AG »0 , 0 , K S Y M ( p ) , N P O P ,

? n X A V F , n Y A V F »P O Z A V F ,I J J , N S c a N , i I , N r O L » J S Y M , X , N 5 T R T » N N , i N r X )

n s c a n = n s a v

PRO C O N T I N U EDO 5 0 0 J J = 1 , N C 0 L DO 4 P 0 I C H A N = I » I S U M I i r H N = N W H T C H ( K H A N )X ( T I C H N , J J ) = Y ( I I C H M , J J )

4 0 0 C O N T I N U F 5 00 C O N T I N U E

GO TO 1 6 0 5 1 0 c o n t i n u e

NFLAG=1CALL J N T P B ( Y S U M , X S U M , N F L A G » 0 , 0 , K S Y M ( 3 ) , iM P 0 P ,

■?d x a v f , d y a v f ,P D 7 A V F ,1 J J , N S C A M , I I » N r O L » J S Y M , X , N 5 T R T » N N , l N c X )

REWI ND I O T A P R REWI ND I NTAP' ^

: CALL c l e a n

RETURN END

84S U P R O U T i N F L A B F L ^ , ( N S T A R T , N S T O P , r N c R F D T M F N S I O N I O U T ( 1 ? 0 )N n i F = ( N S T O P - N S T A R T + 1 ) / T N c R f T 1=0n o 1 r = N S T A R T » N S T O P , i N r R F IT = 11+1.I 0 U T ( T I ) = I / I 0 0 0

1 C O N T I N U FW R j T f ( 6 , 1 0 ) { r O U K T ) , 1 = 1 , N 0 T F )I 1 = 0DO ? I = N 5 T A R T » N S T 0 P , I N C R F IT=11+1I 0 U T ( T T ; = T / l O O - l / i n o o * i O

? C O N T I N U FWRt T f ( 6 , 1 0 ) ( T O U T ( I ) , I = 1 , N D I F )I 1 = 0DO B i = n s t a r t , n s t o p , i n c R f IT=IT+1T O l J T ( i n = I / l O - T / i n o * 1 0

? C O N T I N U FWRt T p ( 6 , 1 0 ) ( T O U T ( I ) , 1 = 1 , N D I F )I 1 = 0DO 4 I = N S T a R T , N S T O P , I N C R F I 1 = 1 T + 1l O U T d I ) = I - I / 1 0*1 0 I F ( l O U T ( I T ) , L F . 0 ) I 0 U T ( I I ) = 0

4 C O N T I N U FWR T T F ( 6 , 1 0 ) ( T0 U T ( I ) , 1 = 1 , N d I F )

10 f o r m a t ( 1 1 X , 1 ? 0 n )RFTURNF N n

85SUp RO U T t N f J N T P p ( n A T A H » n A T . â V » N F L A G » M î X » ' ' 1 r Y » A L P N n M , N P 0 P ,

?D X A V F * O Y A V P »P D Z A V F .T J J , N S C A N , l S r A N , N c O L , I S y M , N X , N 5 T R T » N N , l N C X Y )

OTMFNSr ON I . N r X Y d )DT^^PNSION NP{ >^A»F4) n y MF NSr ON D A T A ( 1 ? ) n T MF N S I O N T P I M ( ? 5 F )O l M F N S r O N I S Y M ( 1 ) , T O U l K 1 0 0 ) n i M F N S I O N N X ( 1 ) » N N ( 1 )DTMFNSr ON ALPNUM{ 1 ) , ALP h A ( T Z O ) , c O R n X ( 3 ) nOURLF P R E C I S I O N A ( ? . Z ) » F I G F M ( 2 » Z )I N T F G F R A L P N U M , A L P H A , PLANK DATA A S T R I K / 1 H * /DATA X M A R K / I H X /DATA R L A N K / 6 H /DATA N F L A G 4 / Q /

1 0 6 0 F 0 R M A T ( 4 8 X , ? 5 H D A T A SWI TCH HAS OCCURRED )1 0 6 1 F 0 R M A T ( 4 9 X , 3 0 H J 0 T N T PROr a R I L I T Y O I S T R I R U T I O N )1 0 6 ? F O R M A T d H l )1 0 6 3 f ORMa T ( 4 4 X , 1 1 h X - A X T S I S » T 6 » 6 X , l l H Y ' A X I S I S » 2 l 6 )1 0 6 6 f o r m a t ( 3 0 X » 6 H D X A V = ^ = » r l 5 , 7 » 6 H D Y A V F = , F l 5 , 7 , 6 H D Z A V P = » F l 5 , 7 )1 0 4 0 FORMAT! I H »67H MAXI MUM PROr a p I Î - T T Y Of f jNrOMMON a L I TY P X r F F D F n - r ONT

I I N U E F X r U T l O N , 2 1 6 )1 0 6 4 F O R M A T ! i x , 2 6 h SYMr OL N / S Y M r OL )1 0 6 5 f ORMa T ! 1 1 X , 1 2 1 ! 1 m * ) , / , 1 1 X , 1 h * , 5 5 X , 5 h P a RT , H , 4 H Of , 1 1 , 5 3 X , I H * , /

1 , T1X ,1?1 ! I H* ) )I F ! N F L A G 4 . G T , 0 ) GO TO 8 0 N F L G p =0

1 0 0 0 FORMAT ! I X , 4 7 A I )NFLGr ON I = ?I RW=1m r l g f n = o

I R T = l 1 n o 1 1=1 , 5 4 no 1 J = i , 5 4N P ! I , J ) =0

1 CON T I N UE r e w i n d I R TREWI ND IRW NFLAG4=1

8 0 c o n t i n u eI F I N F L A G . G T , 0 ) GO t o 13N G r D A T A V + l . 5NR = DATAH + T . 5I F ! NC . L T . 1 ) NC=1I F INR . L T . 1 ), NR = 1N P ! N R , N C ) = N P ! N R , N C ) + II = 5 4 * ! N C - 1 ) + N RI P I N ! J J ) = II F ! J J . L T . NCOL) GO TO 15 I P T M ! 1 ) = I R I N ! ? )WRt T p ! I R W ) ! I P T N ! I n , I 1 = 1 , N r O L )

15 CON T I N UE

8 6

R F T U R N I T C O N T I N U F I 7 C O N T I N U F

R F W I N D I R W I 0 P T = 1

I N = R IM = 7Rh O = 1 , 0 / ( 1 0 . 0 * * F >4 ( 1 , 1 ) = n X A V F

A ( ? , ? ) = n Y A V F A (1 » ? ) =nZAVF A ( ? » 1 ) = n Z A V FCALL n J r O R I ( A » T M , T N , I O P T , R h O , F R R » ' ^ I G F N )

C W R l T r ( 6 » l 0 6 7 ) A ( 1 ,1 ) » A ( 1 » 2 ) , I GFM ( 1 , 1 ) , F IGcN ( 1 , 7 )C WRt T f ( 6 » T C 6 7 ) a (2»1 ) » A ( 2 , 2 ) , f t f f N ( ? » 1 ) , F I G f N ( 2 , ? )

1 0 6 7 FORMAT ( l X » 2 > ^ l 5 , 7 , i n x » 2 F l 5 . 7 ) nXAVF=1. , n / A ( 1 »T ) n Y A V F = l , n / A ( 2 , 2 )A ( 1 , 1 ) = F T G P N ( 1 , l ) * n X A V F A ( 1 , 2 >=P^TGFN( 2 , l ) * n X A V F A ( 7 , 1 ) = F i G c N ( 1 , 7 ) * n Y A V F

A ( 7 , 7 ) = r i G F N ( 2 , 2 ) * n Y A V FnXAVF = FTr,FN (1 »1 ) * A ( V 1 ) -i-FTG<^N(1 »2 ) * A ( 2 , 1 )OY A VF = F I GFN ( ? ♦ I ) * A ( 1 .. 7 ) +e IGFM ( 2 » 2 ) A ( 2 , 2 )nZAVF = F I GFN ( 1 »1 ) * A ( 1 » 2 ) + F I G F N ( l » 2 ) * A ( 2 , 2 ) + F i G = ' N ( 2 , l y * A ( l » l )

1 + F T G F N ( 2 » 2 ) * A ( ? , 1 )W R t T f ( 6 , 1 0 6 6 i n X A V F , 0 Y A V F » n Z A V F 1=0n o i o n N c = i , 6 4DO 1 TO NR = I , 6 4 Î = 1 + 1I F ( N P ( N R , N r ) , F 0 . 0 ) GO TO I TO XXX=MR* NRy y y = n c * n c

Z Z Z = N R * . N C

G U M = n X A V F * X X X + n Y A V F * Y Y Y 1 + D 7 A V F * Z Z Z

I F ( S U M , G F . 1 . 0 ) G 0 t o 1 16 N X ( I 1=0 G O T O 1 6 0

1 1 6 N X ( I 1 = - l1 6 0 C O N T I N U F

WRiTF ( 6 , 1 0 6 ? 1 WRTTF ( 6 , 1 0 6 1 )W R l T p { 6 , l 066 1 n X A V F , D Y A V F , n Z A V F W R I T F ( 6 , 1 0 6 4 )

C CALCi i LATF TAPLFm a x k n t = o

DO 2 2 N C = 1 , 6 T DO 22 N R = 1 , 6 TI F ( M P ( N R , N C ) . G T . MAX<NT) M A X K N T = N P ( N R , N C )

22 C O N T I N U FI F ( MaXKNT . L T . 4 6 ) ,YaXKNT = 46 , N F A C T = M A X K N T / 4 6

X X X = F L O a T ( M A X K N T ) / 4 A . 0

87

NFAC=0I F ( NF ACr . L T . 1) MFACT=1 W R T T F ( 6 * 1 0 5 0 ) P L a N < , N F A C NFAC=NFAr +NFACT00 1 = 1 , 4 6W R T T r ( 6 , l 0 5 0 ) ALPNI IM ( T ) »NFAC

1 0 5 0 f o r m a t ( 5 X , A 6 , 6 X , I 6 )N F A r = N F A r + N F A r i

99 CONTINUFWR T T r ( 6 , 1 O A ? )

: P R I NT D I S T R I R U T I O M ON PAGFr O R D X { 1 ) = 0 , 0 r O R O X ( 7 ) = r O R O X ( l ) + 6 0 . 0 r O R o x ( 5 ) = r O R o x { 1 ) + 1 1 0 , 0

1 0 9 1 f o r m a t ( 1 h i )

n o I F Mn = 1 , 5 4M r = 5 5 - i F N nn o 6 6 1 = 1 , 5 4 A L P H A ( I ) = R L A N K

6 6 C O N T I N U FI F ( NF L G . F Q , 1 ) GO TO 6 0 DO 65 1 = 1 , 5 4

T r t N { I ) = n 6 5 C O N T I N U F69 COMTINUF

n o 64 N R = 1 , 5 4XX = F L 0 A T ( N P ( N R , N C ) )I F (NFLG . F Q . 1 ) GO TO 911 P I N ( N R ) = N P ( N R , N C )

91 CONTINUFI C A R = X X + ( 1 . 0 0 1 - 1 . n / X X X )I F ( I CAR . G T , 46 ) TCAR=46 A L P H A ( N R ) =AL PNUW( I C A R )

64 COMTINUF CORDY=FLOAT(NC)YMARG=XMARKI F (NC . N F . 5 4 - I F N n / l 0 * 1 0 ) YMa R G = A S T R i K . W R l T F ( 6 , l 0 0 8 ) r O R O Y , Y M A R G , ( A L P H A ( I ) , I = 1 , 5 4 )

10 08 f ORMa T ( 1 X , F 8 . 1 , 2 X , A 1 , l ? O A l )65 C O N T I N U F

W R l T F ( 6 , 1 O l 0 )W R t T f ( 6 , l O l l ) r 0 R 0 X ( 1 ) , r O R n X ( 2 ) , c O R n X ( 3 )

1011 f o r m a t ( 6 X , F 1 0 . 4 , 5 0 X , F 1 0 . 4 , 4 0 X , F 1 0 . 4 )NFLG=1V'RI TF ( 6 , 1 06 2 )N5l , iR=lLK'FR=iLOW=NSTRT

70 5 CONTINUFNh I = L 0 W + 1 2 0 - 1N I J P P F R = L W F R + 1 2 0 - 1I F (NUPPFR . G T . NCOL) NUPPFR=NCOLW R I T F ( 6 , 1 0 6 2 )CALL L A P F L 6 ( L O W , N h I ,1 ) no 191 1 1 = N l , N S r A N

8 8

R F A D ( I R W ) ( T R î N( J J ) « J J ^ l » NC0 I . )DO 1R5 J J = 1 » N C 0 L r r H F C K = I P I N ( J J )J C H E C K = N X ( I C H F C K )TF ( J C H F C K . N F . 0 ) GO TO 1 1 7 I S Y M ( J J ) = A L P N U M ( N S U R - 1 )N N ( J J ) = 0 GO TO 1 RR

11 7 I S Y M ( J J ) = A L P N U M ( N S I J R )N N ( J J ) = —1

1 RR C O N T I N U FI F ( NF L GF N . N F . 0 ) GO TO 1R6 W R I T F ( I R T ) ( N N ( J J ) , J J = i , N C O L )c a l l P L T p F 6 ( l S Y M , N r O L , N R L K , T N c X Y ( l ) » l N r X Y ( ? ) » l N r X Y ( R ) ,

1 i N r X Y ( A ) »NCR'=')I R A C O N T I N U F

WRt T c { 6 > 1 Ü R 6 ) 11 » ( T S Y M ( J J ) ♦ J J = LWPR»N U P P F R )1 0 3 6 FORMa T ( 5 X » T 6 , 1 2 0 a 1 ) l ORR F 0 RMa T ( 1 X » I 6 )1 3 1 C O N T I N U F

NFLGFN=1r e w i n d IRWLWFR=NUPPFR+1L 0 W = N H I + 1I F ( NUPPFR . L T . NCOL) GO TO TOR

9 9 5 CON T I N UEl O l 0 format ( 1 1 X, 1 2 ( 1 O H X *********))

NF LGF Nr ORFTURNEND

CM

X H- m I/;

_I > - yj

(\l O'_ 1 X - I.

<-i z

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90SU o.ROUT î Np T R U r K { N r r N T » N P A S S )D I M E N S I O N N N A O r f 1 2 , 2 5 6 ) , M T A P ( 1 1 ) , I P R T ( 2 5 6 ) , I P L O T ( 2 5 6 )D I M E N S I O N N T P L ( 4 0 0 )rOMMON / L A P 1 / X o a R ( 4 P * 1 2 ) »S TT-Ma ( 43 » I 2 ) , RÜT( 4 3 » 12, » 12 ) rOMMON / L A 0 2 / X ( 1 2 ) , N S Y M ( 4 9 ) , N S P S , N S r ANS , N f H a N , l't 9 , L T I D , LT 11 , L t 12 ,

1 L T 1 3 , L T 1 , I X X X , T Y Y Y , i N S T A R T . N S T O P ,I N n J L G . M O D F » U Y P F , M S ^ C » 14 , N c R E »I N S K I P , l N r X , l N c Y , N S r X » N S T Y

N F L G X X= 0 N F L A G X = 0 REWI ND L T l l R p y i N D L I T N F L A G i =0 M EI N=0I X T Y = I X X X * I Y Y Y DO 10 1 = 1 , l Y Y Y MTAP f I ) = I

10 C O N T I N U EDO 50 1 = 1 , 4 0 0 NTRL( I ) =I

50 C O N T I N U FPO 11 1 = 1 , l Y Y YR F & D ( L T l l ) ( MN a c C ( t , J J ) » J J = 1 » N S P S ) m E T N = M F I M + 1

11 C O N T I N U ENl jP = N S P S - I X X X + 1n c n t = n c c m t + iNFLAG=0

?0 0 CONTINUFT T t = M T A P ( 1 )DO 1 1 0 J J = 1 , N S P SI F ( J J . G T . NUP) r o TO 10?I J = J JJ I = J J + I X X X - 1 N7FR0=n I K N T = n I FI !Mr?0 J l J r M T A P ( 1 )MTFMP= NCCNT+1 DO 1 Ol T = U , J I DO 1 0 0 J I J = 1 , I Y Y Y I I J = M T A R ( J I J )I F ( N N A C C d l J , ! ) . L E . MCCNT . A N D . NNACC( 11 J , I ) . N E . 0 ) GO TO 1^ 2 TF ( N N A F r ( T i J , n ) 1 0 2 , 1 0 7 , 1 0 6

1 0 6 I F ( N N A C C ( I I J , n . r - T . NT^^MP) NT'^MP = NNArC ( I I J , I )GO TO 1 0 0

1 0 7 n z f r o = m z e r o + i

1 0 0 C O N T I N UE1 0 1 c o n t i n u e

I F ( NZERO . N F . I X T Y ) GO TO 1 0 5 DO 1 03. 1 = 1 J , J I DO 1 0 4 J I J = 1 , I Y Y Y NNACF( J U * î ) = N r N T

1 0 4 CONTINUF

91

1 0 ? r O N T l N U PN r N T = N C N T + li r ( N r N T , G T , 4 OO) GO TO Q9Q GO TO 11 0

i n ' ; CONTI NUEDO 10? ! = I J , J I n o 10? J T j = l , l Y Y YI F ( N N A C C ( J I J » n . F O . 0 ) N N A C C C J I J » I ) = N T f m P

10? CONTI NUE GO TO n o

10? CONT I NUE n o CON T I N UE

no 111 J J = 1 , M S P 5n ( J J , f Q , NSPS ) r O TO 111I F ( N N A C C n I F ( M N A C C d I F ( N N A C C ( I I F ( N N A C C I I I F ( M N A C C d i J ^ N N A C C ( I I J I = N N a C C ( I I

I > J J ) . L E . ■ NCCNT ) GO TO H I I » J J + n . L F , NCCNT) GO TO 1 11 T , J J ) . L F . 0 ) GO TO 1.1 1 I »JJ + 1 ) . L F . 0) GO TO i n I » J J ) . F Q . N N A C C ( 1 1 1 » J J + 1 ) ) GO TO 1 1 1 » J J )» J J +1 )

I F ( JT . r n . 4 0 0 . O R . I J . G T . 4 0 0 ) r-0 TO 111 I F ( N T A L f J l ) . G T . N T F L ( T J ) ) 0 0 TO 1?? N T n L ( î J ) = N T n L ( J î )GO TO 111

1?F CONTI NUFN T 9 L ( J I ) = N T r L d j )

111 CONT I NUE 100-7 f o r m a t ( 1 X , I G )

V ' R t T f ( L T i ) ( N N A C r ( n i » J J ) , J J = 1 »N.SPS)1 F (VF I N . G F , NSfam. F) r,0 TO 0 9 9 lYT =iVTAq ( 1 )R c A D l L T l l ) ( N N A C C ( T Y I , J J ) »J J = 1 » N 5 P 5 )v f t N = m f I N + 1

N T F M P r M T A B ( 1 )I Y Y = I Y Y Y - 1 no 1 ? 1 1 = 1 , l Y Y Mt.aB ( I ) =MT Aq ( T + 1 )

m C ON T I N UFV T A F ( I Y Y Y ) c N T ^ v p GO TO ? 0 0

9 9 0 CONTI NUEno 1 ?? 1 = 2 » I Y Y YI I i =NTAB ( I )n o 1 1 ? J J = 1 , NSPFIF ( J J . r Q , NSPS ) r o TO 1 1 ?I F (MM ACC ( I I F ( M N A C C d I F (NNACC ( I

T » J J ) . L F . N r C MT ) GO TO 11?I , J J + 1 ) . L F , N C C N T ) GO TO 11?I »J J ) . I F . 0 ) GO TO 11 ?I , J J + 1 ) . L E . 0 ) GO TO 1 1.2 I , J J ) . F Q . N N A C C ( I I I » J J + 1 ) ) GO TO 1 1 2 » J J ), J J + 1 )

I F ( J I . F T . 4 0 0 . O R , I J . G T . 4 0 0 ) FQ TO 1 1 2 IF ( N T q L ( J I ) .FT. N T % L ( I J ) ) GO TO 1 2 6

I F ( N N A C C ( I I F ( M N A C C d I J = NNACC( I I J I = N N A C C ( I I

92iMTnL( î J ) = N T r L ( JT )GO T O . 11?

1 ?6 CONT I NUEN T B L C J I ) = N T B L ( T J )

1 1 ? CON T I N UEW R i T F ( L T i ) ( N N a c c ( I T I » J J ) »JJ = 1 »NSPS)

1?? c o n t i n u eFNn F I L F L T 1 RFWI ND L T l REWi Nn L T l l R F V I N O L T I ?W R l T r ( 6 , l 0 0 7 ) ( N T o L ( I ) , 1 = 1 , 4 0 0 ) no 1 1 1 1 = 1 , 4 0 0IF ( N T R L ( I ) . F Q . I ) no TO 11?J I = ! + 1I -^ ( N T P L ( J I ) . N E . I ) r o TO 1 1 4 N T R L ( J I ) = N T R L ( I )

1 1 4 CON T I N UE 11 ? CON T I N UE

11 = 1MTEMP = I !no 1 1 6 I = ? , 4 0 0I F ( N T r L ( I ) - N T d L ( T - 1 ) ) 1 1 7 , 1 I E , 1 19

1 1 9 I F ( M T R L ( T ) . N F . I ) GO TO 1 1 7N T R L ( I - l ) = n t e m p I 1 = 1 I + i N T F M P = I I GO TO 1 1 6

1 1 q NTRL ( I - l ) =NTF;yp GO TO 1 1 6

1 1 7 N = N T f L ( I )N T o L ( I - l ) =NTFMP M T F M P = N T P L { N )

1 1 6 c o n t i n u e

N T R L ( 4 0 0 ) = NTFMPW R I T f ( 6 , 1 0 0 7 ) ( N T r L ( I ) , 1 = 1 , 4 0 0 )L ''I F R = 1 LOV' = N S T A R T

7 0 F FONT I NUEN!.iP P f R=LWf R + i ? 0 - i Nh t = L O w + i ? 0 - iI E ( NUPPFR . G T . N5PS ) NUPPFR=NSPSl n i E = N U P P F R - L W F R + iW R I T E ( 6 , 1 3 3 5 )

1 0 0 5 F O R MA T (1 H I )CALL L A R F L A ( L O W , N h I , 1 )no 7 1 0 1 1 = 1 , N SC A N 6Rf a n ( L T l ) ( N N A F G ( 1 , J J ) , J J = 1 , N S P S )no 1 1 5 J J = 1 , N S P SI R = N N A C C ( 1 » J J )I F ( I R .LF. 0 ) GO TO 115 N N A C C ( 1 »J J ) = N T R L ( I R )

1 1 5 C O N T I N U FI F ( NELGXX . G T . 0 ) GO TO 1 ?7 WRt T f ( L T l ? ) (NNACC ( 1 , J J ) , J J = l ,N.SP.5)

93

1 P 7 rOMTI . MUF J I = 0DO 7 1 1 J J = L WHR » N UP P F R JT = J I + 1M = NiMACC ( 1 » J J ) - ( i MNAr r ( i , J J ) - i ) / 4 K * 4 % + ? J P R T ( J J ) = : N S Y M ( M )I P L O T ( J ! ) = N S Y M ( N )

711 r OMT T NUPW R t T f ( 6 » 1 0G3 ) T I ♦ ( t P R K J J ) , J J = LWFR »NI JPPfR )CALL P L I R F A ( I P L O T , I D I F » N r L K , T N C X » I N c Y , M S T X , N S T Y ,

1 N C R F » N F L A G X , N F L A G 1 )1 0 0 3 F O R M A T ( 4 X , 1 6 , 1 H * , 1 ? 0 A 1 )7 1 0 C O N T I N U F

RF' - ' IND L T l NPLAC-X = C Np LGXX=1 N P L A G 1 = 0l w f r = m u p p f r + iL 0 W = N H I + 1I F ( NUP PF R . L T . NSPS ) GO TO 7 0 5

5 7 0 C O N T I N U Fn c c n t = n c n t - iFNn F I L P L T l ?Rp WI ND L T l ?REWI ND L T l I X X X = I X X X - 4 I Y Y Y = I Y Y Y - 4 L T l 1 = 1 3r f t u r n

^ND

94SUr ROü T i N t S F O M R n ( N r L U S T , K O U N T , r N î T C L )rOMMON / L û r 1 / X o 4 R ( 4 3 » 1 2 ) » S I F M A ( 4 3 , 1 2 ) , R 0 T ( 4 3 , 1 2 , 1 2 )rOMMON / L A R 2 / X ( 1 2 ) , a L P h A ' 4 9 ) , N S P S »N SC A NS, Nc H A N , L T 9 , L T l 0 , L T 11 »L T 12 »

I L T 1 3 , L T 1 , I X X X , I Y Y Y ,1 N S T A R T , N S T 0 P ,1 N r T L G » M 0 d F » I T Y P r »MSf C » I 4 , N c RE»I N S K I P , I N C X » I N C Y » N S T X » N S T Y

nOURLF P R F C I S I O N A ( 1 2 » 1 2 ) » F î R F N ( 1 2 » 1 2 )OTMFNSTON M F R n r f Z n n ) , M P 0 P ( 2 0 0 ) » N r X F r ( 2 0 ) » C ( 4 3 » 7 8 ) » F ( 1 2 * 1 2 ) n i M F M S i O N C 0 V ( ? 4 )F O ' J î V â L F N r F ( r O M ( 1 ) , N S P S )

1 0 0 0 r 0 R V a T ( 1 X , i 6 » 1 2 F 1 0 ^ t )1 0 0 1 f o r m a t ( 1 X , 4 h XRAR )1 0 0 2 f o r m a t ( I X » 1 6 H D Î 0 NOT r ONVFRO )1 0 0 3 f o r m a t ( 1 X »7Hr ( "L l JST= , J6 » 1 4MMFRr,c ( 7 r L ! 1ST J = , 7 6 )1 0 0 4 FORMAT ( 1 X , 5 h RmO= , 1 5 . 7 , 5 hi ^RR= , f 1 5 , 7 )1 0 0 3 FORMAT ( l X , T ? c i n , A ,1 0 0 6 F O R MA T ( I X , 1 2 T S )1 0 0 7 FORMAT ( 1 X , 23HVFROT A'O W I L L TA<F PLACE )TGÜB F O R MA T (1 H )1 0 0 9 f o r m a t ( 1 3 H r o v e Ma t r i x )1 0 1 0 f o r m a t ( 1 2 H NORM r i c R N )1 0 1 1 f o r m a t ( i r h p . A . r o v . M a t r i x )1 0 1 2 f O R M a T ( 1 h , 6 haSUM= , r i 5 . 7 , 7 H r L U S T r p , 7 4 )1 0 1 3 f o r m a t ( 1 X , 2 8 M X n A R (7 , J ) , J=1 , 1 2 ) , T = 1»KOUNT )1 0 1 4 FORMAT ( 1X , 2 9mS T6M, a ( 7 , J ) , J = 1 , 1 2 ) , T = 1 , K 0 U N T )1 0 1 5 FORMAT ( 1 X , 5 5 h ROT ( I , î CM AN , J C m a N ) , JCH AN = 1 , 1 2 ) » I CM AN = 1 , 1 2 ) , I = 1 , KOI 'NT

1 ) )

1 0 1 6 f o r m a t ( I X , 1 6 , ( 1 2 ^ 1 0 . 3 ) )N F LG = 0r Z F C H = F L O A T ( N om A N ) - 2 . 0 R F U I MO L T I O R F ^ I N O L T 1 9 Rm O = i , 0 / ( 1 0 . 0 * * 3 )] F ( M S K I P » F O . 0 ) r-0 TO 60 0 7 1 = 1 , N S K J PCALL S < R f T N ( L T i O , 1 , N O P )

7 C O N T I N U F6 C O N T I N U F

0 0 3 I C L U S T = 1 , N C L I J f t v,crRr,r( i c L U S T ) = i r L U S T

3 CONTI NU' ^1 ^ ^ N r H A N I N = I M I 0 P T = 10 0 10 I C L U S T = I N I T C L , N C L U S T I F ( N f L O , C T . 0 ) GO TO 11 I F (KOUNT . C F . 4 3 ) GO TO nk o m n t = k o i .i n t + iI FLAC- =K0UMT ■CALL F F T C O R ( T F L A G , C , MROP, Nf l G , I N î TCL ' )WR I T f ( 6 , 1 0 0 1 )W R i T f ( 6 , 1 ü ü O ) I FLAC- , ( X7AR( 7 f l a g , ! ) , 1 = 1 , 1 2 )Ml =1 MJ = 1?

95VK = 1 ? n o 500W R T T F ( 6 , l 0 0 0 ) TFLAO» ( r ( I F L A r , , M R ) , MR= Mt , M J )

5 0 0 C O N T I N U FCALL AMTRX ( I F L A G * X R A R , C » A , N C H A N ) w R t T P ( 6 » 1 0 0 8 )V R T T p ( 6 » i O O o )WRt T p ( 6 » 1 0 0 5 ) ( { A(MT » M J ) » M J = 1 » 1 2 ) »MI = 1 , 1 2 )CALL n J C O R I ( A , I M , T N , l O P T , R u O , F R R , r i G F N ) WRt T f ( 6 » 1 . 0 0 4 ) Rh O » f RRW R T l F ( 6 » l t - 0 5 ) ( ( a ( M T , M J ) »MJ = 1 » 1 2 ) , ^ 1 = 1 , 1 2 ) H R I T F ( 6 , I 0 0 8 )W R T T r ( 6 , l 0 0 5 ) ( ( F T F f N ( v T , M J ) , MJ = 1 , 1 . 2 ) , M l = l , 1 2 ) I F ( cRR . F Q . 0 . 0 ) CO TO 15 M r R c r ( t c L U S T ) = 0k o i j n t = k o u n t - i v R t T F ( 6 , 1 0 0 ? )CO TO 10

15 C O N T I N U FCALL ROTA ( I FL AG , RO T , F I CRN , MCH AN , A , S I CiV A )Mf r g f ( I C L U S T ) =KOl )NTyRT Tc ( 6 ,T 0 0 ) TCLUFT , M r R c c ( | r L U . 5 T )MPOP ( < OUNT ) =v i POP( I C L U S T )I F ( KOUNT , F 0 . 1 ) CO TO 10M C L U S T = K 0 U N T - 1no 2 0 I CHF CK = 1 , 2 0N F X f c ( I C H C T K ) = 0

2 0 C O N T I N U E MCHFCK=1n o 25 J C L U S T =:1 ,NCL! 1STTf ( V c r g p ( j c l u S T ) . L T . M C H f ^ C K l c O TO 25’'■Vm f c K = MCHFCK + iTc ( V F R G c-( J F L U S T ) . r Q . KOUNT) GO TO 2 6 J ^ L AG = N f RG=’ ( JCLUST ) n o 80 ICHAN = 1 ,NCHANX ( T C H A N ) = X R A R ( J F L A C , I c h a n ) - X 8 A R ( K O U N T , I CHAN)

-70 C O N T I N UETr LAG=KOUNTc a l l K C H F C K ( I F L A C , R 0 T , X , S I C M A , A S U M , M C H A N )'■'R T TF ( 5 , 1 OOr )WR T T< ( 6 , 1 01 2 ) a S U M , J F L A CI F ( A S J V . G T . c Z f c h ) CO TO 2 5I F L A C = J F L A GCALL K C H ^ c K l I F L A G , R O T , X , S I GMA , ASUM, NCHAN)HR I T F ( 6 , 1 0 0 8 )H R l T F ( 6 ,1 01.7 ) A S U M , J F L A G TC (ASUM . C T . C Z ^ C H ) CO TO 25 N E X F c ( 1 ) = N F X r C ( 1 ) +1 N. f i i p = NFXFC ( 1 ) + 1

N f x f c ( N S U R ) = J F L A G 2 5 C O N T I N U F2 6 I F ( N r X F Ç ( i ) . F Q . 0 ) GO TO 10

no 501 KK=l , N5UR

96W R t T p ( 6 >1 0 0 6 ) K K , N f x F C ( K K )

501 CONTI NUEM S U P = N F X F C ( 1 )+1 TO T A L = MP O P ( KOUNT)OO 31 I R U N = 2 » M S U R N S U P = N F X F C ( TRUN)SUM=v!POP(NSUB)T 0 T A L = T 0 T A L + S U M

31 C O N T I N UF INl ' MsOH F M - V P O P ( K O U M T ) no '3 3 I c h AN = 1. »NCMANX ( I C H A N ) = X R A R ( K O U N T , I C H A N ) * O P N / T O T A L no 4 0 J CH A N = I C H A N , N C H A N I N U M r l N t j y + ln { T t h a n , J C H A N ) = C ( KOUNT, I N U M ) * 0 F N / T O T A L

40 CONTI NUE 33 CONTI NUE

no 4= I RUN=?, M. SUR N S U R = N F X F C ( T R U N )I NUM= 0n P N r W P O P ( N S U P ) no 50 I C H A N = 1 , N C H A NX ( TCHAN) =X { I C H A . N ) + X ' ^ A R ( N S U n , T C H A N ) * n r M / T O T A Lno 33 J C H A N = i r u A N , N r H A NI NUy= l N i . J M+ lP f I C H A N , J C H A N ) = R ( I C " A N , J C H A N ) + C ( N S U B , I N U V ) * n F N / T O T A L

5 5 C O N T I N UF 50 CONT I NUE 45 CONTI NUE

no 6 0 I CHAN = 1 , NCHAN no 65 JCHAN = ICHAN ,NOHAMA ( ! C H A N , J C H A N ) = R ( i r H A N , J C H A N ) - X ( T C H A N ) * X ( J C H A N )A ( JCHAN , TCHAN ) = A ( T ri - i / \N, JCHAN )

65 CON T I N UF 60 CONTI NUE

W R T T F ( 6 , l 0 0 q )W R l T F ( 6 , l 0 0 5 | ( ( A ( W T , M J ) , M J = ! , 1 ? ) , H l = l , l ? ;CALL n J C C P I ( A , l M , l M , l O P T , R H O , E R R , n i G F N )W R I T E ( 6 , 1 0 0 4 ) R H O , c p RWR T T f ( 6 , 1 0 0 3 ) ( ( A ( M T , y j ) , MJ= 1 ,1. 2 ) » y I = 1 ,1- 2 )H R I T F ( 6 , 1 O O B )WRTTF ( 6 , 1 0 0 5 ) ( ( t ^ i r r N ( Mi , M J 1 , MJ = 1 , 1 2 ) , M I = 1 , 1 2 )I E ( cRR . N F . 0 , 0 ) r-O TO 10 W R I T E ( 6 , 1 0 0 7 )I E L A G = N f X F C ( 2 )M P O P ( I E L A G ) = T O T A LI NUMr Ono 70 l C H A N = i , N C H A NX R A R ( T ELAG, ICHAN ) = X ( i r u A N )nn 75 JCHAA'= I F maai ,MFHAMI N U M= I N U M + 1C( I E L A G , I N U M ) = P ( I C H A N , J C H A N )

7 5 CONTI NUE 70 CONTI NUE

97C A L L R O T A ( I F L A G » R O T » !^T G E N , N f H AN » A » S I G M A )D O R O j c l u s t = i , n c l u ? t

D O R F I R U N = ? , M 5 U R N S U R = N R X F C ( I R U N )I F ( M F R G F ( J C L U S T ) . N F . N S U R ) GO T O 8 5 M F R G F ( J C L U S T ) = I F L A G

8 5 C O N T I N U E 8 0 C O N T I N U E

m e r g e ( I C L U S T ) = T f l a g I F ( N F X F C ( 1 ) . F Q . T ) G 0 T O 9 4 I S W = 0 J C H F C K = ID O 9 0 J C L U S T = 1 , N C L U 5 T I O U M s M E R G F ( J C L U S T )

9 1 I F ( M f R G E ( J C L U S T ) . L T . J C H E C K ) C O T O 9 0 I F ( M f R G F ( J C L U S T ) . r - T . J r H F C K ) c O T O 9 2 T F ( I S W . f Q . T ) G 0 t o n ?J r M F r K = J r H F C K + T T F ( J C H F C K . F 0 . K 0 U N T ) ^ 0 TO 9 4G O T O 9 0

9 2 M F R G ^ I J C L U S T ) = M F R G f ( J c L U S T ) - ]I S W =1G O T O 9 1

9 3 I F ( J C H F C K . G T . K O U N T ) G O T C 9 4 I c w = nI N ! i M = 0

M P O P ( J C H F C K ) = M P O P ( T D U ^ n n o 9 9 T r H A N = l » N C H A NX B A R ( J C H E C K » I CHAN) = X B A R ( I D U M » I C H A N )S I G M A ( J C H E C K , I C H A N ) = S I G M A ( I D U M , I C H A N )

D O 1 0 0 J C H A N = I C H A N , M C H A Ni n i j h = i n u m + i

r ( J c h f c K » i N t j M ) = r ( t o u M , T NUM )

R O T ( J C H E C K , I C H A N , J C H A N ) = R O T ( I D U M , I C H A N , J C H A N )R O T ( J C H E C K , J C H A N , I C H A N ) = R O T ( I D U '.S J C H A N > I C H AM )

1 0 0 C O N T I N U E 9 5 C O N T I N U F

D O 9 6 L C L U S T = 1 , N C L U S TI F ( M F R G F ( L C L U S T ) . N f . i n U M ) G O T O 9 6

m e r g e ( L C L U S T ) = J C H E C K

Of , c o n t i n u e

J r H E C K = J C H ' ^ C K + 1

9 0 C O N T I N U E

9 4 K 0 U N T = K 0 U N T - N F X F C ( 1 )1 0 C O N T I N U E n C O N T I N U E

W R I T f ( L T 9 ) ( c 0 M ( T ) , 1 = 1 , ? 4 )W R t T f ( L T 9 ) ( { X d a R ( I , J ) , 1 = 1 , K O U N T ) , J = 1 , 1 2 )W R t T f ( L T o ) ( ( S t g M a ( T , J ) , 1 = 1 , K O U N T ) , J = 1 , 1 7 )W R l T r ( L T 9 ) ( ( ( R O T ( T , l C H A N , J f h a N ) , I = 1 , KOU N T ) , TCM A N= 1 , Nc h A N ) ,

1 JCHAN = 1 , NCHAN)W R l T c ( 6 , l O l 3 )D O 5 1 0 1 = 1 , K O U N TW R t T f ( 6 , 1 0 0 0 ) I , ( X p a R ( I , J ) , J = 1 , 1 2 )

5 1 0 C O N T I N U E

98W R T T F ( 6 , 1 n i 4 )0 0 5 n 1 = 1 , KOUNTW R î T r ( 6 , l O O O ) T , ( S T r,M A ( î , J ) , J = 1 , 1 2 )

511 r O N T l N U FW R t T f ( 6 , 1 Ù 1 5 )0 0 5 1 ? 1 = 1 , KOUNTWR T T f ( 6 , 1 J 1 6 ) I , ( ( ROT ( J , I CHAN , JCH AN ) , JCHAiN= 1 , 1 2 ) , I f h a N = 1 , 1 2 )

'^1? CON T I N UE0 0 5 1 ^ T = 1 , N C L U S TI F ( M f Rc f ( T ) , r . T , K O U N T ) r -0 TO 6 1 4WRt T f ( 6 , 5 1 F ) T , M F R C F ( T )

5 1 5 FORf /AT ( I X , 7 h c L U S T f r , t 4 , i x , 5 h C L a S S , T 4 )5 1 1 C O N T I N UF 5 1 4 CONT I NUE

0 0 6 6 0 1 = 1 , KOUNT 0 0 6 ? 0 I C H A N = 1 , N C H A N 0 0 6 1 0 J C H A N = l , N C H A NR ( I C H A N , J C H A M ) = R O T ( I , J C H A N , I C H A N ) / S I G M A ( I , I C H A N )

6 1 0 C O N T I N UF 6 7 0 CONT I NUE

0 0 6 5 0 i r H A N = l , NCHAN 0 0 6 4 0 K C H A N = 1 , N CH A N 61 iv = o , 00 0 6 1 0 JCHAN = 1 , NCHANS U M = S U M + R 0 T ( I , I C H A N , J C H A N ) * R ( J C H A N , K C H A N )

6 1 0 r O N T l N l l EA ( I C H A N , K C H A N ) = S U V

6 4 0 C O N T I N U F 6 5 0 r O N T l N U E

W R I T E ( 6 , 6 0 0 ) I 6 0 0 F O R M A T ! I X , 1 1 H C L A S 5 E L L I P S E , 1 6 )

W R t T e ( 6 , 1 0 0 5 ) ( ( A ( T A , J a ) , J a = 1 , N c h a N ) , t a = 1 , N c h a N )6 6 0 CONT I NUE

RF' - ' INO LTPr e t u r nEND

9 9

St i pROUTî Nc- F F T r O R ( T f L a G , C »NPOP j N f L p , N )

rOMMON / L A p 1 / X P 4 R ( 4 3 » 1 2 ) , S T f M a ( 4 3 , 1 2 ) , R 0 T ( 4 3 , 1 2 , 1 2 )COMMON / L a q 2 / X ( 1 2 ) , a L P h A ( 4 9 ) , N 5 P S , N S C A N S , N c H a N , L T 9 , L T 1 0 »L T 1 1 , L T 12 »

1 L T 1 3 , L T 1 , I X , I Y ,1 M C T A R T , N . 9 T 0 P ,1 N f T L C j M O f i F , T T Y P f , V c ; p c , T 4 » N c R f ,

i N S K î P , î N r X , T N C Y , N 5 T X , N S T Y « n i ^ F N S I O N N P O P d ) , r ( 4 3 » 7 P ) » M 0 A T { ? 3 F ) d a t a N C N T / 0 /ÎNI,IM = 0N F L G 1 = 0

N F L G P = 0DO 5 I C H A N = 1 , N r H A N

X q A R ( T A r , , T r M A N ) = 0 , 0 * nO 1 0 J CHAN= T C MA N » N r H A N

I NI . . ' M=I NUM + 1 C ( T F L A G , T N U M ) = 0 . 0

10 C O N T I N U F 5 C O N T I N U F

<NT = 04 0 C O N T I N U F

I F ( N C N T . G F . N S f a N F ) GO TO 7 0 N F L G ? = 0R F A n ( L T l 2 ) ( N n A T ( J J ) , J J = 1 , N S P S )n c n t = n c n t + i

N F L G I =1N F L A G ? = 10 0 2 0 J J = T , N G P qCALL G F T ( X ( 1 ) , N S P S , 0 , N c H A N , N S C A N G , L T 1 0 , t f R R , M p L A G 2 ,

l N S T A R T , N P T L G , ^ O O F , N r R F , T T Y P F , M S F C )I F ( N O A T ( J J ) . N F . N ) PO TO POK N T = K N T + TN F L G 2 = 1A I = F L 0 A T ( K N T )

I N ' j M = 0DO I CHAN = 1 , NCHANX p a R ( I F L A G , T C H A N ) = ( 1 . 0 - 1 . 0 / A T ) * X P A R ( î F L A G , I C H A N ) + X ( T C H A N ) / A TnO 2 6 JCHA.N = I CHAN , N f h a NI NI I M= I N! J M+ 1r ( t '^L AG, J N U Y ) = ( 1 . 0 - I . 0 / A I ) * C ( T F L A C , t NUM ) + X I î ^ r a N ) * X ( J t m a N ) / A î

2 6 C O N T I N U F2 5 C O N T I N U F

GO TO 2 0 3 0 C O N T I N U E '

I F ( N F L G P . F Q . T ) r O TO 20TF ( M D A T ( J J ) . N F . M + I ) GOTO 20N5AV= NCNT N F L G P = i

2 0 C O N T I N U FC WR I t f { 6 , 1 0 0 0 ) NcNT , KNT , N S A V , NpcKi j P , N , N f L g 2 , N f L g p

1 0 0 0 F O R M A T ! I X , 7 1 3 )I F . ( N F L G 2 . N F . 0 ) GO TO 4 0I F ( N F L G P . F Q . 0 ) r-0 TO 4 nN p r K U P = N r N T - N 5 A V + l r a l l p G R f c d ( L T 1 0 , N p c K U P * I 4 , R F )

1 0 0

S U R C O U T I M F A M T R X ( I F L A ^ , X R A R , r , A , M r w A N l n y V r N s i O N X r a R ( 4 T , 1 ? ) , r ( 4 ^ » 7, n )

nOl. iRLF P R E C I S I O N A ( i ? , i ? )INMMrOno 1 î ^ H A N = i , MrHaM no ? j r H A M = T r w A M , M r w A M I M ' J V = î M U M + 1A ( I C H A M , J C H A M ) = C ( I F L A G , 1 MUM) - X B A R ( I F L A G , I C H A M ) * X B A R ( I F L A G . J C H A M ) A ( JCHAN , I CHAN ) = A ( I r(JAN , J t h a V.)

? CONTI NU' "1 CON T I N UF

RFT' iRN PNn

S ' R 0 U T I M F R 0 T A ( I F L A G , R0 T , P I G1“ M , N C H A N , A , 5 î G'-1A 1ni MFNSl ON R 0 T ( 4 G , 1 R , 1 ? )n T ^ ^ NS l OM G Tg Ma ( 4 ? , 17 )nOlJRLP P R E C I S I O N A ( i ? , l ? )n'Mjn.i r pprrjGTn,v r t r,cN ( i ? , i 7 )no 1 I C H A N = I ,NrwANS I G M A ( I f l a g , I C H A M ) = A ( I CHAM, I CH A N ) n o ? J C H A N = 1 , NCHANROT ( I F L A r - , I CH AN , JCH AN 1 =F I r, r,M ( j r n AN , I C H A N )

? C ON T I N UF1 OONTI MHP

RF TURN FNn

S U R R O U T l N r Sr u r r K ( T F L A G , ROT » X » S IGM A , AS' JM , NCM AN )n i V F N S T O N ROT ( 4 ? , 1 , 1 ? ! , S Î GM A ( 4G , I ? ) , X ( I )A c i i M = n , nn o 7 i r w A N c T , N r H A N

= 1n o 4 JCH A N = I , M'-H AMS!JV = 5UM + R 0 T ( I f l a g , t o h a M , J C H a n ) * X ( J o H A N )C O N T I N U FASM M = A S U M + S 1J Ai * S U M / S T G M A ( I F L A G , I C ! J A M )r O M T I N U Fp r y u R Nc-Ajn

101S U n R O U T î N F f L A S S { N r L A S S » N T f S T j N P a SS 1 rOMMON / L A R 1 / X R A R ( 4 3 » 1 2 ) ♦ S T r,M a ( 43 , 1 2 ) , ROT ( 4 3 , 1 2 , 1 2 ) rOMMON / L A R 2 / X ( 1 2 ) , a L P h A ( 4 9 ) , N S P S , N S r A N S , N r H A N , L T 9 , L T l 0 , L T l 1 , L T 1 2 ,

1 L T 1 3 , L T 1 , I X . , N D U M M Y ,1 N S T A R T , N S T O P ,l N R T L 0 , M 0 n F , l T Y P P , M q F r , I 4 , N r R f ,1 N . S K I P , i N c X , I N C Y , N 5 T X , N S T Y

n î M R N S î O N W ( 1 2 ) , ^ T A P ( R )O I M R N S I O N N n A T ( 2 5 3 , P ) , P R N T ( 2 5 5 )HTWENSI ON C Q M ( 2 4 )F Q U î V A L P N r R ( C O M ( 1 ) , N S P S )REWI ND L T 9 RPWI ND L T l O RPWI ND L T l RPWI ND L T l 2 Re w i n d l t i 3r Z P r H = N r H A NI F ( N S K I P . P O . 0 ) GO TO 60%DO 6 0 2 I = l , N S K î P C AL L S K R R I N ( L T l O , l , N O P )

6 0 2 C O N T I N U ^601 CON T I N UF

Rp a d ( L T 9 ) ( p OM( I ) , t = 1 , 2 4 )Rp a D ( L T 9 ) ( ( X h a R ( r , J ) , I = l , N r L A S 5 ) , J = 1 , I 2 )RPAD ( L T 9 ) ' ( ( 6 i r -M A ( T , J ) , I =1 , N r L a SS ) , J = 1 , 1 2 )R P A D ( L T 9 ) ( ( ( R 0 T ( I , i r H A N , J r w A N ) , I = l , N r L A 5 5 ) , i r H A N = l , N r w A N ) ,

1 J r M AN = l , M r H A N )DO 1 1 = 1 , 3

1 ' n A R ( i ) = iDO 10 I F N D = 1 , N 5 C A N SRp a d ( L T 1 2 ) ( N d a T ( I ,1 ) , 1 = 1 , NSPS)N P L A G ? = iDO 20 I S U p N = i , NSPSr A L L G P T ( X ( 1 ) , N S P S , 0 , N r H A N , N S P A N O , L T I O , I p R R , N F L a G 2 ,

1 M 5 T A R T » N P T L G , M C n p , N P R F , T T Y P P , M S P C : )I P (NDAT ( l S ' . J o M , l ) . G T , 0 ) NRAT ( I SUpN , 1 ) =:-'!

SV A L L = 1 . 7 3 * C 7 - F p h DO 23 I G L A S S = 1 , N C L a f S nO 3 0 I p h a N = 1 , N r n A NW ( I C H A N ) = X ( I C H A N ) - X H A R ( I CLASS , I C H A N )

30 p QNTTNUF A.ci . tMsO.ODO 3 5 I C H A N = 1 , NCHAN Cl i Ms O. 0n o 4 0 JCHAN = l, , NCHANSUM=SUM+W( J c h A N ) * R 0 T ( Tp L a S S , I C H A N , J c H A N )

40 C O N T I N U F4 1 a S U M = a S U M + S U M * 5 U M / S T G M a ( i c L a S S , I C H a N)

35 CON T I N UPI F (ASUM . G T . S M A L L ) GO TO 2 5 s m a l l = a s u m

N d A T ( I S U R N , ! ) = I CLA,SS 25 CON T I N UF 1 0 1 6 p ORMa T ( 1 X , 3 1 6 » F 1 0 . 2 )2 0 C O N T I N U P

1 0 2

W R t T c ( L T I ) ( N n A T ( T , 1 ) » î = l »NSPS)10 r O N T l N U F

e n d F I L E L T IRe w i n d l t iREWI ND L T l ?REWI ND L T I O DO 6 1 0 I Z = 1 , N S C A N S I V = M T A R ( 1 )R p a d ( L T 1 ) ( N d a T { T A , t Y i , T A = 1 » N 5 P S ) N T c w P = Y T A n ( 1 )

M T A F ( 1 ) = X T A R ( ? )M T A P ( ? ) =MT A R ( R )v1 T A R { ^ ) = N T E M PTF ( TZ . L T . R ) GO TO 6 1 0n o 6 p O I A = N S T A R T . , N c t OPTF ( T A . P Q . 1 ) GO TO 6 ? 0TP ( J A + 1 . P - T . N S T O P l PC TO 6?DT I Y=v i TAn ( ? )TP ( NPASS . P Q . N T F S T ) GO TO 621 TP ( N D A T ( T A , T T Y ) . L T . 0 ) GO TO 6 2 0

621 C O N T I N U EIM=MTAR(1)I N = M T A R ( ? )M = N D A T ( T A » T M )N = M DA T ( T A - 1 , T N )TF . N P . N) GO Tn 6 p 0 I L = M T A R ( R )L = N D A T ( I A » I L )I F (Y . N F . L ) GO TO 6 5 0 N D A T ( I A , I I Y ) = M GO TO 6 2 0

6 p 0 T M = M T A P (1 )m = Npi aT ( T A - 1 , t Y)T N = M T A R ( R )N = NDA.T( I A - 1 , I N )I F ( ' " . N F . N) GO TO 6 ? 0 L = N D A T ( l A + l , I M )TR (M . N F . L ) GO TO 6 2 0 N n A T ( . I A , T I Y ) = M

6 ? 0 C O N T I N UEI P ( I Z . L T . R) r- 0 TO 6 1 0 L=WTAP( 1)WR T T p ( L T l 3 ) ( Nr a T ( T , L ) , I = 1 » N S P S )

6 1 0 C O N T I N U PDO 611 1 = 2 , R L = W T A R ( I )WRTTp C L T i R ) ( N r a T ( T L , L ) , I L = 1 , N S P S )

611 O O N T t NUF RP' - ' IND L T l REWI ND LTD RPWI ND L T i R REWI ND L T l 0l o w = n s t a r t

LWFR=1 POO C O N T I N U E

103Nh t = L O W + i 7 0 - 1 N U P P F R = L W P R + 1 ? 0 - iI P ( NUPPPR . G T . NSPS ) NUPPPR= NSPST n i F = N U P P F R - L W F R + lW R T T E ( 6 » 1 0 0 7 )

1 0 0 7 F O R M A i d H I )c a l l L A R F L A ( L O W , N H T , 1 )no SOI t t = i , n s c a n sR P A n ( L T T 7 ) ( N n A . T ( J J , 1 ) , J J = l , N S P S ) n o 8 0 3 J J = L W F R , M U P P p R T P s N n A T ( J J , 1 )T R N n = T R - ( i n - l ) / 4 F * 4 S + 2 P R M K J J ) = A L P H A ( l R N n )

8 0S C O N T I N UEf a l l P L T p f a ( P R N K L w p R ) , I n i F , N r L K , I N c X , I N c Y , N 3 T X , N S T Y , N r R F ,

1 i NPL ACX , N f L A G I )WR Tire ( 6 , 1 0 0 8 ) t T , ( P R N T ( J J ) , J J = L W P R , N U P P c R )

1 0 0 8 F O R M A T ( 4 X , I 6 , i H * , 1 ?0A 1)8 0 1 C O N T I N U E

R P Wl Nn L T l 3 N FLAG1=0 NFLAGX = r'L WPR= NUPPFR+iL O w = N H l + ii r ( N U P P F R . L T . N S P S ) G O T O 8 0 0

8 0 3 r O M T I N U FNSCANS = N s r A , N S - 7R p TURNFNn

APPENDIX C

Channels Dependence C o n sid e ra tio n s

Iso m e tr ic p lo t s and p r o b a b i l i ty d i s t r i b u t io n s o f each channel o f

d a ta , a long w ith th e j o i n t p r o b a b i l i ty d i s t r i b u t io n s betw een p a i r s o f

c h a n n e ls ,w e r e examined to e s ta b l i s h a g e n e ra l view o f th e Purdue

F l ig h t L ine Cl d a ta . T his g e n e ra l view was th en used in develop ing

th e c l a s s i f i c a t i o n scheme p re se n te d in th e t e x t , b u t one a re a o f

a n a ly s is was n o t d is c u s s e d . T his a re a i s concerned w ith channel

dependence and w hether i t i s n e c e ssa ry to use a l l channels o f d a ta

o r on ly a few s e le c te d ch anne ls to o b ta in a re a so n a b le degree of

c l a s s i f i c a t i o n su c c e ss . The purpose o f t h i s s e c t io n i s to d isc u ss

th e p ro s and cons o f u s in g a l l ch anne ls o f d a ta v e rsu s a few s e le c t

ch an n e ls o f d a ta .

In d ic a t io n s o f Channel Dependence

E xam ination o f th e is o m e tr ic s p lo t s o f th e d a ta re v e a le d th a t

i t was v e ry easy to v i s u a l ly c o r r e l a t e a l l p o r t io n s o f th e d a ta to

th e pho tog raph o f th e ground sc e n e , and th i s was t r u e fo r a l l channels

o f th e d a ta . Many o f th e ch an n e ls o f th e d a ta appeared p h y s ic a l ly

s im i la r , a lth o u g h th e d a ta becomes p h y s ic a l ly n o is ie r in th e in f r a r e d

c h a n n e ls .

104

105

Exam ination o f th e j o i n t p r o b a b i l i ty d i s t r ib u t io n s a ls o in d ic a te d

th a t th e re m ight be a l i n e a r dependence betw een s e v e ra l ch an n e ls . The

j o i n t p r o b a b i l i ty d i s t r i b u t io n s betw een th e f i r s t 6 channels appeared

sim ilar" and p o s s ib ly l i n e a r . The same was t r u e w ith channels 7

th ro u g h 10 and channe ls 11 and 12. However, d e g rad a tio n in th e

s im i l a r i t y was n o tic e a b le in th e j o i n t p r o b a b i l i ty d i s t r ib u t io n s

betw een channe ls th a t became f a r th e r a p a r t s p e c t r a l ly . For exam ple,

th e j o i n t p r o b a b i l i ty d i s t r i b u t i o n betw een channels 1 and 2 appeared

v e ry s im ila r to th e j o i n t d i s t r i b u t i o n betw een ch anne ls 5 and 6, b u t

th e j o i n t d i s t r i b u t i o n betw een channe ls 1 and o appeared s l i g h t ly

d i f f e r e n t .

These o b se rv a tio n s r e v e a l th a t i t may be p o s s ib le to p re d ic t

o th e r channel m eans, v a r ia n c e s , and co v a rian ces used in th e e l l i p t i c a l

d e c is io n r u le from th e means, v a r ia n c e s , and co v arian ces o f a s e le c te d

channe l o f d a ta . I f t h i s i s p o s s ib le , th e n th e c a lc u la t io n s o f th e

m eans, v a r ia n c e s , and c o v a rian ces from th e raw d a ta could be e lim in a te d .

I f th e l i n e a r p r e d ic t io n c o n ta in e d v e ry l i t t l e e r r o r , th en i t would

a ls o be p o s s ib le to e l im in a te th e p re d ic te d channel o f d a ta e n t i r e ly ,

s in c e i t would c o n ta in v e ry l i t t l e new in fo rm a tio n .

F ig u re 29 i s an in d ic a t io n o f th e j o i n t p r o b a b i l i ty d i s t r i b u t io n

betw een ch anne ls 1 and 2 . The l in e d a re a s c o n ta in no d a ta p o in t s ,

w h ile re g io n 1 c o n ta in s a t l e a s t one occu rren ce o f each d a ta p o in t

and may c o n ta in as many as 37 o ccu rren ces o f each d a ta p o in t . Region 2

c o n ta in s th e crop sym bols, as i d e n t i f i e d on page 32, and has as few

as 38 o ccu rren ces o f each d a ta p o in t to as many as 1,702 occurrences

106

vu w

'Ta ©

RBGION 1

« 182REGION 2

= 180 <u

ss su

REGION 1

160 162 164 166 168 170 172 174 176 178 180 182 184

Channel 1 Mean Values

FIGURE 29

CHANNELS 1 AND 2 MEAN V A LUES

107

o f each d a ta p o in t . The crop symbols r e p re s e n t th e lo c a tio n s o f

th e mean v a lu es o f th e f i r s t 75 i n i t i a l c lu s t e r s o f th e Purdue d a ta .

Region 2 appears to be a l i n e a r re g io n and th e lo c a t io n o f th e mean

v a lu es o f th e c lu s t e r s appear to be l i n e a r ly d i s t r i b u te d , a lth o u g h

s e v e ra l c rop types would have d i f f e r e n t in te r c e p ts fo r t h e i r r e g re s s io n

l i n e s . F ig u re 29 a ls o in d ic a te s why i t i s d i f f i c u l t to c l a s s i f y

c o rn and soy as being d i f f e r e n t f e a tu r e s . The p ro b ab le re a so n fo r t h i s

d i f f i c u l t y i s th a t b o th crops a re row crops and th e scanner f i e l d o f

view is averag ing over an a re a c o n ta in in g a c e r t a in p e rce n tag e o f

b a re s o i l and v e g e ta t io n . The c o n d itio n and type o f s o i l cou ld a ls o

v ary w ith in th e ground scene f u r th e r co m p lica tin g th e s e p a ra t io n o f

bo th f e a tu r e s . The non row crops such as o a t s , w heat, and ry e appear

re a so n a b ly d is t in g u is h a b le . F ig u re 29 a ls o i l l u s t r a t e s how in fo rm a tio n

could be l o s t i f channel 2 w ere re g re s se d on channel 1. The o a t ,

w heat, and rye in fo rm a tio n would be com pressed in to a l in e c o n ta in in g

th e soy and co rn in fo rm a tio n , and th e re fo re cou ld p o s s ib ly be l o s t

u n le ss th e in fo rm atio n cou ld be d is t in g u is h e d in an o th e r s e t o f ch an n e ls .

F ig u re 30 in d ic a te s in fo rm a tio n s im ila r to f ig u re 29, excep t

th a t th e in fo rm a tio n in channel 3 i s p lo t te d v e rsu s channel 1. A gain,

re g io n 2 appears l i n e a r . The mean v a lu es from th e non row crop c lu s t e r s

a ls o appear l i n e a r , b u t t h e i r s lo p es and in te r c e p ts have changed

s l i g h t l y . A re g re s s io n between th e se two channe ls would in d ic a te a

more se v e re lo s s o f in fo rm a tio n th a n in f ig u re 29, because o f the

s lo p e changes.

204

REGION i

REGION 2

/ /^REG IO N 1

1----------- r1 6 0 1 6 2 1 6 4 166 168 1 7 0 1 7 2 174

C h a n n e l 1 Me a n V a l u e s

FIGURE 30

C H A N N E L S 1 A N D 3 MEAN V A L U E S

176 178 1 8 0 182 1 8 4

o00

109

F ig u re s 31 , 32 , 33 , and 34 i l l u s t r a t e th e d i s t r i b u t io n and

v a r ia n c e s and c o v a ria n c e s o f th e crop c lu s t e r s co n ta in ed in channe ls

1 and 2 and ch an n e ls 1 and 3 r e s p e c t iv e ly . The v a r ia n c e s and c o v a rian ces

do n o t ap p ea r to be se p a ra b le acc o rd in g to crop ty p e , b u t do appear

to be l i n e a r ly d i s t r i b u t e d . The g raphs o f th e c o v a rian ces v e rsu s th e

v a r ia n c e s appear to c o n ta in le s s s c a t t e r th a n th e graphs c o n ta in in g

o n ly v a r ia n c e s , becau se o f th e common channel used in bo th c a lc u la t io n s .

P ros and Cons

Two g e n e ra l s ta te m e n ts can be made concern ing th e use o f a l l

ch an n e ls v e rsu s a s e le c te d few ch an n e ls o f d a ta . F i r s t , i f a few

ch an n e ls o f d a ta cou ld be s e le c te d th a t would g iv e re a so n a b le su ccess

i n c l a s s i f y in g th e ground scen e , th e n th e re would be a requ irem en t

fo r n o t re c o rd in g th e u n s e le c te d ch an n e ls o f d a ta , le s s d a ta to manage,

and le s s tim e re q u ire d fo r th e m a th em atica l com pu ta tions. On th e

o th e r hand , u s in g a l l ch an n e ls o f d a ta im p lie s ta k in g advan tage o f

n s im u ltaneous m easurem ents and hence th e maximum d is c r im in a t io n

a b i l i t y o f th e d a ta .

The second s ta te m e n t th a t can be made i s th a t th e c l a s s i f i c a t i o n

scheme used w i l l p a r t i a l l y de te rm in e w hether a s e l e c t few or a l l

ch an n e ls o f d a ta w i l l be u t i l i z e d . For exam ple, th e su p e rv ised

m ethods a re u s u a l ly more a d a p tiv e to s e le c t in g a few channe ls o f d a ta .

The su p e rv ise d approached has th e b e n e f i t o f a p r i o r i knowledge o f th e

ground scene w hich can be u t i l i z e d . I f th e lo c a t io n s o f s e v e ra l

f e a tu r e s a re known in th e ground sc e n e , th e n th e d a ta can be examined

to de te rm in e how many ch an n e ls a re needed to c o r r e c t ly c l a s s i f y each

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C H A N N E L S 1 AND 3 V A R IA N C E S

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C H A N N E L 1 V A R IA N C E S AND C O V A R IA N C E S WITH C H A N N E L 3

114

f e a tu r e and n o t m i s d a s s i f y th e o th e r known f e a tu r e s . One f e a tu r e may

r e q u ir e 3 ch an n e ls fo r c o r r e c t c l a s s i f i c a t i o n , w h ile an o th e r f e a tu r e

f e a tu r e may r e q u ir e 3 d i f f e r e n t ch a n n e ls , and an o th e r f e a tu r e may

on ly r e q u i r e 2 ch a n n e ls . Using t h i s type p f in fo rm a tio n cou ld le ad tc

e l im in a t io n o f some channe ls o f d a ta . A re d u c t io n in th e number o f

ch an n e ls w ith o u t re g a rd to th e f e a tu r e s c o n ta in ed in th e d a ta u s u a lly

enhances th e c l a s s i f i c a t i o n o f some f e a tu r e s , b u t a t th e same tim e

in c re a s e s th e d i f f i c u l t y o f s e p a ra t in g o th e r f e a tu r e s . I f a d i f f e r e n t

s e t o f ch an n e ls i s used f o r each f e a tu r e , th e n re a so n a b le s e p a ra t io n

o f a l l f e a tu r e s can u s u a l ly be ach iev ed . However, th e re i s no

g u a ra n te e th a t an unknown f e a tu r e w i l l be c a l s s i f i e d c o r r e c t ly .

The u n su p e rv ised approach p re se n te d in th e t e x t was developed fo r

th e a n a ly s is o f th e E a rth R esources Technology S a t e l l i t e d a ta , which

i s a c o n s id e ra b le volume o f d a ta . For exam ple, each image from th e

s a t e l l i t e co v ers ap p ro x im ate ly 10,000 square m ile s , and , because o f

th e c o s t and e f f o r t , a p r i o r i knowledge or ground t r u t h c o l le c t io n

needs to be m inim ized and o p tim ized . This can be accom plished only

a f t e r th e d a ta has been an a ly zed , s in c e th e r e s u l t s o f th e a n a ly s is

a re d esig n ed to in d ic a te w here ground t r u t h c o l le c t io n i s needed. For

t h i s re a so n i t may be more r e l i a b l e to u se a l l ch an n e ls o f d a ta fo r a

maximum amount o f d is c r im in a t io n a t th e c o s t o f more com puter tim e.

The f i n a l d e c is io n conce rn ing w hether o r n o t to u se a l l channels

o f d a ta appears to be co m p lica ted by many in p u ts and tr a d e o f f s fo r

th e u n su p e rv ise d te ch n iq u e p re se n te d in th e t e x t . Computer ro u tin e s

and c r i t e r i a co u ld be developed f o r d ec id in g w hich channe ls a re to be

115

co n s id e re d l i n e a r ly dependen t. The c r i t e r i a f o r l i n e a r dependence

would then have to be e v a lu a te d by c o n s id e r in g th e amount o f in form a

t i o n lo s t in th e c l a s s i f i c a t i o n when th e t o t a l number o f channe ls

i s reduced . The second c o n s id e ra t io n concerns th e amount o f com puter

tim e re q u ire d fo r d e te rm in in g channel dependence and c l a s s i f i c a t i o n

v e rsu s c l a s s i f i c a t i o n u s in g a l l channe ls o f d a ta . A d d itio n a l in p u ts

to th e se c o n s id e ra tio n s a re th e t o t a l number o f channe ls o f d a ta th a t

a re reco rd ed and th e s p e c t r a l bandw idth lo c a t io n s . I f many channe ls o f

d a ta a re re c o rd e d , i t may be w orthw hile to reduce th e number o f channe ls

used in th e c l a s s i f i c a t i o n from l in e a r dependence c o n s id e ra tio n s . On

th e o th e r hand , i f on ly a few channe ls a re re c o rd e d , i t may be f a s t e r

to c l a s s i f y th e d a ta u s in g a l l o f th e channe ls w ith o u t l in e a r dependence

c o n s id e ra tio n s . T h ird ly , and assumming th a t th e same sen so r is being

u sed , th e re i s th e q u e s tio n o f w hether o r n o t th e channel dependence

c o n s id e ra tio n s w i l l rem ain in v a r ia n t fo r d a ta c o l le c te d a t d i f f e r e n t

t e s t s i t e s , which c o n ta in c o n s id e ra b ly d i f f e r e n t ty p es o f t e r r a i n

f e a t u r e s .

The m ain re a so n fo r n o t in c lu d in g channe l dependence in th e d e v e l

opment o f th e u n su p erv ised approach is th a t th e e v a lu a tio n o f th e

c o n s id e ra tio n s p re se n te d above can on ly be o b ta in ed a f t e r th e d a ta has

been analyzed and ground t r u t h in fo rm a tio n has been c o l le c te d . The

in fo rm a tio n i s needed p r io r to th e d a ta a n a ly s i s , i f i t i s to be

u t i l i z e d e f f i c i e n t l y .

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