Fuzzy Clustering of Large Satellite Images usmg High Performance Computing

Fuzzy C lustering of Large Satellite I mages usmg High Pe r forma nce Comput ing

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ADS T RACT

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1. INTRO DUCTION

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2. FUZZ Y C LUSTERINC

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2.1 Fuzzy <:- !\Iea".

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2.2 Incocl"0cating Spati"l Information in t 'uzzy Clust"cing

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1'1", t'uzz)' c:-M",,,. ,lguo-"h", "j, •• ,-,,"i,1 i"ro.", .. iot, (SFC~I)' ,tiff"", lrom II", d ... kAI FC~I ~IKNi'h'" onl)" i" '''' ",';n,,'.'" of '''' """"h,,.-.hil' ,-.1",,,,. Ttw- ,,,.," i<\<,.. .. to "".i''''' the ,-.1"" "'j loy ""'1& 'Il<- n"""h,,,,,,,,, ,,,I,,,,,, of 'he p'«" _~"R to. "",&''''''''' of ""<" i, M"", .""",f,ull)", II .. ""jw;«d ,,,'''c. "u Is ,"'""",,,, rro", the ,-.10 .. "IJ'" .-k"",riheo-l i" ~;q , (4).

P:2:0,q:2:0 HI

In t;q, (~). ,he 1""'01" h'i """"""'"' ,be 'I"',i,. inlornu<,ion (roml~"ffi ocr<>r<ling '0 t;q. (b)) ,r.d P """ q.re ,)., '''''''''''''<" ft-hid, """"-,, ,I., ",,,,Ii, .. 'ml~"' o""" of II. , h ,,. R'.-I ' 1'0"01 'n~'--" ",I.H'_ Whc., p _ 1 0'.' q _ 0, "'''' of ~"'n. U", ,...,n»e .. hiv ,,,,I..,,, OOI"""'"""oh,,& '0 "'" d" •• k AI FC~1 ~Iwri'h'", 1'1" ,'~h_.".,.1 in ,h" I'")"" R", P ~ J A"" q m J

hOI - L: ".j. ""';'

N(i) _ ,",i~hl:>ot-hoorl of pixel; ''I

The ""ighh",bood ,v(i) of A pixel i l~""'" "" , )'" ,,",,' ;, ond ooIumn I, of U", ,m_S" ron'."" ,I>< pixel ••• ,.i,'S' '"" ,0'" "'"' """mn i"dka In , .. "'" W,+~ •. i. + <I..). 6. € ( - (II' S - 1)/2. - (II' S - I )12 + 1. , _ .. - r. 1. _. , . (NS -1)/2 - J (,H _ 1)12). &. E { _ (N~' - 1)/2. _ (NS - 1)/2 + 1. , _ 1. 1. .(NS - 1)/l - I.(NS - 1)/1)}. NS hd"K " I' od<l ",10 ... ft-hi<h ,\eli,,,,, 'he ,,,,isht-.:>u,,,,,,,,1 ,Lre. Til<- WC~I Alp;'''", (Alp;Il,," ~) h"" 0 ,,,,,", ."",'u« ,,, 110., of Aigo.-,II"" I. , .. , it "",,. _,'" ex". " ..... , ... y ""d """""'01""" '0 stu« A,", ""'"pul. ,b • • "", 1,,1 i"ro.",otion, s, • .., 4 "ori 6 "'" "",Iition,. .. -it. ""'l"'" to , .. FC~r .Ij[orith,n. 11", ,,,,,,W inbm .. , Ootl '0" I", _,,,,,,,I i" "" .. Mit;.x,," ",o'rix ",i,h n n",', .,.-1 < mI""" ... R'''' ,t> ,,",,,.,to' '''', ,"""Is O(n',, ' .\'5') """,.."" ... lI""w<1"." <.rclul i,"ple""-",,,.,iot, <,." ",,,,,I ,n., "OI"Age of ,I>< ""i", "'" of ,.,,1 ... hV' I~' "",,,pu'ing ,I."" "" n. ,)' 0'" ,.,,10,'-

Th< G"""",A" "c~,"-1_1>Ko«1 F,,-,,)· <)-~1"", .. (G " FC~I)' ito ,...00 "" ,he ""'" of .. '"~ A "11"'0'"",,, ''''''' '" 'he oI:>jecti>" l"nctiot, .. ,ori ~ ""',,,,~'-I ,",.,iI"It), l"I><' ion, I" ",,\cr 1<, ",,,,,I ,he ",-",<I of , ....... ""',001 )"'''''''''''"' • "'" ,of d,,,,,.,. ",I",~"" 1,"'0''''-'0''', (~ ,. _ . 'Ie). o~, i,~".I,,,,,, ,n II. , ,~,j<""" " I,md ,m, (t~l_ (6)) _

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.t, E .. ' i"",(~ (he ""n roO'" 1', E H' b ) _ G '''"''& ~~I ' (2)

. , C.mpu!.!h •• pa!wi inform"ti." h ij for; _ G.j _ G 1< n""""P1" e 'he "",,,,"""'10,1' ".h"" aij fOf; _ G.) _ G '''';''S ~~I (lJ 6, Ad) .. 1 'M "",,,,k""'ip NI ... "'i''S ~~,. (~) 7, ""til (",,,pp;'IlI 001.1;';0" ... ,;'fic,i )

The f",,,,,.,,, h', in r..,. (6). ;, .\efi, ... l .... K(X. Y) _ "x!>l-,{'(X. YlI""), ~,...." ,,< _ E~_ , ,('(X , Vl/" ;" 'Oe

".fiR''''' of pixel> ""'" the ent;,... ;,n'W', ,r ;" A ."~I~',,.,.t ,-.-...,,, of'l>c ;"''11'' X. ;_ •.• ~. <\<''''''''' 'h" ",,,,,.~ of pi'd' ,,,I,,,,,, i" .be ,,,,,,,101>,,<1_1 of , ,;xc>] i. 1'1", ,~ti" .. t ;"' .. ul ,lie """"1>."':h;,, ,'010.,.. "-",(",,,Is .,><1 ..... ,,"'t"'" ~ .re """",il.....-l in the follo.";"g ",nA''''''',

\' E~_ , "::;(h·(X,. 1'j)X; + q; I\(.r;. l'j)X;l J - E::', "::;(/( X i.I'j) + '1;1\(.'(,.1'1)) ",

", Th., CK~'C~I .lgori,hm h ... ,lie "",ne ., "",,,,'" of 'he <1M.k.1 rC~1 "'" i,,,",,h ... ""',,., ~X'''' (·('mlmtAt"" ..

I><fuk tl .. ;t",.t;,,, v.-oc< ... Th.",_ ;t 6"" <",,,vut"" th< ."lOOt ... ",,1 i",,*," .~ (til< OOInvl<xilJ' ....-.1<1' ul thi, OOI"l,, "~'iool ;" 0(" d - ,,"5'). ",.1 th.·,,;t com)",'"" ,I .. n ..... " .,.1 n.nA,,,,,, of ,h., ",";re im.~ (of rompkxi')' onk..- 0(" . d))_ I" ",~lilio" .he ... ;" • "'PI>k,,",~",y "''1' i,,,",1< tl .. il..-,I '''' 1""""". Ih •• ol "''''IHn;,,, (he ~ ... ,. """,or. (of OOl"i->k'x;ty or<i.e, 0«' -d)). ~ I""""",. ,he "'1,1""""",,,, of, h< E ocii<k-.o" <Ii.< .,"". ,,,,,,I ;" t b., F(;~ 1 ~'ilh ,h. ""lxH",utiAI "'-'I rl;',.""". i",!.""" otho;r ",,,. '''''''In, •• ,,,,,,.1 "",,"_ I" ... k1i,KH' '0 , .... '''l~'I.,''"m.,y """"'(AIi,,,n .. 1 """', GKFDI .. 100 ".,..Is .... ,'" <",t<o ...... "t"."...,., In< ,h., ,,,IOothcr.....-l ; """';~ ( .. , J ,,"',,"'''',)

R,><1 h '1M; q I""""~"" (" ""'",e",,,)_

1, 1,,"i.li« ,1M; "",,.!. ,,,,)oip ,-..h"", U'j

2: Co",pto/< !h. """"Ih"'; ''''"''' :( . ., C~mp.'< '~,m"ll< ."' .. '" (f') ond .. ,,"""" (u') . , , ·~",,~t

1< f;,/l"'.I.,~ ,,,,,,,,,,.1 ... qj for) _ G ''';''S r..,. (9) '" E"l i" .. (~ the "",oroOlo ' j lot) _ G ,..;", ~~I ' ($) 1: I!""",,,p"'e ,I.- "",,,,"""'hip ".h"" a" fm; _ G.) _ G "';''S ~~I (7) 8, until ( ",,,,,~i.~ "".Ii' .... ' "'i.!i<-d)

Ik><h ~'C~I .,.1 CKFC~1 .I~it I" .. 1\>" ... 1><'<'Tt " ......... f"I~, AWIi<'1 ' 0 "'''''l<1~ ~I!U i"VIl!"" p",,';'og '0 ,,,,I.,,,, I I", ""ml,,-~ of ... " ...... bi.,l .. ",.1 !,; .. ; ,,~ 11 .. .oInl"'" wv.'R.-.!s 0 pi<-<-<~' i'" hm,_,.""", IAbd i,,,'" 0" 11", ",I"" h. ,.1. ,Jo"re .re onl)' r.,~· I-'" 1><'1'> "'1-""1 ;'IlI "","It. 00";'.....-1 lOr ",t d lit e i",.I!""." 2 .3 Evalua tion of the Clustering Q\l"lity

I" ,I,., """""' of ",,,,,,.,,.,,,,,,,t d....;oc"ion. 'here ;. ,., V""·;..,,, kJ""'· ..... ge 01\ ,I .. d"".", .'"I<W..,. Th .... '"".'s,,';''' .h" 4""li')' or. I","itiot, "'~.;""d i~' 0 du>te,;r.g '!w>rith,,, is ''''' An '-"")' , .. k, The 4uAli'y "..,""u"'"

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( 10)

0 .. of , , .. ,', .... '''"'-,k> of ,h. i,,<lien rotl'p,,',,1 ""<1,,,","'-.1' 0" ''''' ''''''nl><,.,hip , .. 1""" i, '!.<ir "toO""""""" ~q.,-""k,,<}' OI' , ,.' num'''''- of d,"'t~'" i.e, 10,- I"rger , .. I<"", 01 • ,ho ,-"1",,, of " pc; ' r< .1.0 \.o<rg<'" 1" ,..-.Ie, '0 I; ",i' ,h" ,,,,.k,,,,)'. , I", ,,><oI;iit-.1 '''';'''''. <1"",,;1>«1 ;" .'-1- II. 10 ..... '"" 1""1_,1 i" Rd _"

, I'''PC '' 1- --(I- l'pc) ,- ,

Ik>th "PC A"~ ,'",pc ol,o,,~1 I", ,nAxim;",,! ",ul ,'",i, oomP" 'MK>t' i, of ""I" O(~ -.),

( 11)

.\loo' of. tI", ,·.M;')' i,~h""" ;n,tol"i,,, ),,,,10 'be ""-,,,t,,,,,,h;p ,,,,I..,. .,~I ,II< , !"'~ "'" t ...... 1 '>n ,ho, ''''.",M'iootl

of ,Ii." ,,,,,,,, "'-~.""" ~"A ,,!.-l """,roi<j" '" ""' • ..,.,n ditf""'"t ""," roi<!> ill """-,, '0 """'''''' 001"1 ...... ""'" ,,"ul "'1"'.'xo,- [);If,~"" «."hi,,"'~,, ,,, "l,ho,.. on ..... " "'" ",n S"''''''''" ""V "'''nh", "f , .. \i,I;'y imh".".," TI. ", """ I><J'.' ioo, h .. " .h""", 'lte .. ,,'" «)ll'l>kxi')'''''''''', 00' ,,,,, rofro>""",Ii,>:/: 1-"',.11.1 impk""",w ioo roo,],! """,I ,n,,,,, '" """ ",,,,,m"''''''t'''' ."""""'" """"""" •. !1M-hog ,h i, I" ' ni,,,.., ." """"",I 'he K .. ,,,,, ext",,,",,, of X", 1I""i in".::x" ""d ''''' I'mlF i,,<Ie, 1>"""""'" ill ltef."

Th., K~",\ <"cll'ioo, of Xi< i.It.",i i,,.-Iex i. ,!.,.."iI ... -.1 ill f.q. (12) ~'her. V <Ie"""" the """"Ie" of All ' '''t o, 'n", fi",' ",,-,n <ol ''''' """'."'." .-;. " "",""",e ,of ",onl""''''''', ~' h;'" ,I", "",oKI '0" ~' .. ;",,,,,1,,.-.,,1 '0 I>"".h« , , .. ,ke",,,,,i,>:/: of. ,,,,, "un"",.'", "j"", C l"'-'Ot,,,,, I"g", 1'1", ,\c"o",ill~'''' ""-"Su",,, ,j .. "'-1"" .. 100 b<'~""n d",,,.,,,. tI" .. A goo<1 <h,,,'<ti,og =""1"""'" '0 , 'm"lI ,,,h.' of 1'.-, Til< ,"","pb;'}, """-,, of 1'" """)""M'" i. 0 (" c,d+c? d) ,

( 12)

Tho: I'B.II F ;,.Iex (.;.\ IJ) """';'" ,10"", r""', .... "'HI ,"'0,~1 h< n"";oni,,,,_ Tho: fin;' r""".- (I/~) p"".Ii"", • I"g<' ,,,,,,,,",,, of d""t~ ... t he"""",", o"e .. rei .. ,,! ,,, OOInl"':<'_ (E,I J~) ",~I 'he I .. , """ (D,) ""' .. " ..... ,h. "'1"".';'"' ltd",,,,, d, .. '.",_ Th" oomph;') "",It", "f ;,. " MnIH" .hm, ;. 0(" ' < ' d + c? . d)_

( 13)

~' i'h " " E, _ L d(X,. V), J~ - L L u::;d(X, ' j). ( 14) ,-, ,_, J_'

All,IH"" 'I, .. I;,}' ''''''''''' '". ~"'" ,....,.I;n , . " "n.ll' .... tint, p.,"l ~, l ,,,,-;,,,,t> r". tI",;, """pu',',,", . """ <Io~-.,l _

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" , ~-- - - - --- -- --- --' n""". L 10 ...... 10,-;'-.: .,., "~",Lo,,"'" of ,10.,. "'0<1""" ... ' ''''''--'''

3. PARALLEL FUZZY C LUSTERIN G

'11., ",.h, """i",,,,,"U' 0( . '.".'~·I r", .. y d,,;'",;,~ .~i""" """I fo< i"..,.;e "'g'''''''''''''' '''' .,-";'1 IonNhn,g 'he "h', '" 'H"I« ,n ,he h",""")" of _ ." I"""""""". ,1"",01."" 'he <<II" ...... , ...... "" we,,')' "" """"ihle "' .. " ,he

"'~ ."~ Ha,i, ,he ""n"",,,""' ;':"" .... ~""" "~"", '1"1", d_.,ol F(;~ I 'lg<.-"h", I ... 0 """,''''''')' ont..o- of 0(".'" . d· N",,) _ Si"L'" r.,. I.,oe ;"UW~ ' he """,h,,,

of pixel., II , .lg<,ifi<.",,}, "''(''~ ,he otl"" , ... 1",-,", ,he ".,,,,>\1 IM,.II<I;,,,;':", ,p"""",h 001 .. "', of ~h'i<li"g

"., i,,_ in .. m"I)' >l""" '" I~ .'" .,"'"' ..... If ,IN: "''',,'''''' of 1'''''''''''''''' .. I' 'he <;00"1"""';"" '0 I., dol", "" """h v""""""'" "' of onk-r 0(" . '" . J. ,\'",, 11').

3.1 P~r" lIcliz~tio" of F1IZ~Y C-Men".

I" ,h" """' ''''' .. ,"""',il .... 1 ,I", ",,,.IIc~i, • • ;.:.,, of F(;~I ~, I~' K~"" '" .1.' The loW" ""'" l. to ,Iii';'''' "'" jm"&,, in.,; ""'IY .1...", "" 1'"""""","" Th",,- i" 'he <""" of f' 1"""'''''''''''. ,t.. i,,_ .. "h'i'","' i" /' .Ii"",,: S,.s,., .. .s" ,,,d ~ p ."'~b ~'i,h.1l <00,,1'"'''''''' i,,"ol-· i,>.O: 'he pixeb;" .1;"" S .. TI~, I~ P .-ill .,.,..., 11", <:Of"",,,,,~hn,g 'm.v ,I;'" «X;) •• • , ) .,., ,he ........,;.".1 1"''' of , .... ,n.'';, "" ., . i"" 13 ,I><: ".c ... , ....... hi" ,>OJ,,,,, (U; _ ( ... j);O$, . j _ ~. O".he ",hc~ ,,,,,,.1. II", "-1 Qf <e,,'''''''' ((I'j ) _1.<) ~';n .... revlie.,ef~. ,i"",., """It i,,,,,,",,,,..ctt I~ .hoool~ n.'-e ,he e"TT<"~ •• dmA'". of ,he ",",,'-";'b. n", di,,"lm''''' of ' he mA,n .1.," _",,-""" "''''' I"''''''''''''' .. 0110"".,,,1. f<.- P _ J 1'_ "" 0,.1 c _ 3 d,," ..... in ~.;g" ... l.

h , on\cr '0 <""n ... th., """" ~ I ... ....,... '0 , .... on " ",,, "",i""".,. of 'he """""" .... gIo~,"1 I"""";'~ "'-1' ,. ,-.k>1 A' """" " ... , .... " The I""" ;'k .. I><hi,.' ,,, .. ~;,,~ .1<,,", ,,, ,Iero,,,,...., II", 'u,,'" '''''oh,,''g All pi",,,, jn ''"TtiAl .", .... oorr<>"o,.li", '0 1'",01, ill i" .. go >I""" .• For i",'A',""" ,he oomv"''' io,, of ' he "",,' ",i<I •. ,n E'l_ (2). <on 1M' "",,,i,,,,,, .. '~k .. ·"

( IG)

],,,,,,,,,,,,,,,, p ~'ill ""'''pu, e ,I", .... ", E .. ~, "::i X ( ... 1 L .0$, "::i , ""', "II """'" 1",,';"1 .,"" •• '" .. Me.1 "'«'" I"" ;n 0.-<1", '0 "'0"1'"'< tl., "',"',,..,.,. .,.1 ,""Hoi, .. "", of ,I", 1 i ",,,''-'';'1 ... ,"""',il ... 1 in ~~I ' (1,)_ If ,h. , .. ,.1"'1 j,,,pIe,,,,,,~.,;.:.,, .. 1..-1 "". ,,,(".'"~ ........ ,,~ lih'.'1" (e,g. W'l) .• " "ff.,k,,, ~")' of <"OI""'i""l), """,!"" i,'1: ,h.

gloh.1 '"IIl> ~AII t,.. 1""lom...t 1»' ' I>illl\ ,he ""t,>Oe ", .. ,M;"', (~ ,g. KPl ..llI .. <luoo III""';"") , '[1", "nl<ture of ,I., J"'nolld "A,io,,' of FC~I c""'''''I''''.li, 'l! '0" ~"""'" I"' ........ " 1''' ,~I~,l in Algori'h'" 4,

All I'''''''''''''''' """",ot" ,I", .,"'''' romVllw""", on ,I", oor"",,,,,,"'illl'! im"l'!" .I;.c." A, """h i le'.';"" . 1l,,-'re "'" I.."h ,I", "",,,I "'."1"".' .... (in,,~,' i'\l< tI", ",,01, ",h"", <"O<T""I"".)i,,~ '0 ,t.; ;"UW' , I"", ~,",l 1.0 ,he <"''''"' ~) A'. ) ,ho" ~koI"l OOUl»ll"';"''' f<>r "",i,,,"i~ ,ho" ~"roi<b. of .1"" <:-,It""" "'" of <"""<r.. 1'1, .. , AI , h. ",.J of ,I,. ite,.,i,... """"'"" .1I I~' .... '" , he "",ire "'" of .-emro>-l., .,., ,I ... d_ifi<,1 i"UW' <"" t,.. ''''''1"",,1 I?' ,", I.>' "'''' of tI. , Im:>co""""'_

J. it" .. 0 . , "'I",at

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~, Coo'PU'" Cj (!,) .. L.u •• ::;(p) X ,(I'). j _ C; &. O.nl""e Cj(Pl " Los. ":'j(p). j - G 7, C.II KPLlllr..:luco '0 COIIII"n" Cj .. Cj(l) +, .. + Cj(l') f<>r "II j _ C; *' C.II KPI..Illr..:lueo '0 " " "1""< Cj .. Cj( I) + __ + Cj(l') h " II j _ G I>. Coonp,,'e I'J " CJ/Cj, j .. C;

,t}. UlxlAoe ,he 1oc.1 ",,-,"t,,,,,,hi~ "AI""" "."JW.; E s., j .. C;

, " OHnl",'e t"rr(P) .. ",,,x.u • .;_r:< 1_;jw(P) _ ... ,(P)I ,2: C"II KPI..Illr..:lu<o '0 COInpu'e Err _ 01""( Err(I). ' . , • Err(P)} ,." i'"" _ i,., + I ,. , · V - "~r·;ES. ,j - C; 11< "ntH f: .. <, ".- itc. > it< •• \Ja~ ,t;, eo,,, ,,,,,. 'he "'us"_" , .. 1."'';0" ".,,,,,,,,,-{.) 11, if V~- I ,hon ,8, eoru,trllct 11 .. d_ioo) i"UW' II>. ond if

The OOIHI"""""'" of , .. <I"",,,, ,·~Ii<l .. ion II,.,""""'" i",<>1", v.i< .... of ,he pix,,1> ".1 ,hei, II,.,,,,t.;r,,hill> for , I", ''''';.-.; ;'ruog<:. ",,,,h,,,,, '0 ,ho, ,,,,,,,,,,,i'l' "l'j,hll i,'-S ,he , 1o!",1 "m'I"" "'""" ;"'0 k",,,1 "'''''' """""I'M.I;n~ '0 ll ... 1""",- '11", J"'rtiAl """I,,, oI~Ai,"'t ., ' he ~ ""'d AI< ""'lLl~o...t '''1:'',1><, t~· rot""',i", <>1-'<1'", ;", ... For i">,,,, .... ,,, ""''')'''''' tI", \ 'K ;,.~",. ,k"",;),,," ;n 1::<" ( I?). ll.~~ "re ,~-U '"on' I .... ,' 'M' 'h" ""l~""ivc "1"-"'"' ''''''' k",li,ot: to t~'O CAl]" or 1IP1..Ill roduc. fu ,,,,,",,,, ,10" fi"" 'etm ib 'he "''''''''A'O< (~'hich ",,-..-b 11" ~I ,HOI of """I., ,,,h.,.) ".1 'he """I""";"" or 'he ",x." ",,,,o~ (.-hkh ,,,,,,,,.,he gkol",l.m" of d.rl;"", .. ;"".1 '-";'OflI) '1'1" ""',. of "'" roo"",""';"', of "'" chl>t .. "AI;');')' i,~hc"" ,,,,",,,il . ,) ; II 'he l""" ioo .. """,;"" I." to ;lL ' he _'''''''' i,,1 ~,'" ' he 1" "Al k'l < .... Are p,,,,,,,nt<..-[ in TAI>k l.

3.2 P ",,,lIclizatiotl of the Spatial V"ri"tlt~

Tloi, _k>n ,"""rif><,; ,I ... 1>rO\.,..,.-l p",.lIdi, .... ';.", of 'Il< 5~·C~1 R,l<1 CI\I'C~1 .lgori'hm, 1""".", .. 1 in """ion 2.2. T he p",.II<Iw,.iot, of S FC~ I (Alxo< i, I"" 5) 1'01 ........ Il< """ .............. he 1"".lIdiwiot, of FC~I. 10." i. " ,,,,oin, <;On'" p"" ;.,,,I., <kon<,,'~ "",,,,I '0 'he ""'''I~'''';'~' of , I", ' 1",'iAl i"~"",..,;.", , 5i""" ,I ... «.Imp"'.';"" of h.; ,,,,,,\oi .b" " ..... " I"''''hl" ,-..I ...... ;to • '''';~hotb,''''1 01 ,,;xcl j , for ";><1> "" Il., bo ........ of Il'" ;,,~ .1"" ....Jg""d ,,, I~ p. it ;, ''''''''''''''y t" h.,,, """""" '0 ""-""",,,,,hil> '"hK'" mr .... potlt!in~ '0 ,,,,~hho,itog ,Ii<w, '1'1""" in ",~Ii, •• , '0 ,10" "~k"" ',,, """1'''''' ;'. '' of 'b" ""","';'1,. i" Il .. j>O'AIi<1 ;"'pl<"."".ti,., of SFC~I ;, i. '~I'). to tr.""f., """'" ,,,.,,,h.r>hip"""1et- ,..1""" ""'~""n ,he ~ de.ling ... ith ""'g""","in.o: .1"",,-

TI ... '" 'I''"''' of ''''" I~ i",,,",,,,1 i" .he ""no"",,,"";"', I""""'" .,.1 ,IN: ''"''''''' of .1>< ,,,,n,f<-,,..,d ,,",to .x,,,,,l<1 00 ,he ;m.<g< l>'I"ition;'\II: '·'''''n'. TlI<fe.re ,~"O ",..;n 1>'I" ;U.ooin~ ,·AriAno" one rot"""'poM ing ,,, ,I", c ... ~-h,'" "" *' OIW of ' h" imAg< ,Ii"""";"',, i, p"rtit;."...-l (I<...-linll ,,, horiw"'AI or w"ie.1 , 1"",,) ",.1 .,,,~I.,,- ,.'" ~·oo, Idl, tI .. ~'id,h .,wl .he I-o;~h' of .he ;,.,~ .r< ,Ii,';'k,1 I" ,m"Il,~ .1""" (~...-1i"g '0. 3ri'l \;1<.. p""i';'~,inll) ' l'ir;t,,~ 2 ill",,, .. ,,,, '-"<0 c""'" ror.-...potwling to IlOfi<otu.) .. \<l gr~1 )ik>- ."litt;"g of , II<" illlAg<.

! ... , ' .. <"<Mo;;'-k, .n i"i, i.1 inuw; of .. ," h • IV phcl> ","1 ~ ''''i&l,I""I......-I of .;'" N S ~ NS I" ' he c_ of An hor;_"~1 .",;";,,g of ,h. ;"'"K<. tI., """""""" ,k. h"" ~' iU, ,1>< ;,,,_ . 1"" p ,bo"I,! ,"''',,',,''''' ... ,"'1)' ,,,

1'<""""""'" ...... Ii"ll! ... i1h , I", .1""" p - I .no p + I. ",\<l ' 1« .;"" of ,Joe OAtA '0 e., tr"",IOI""-] At <"'><h """1/,,,,,,,;,-. "P""" ;'M' ;. < • .,. NSIl_ "1'10, ... ",ecl" I"r P"'''''''''''' ,Ir.ling ~,ith ,1., .,~ , "" hot,,",, i" "'go: ,Ii""., "",,10 1'''''''''''''' ""M C . ' - ,YS/2 ,I.,. ,,, ...... h 01 it> , .. i&!thoting ~ .,It! ,..,.,.,;, .... ,e., .. m •• "'''''''' of dA'A. In ,he """" 01 . ,,,rt,,,Al 'I'\;tti, >t of ,10< ;"'''11''. tI", """,1"" 01 "'-"'"I/""",;,~ OJ"""'""'" .. ,h. ",,,.,. I." tI",,.;,. of d.,. " .. ",ler,...-] At """h CAli is C - h - NSI2 , 11011<". in the <""'" 01 inlAg<> ~' i 'h •• iR"ificA'" <l iif,"",,,,,, I"-~~,-"",, ,he ~' "hh .,It! ,1", hclrsh'. ;" ""w". '0 ",inimi" 'he . ,""''''' of ,,",,,f,,,,,,,1 ,I., •. i, .. <h;,.'oIo: to ,l;,-;,lc ,!w: 01;,,",,,.;, .. h,,';"!!" t..'l«"" ..;"'.

Allot","r iml>Or'.'" ",m.rk i> rei .. ",) ,,, , I., COI"PU'Atiott of 11 .. ,ire of ""'"' i1llAg< ,lire, L". , .. """i,kI , tv.t , I., ion...., ... pli ",,1 10" .10 huri"""AlI)" .. ,.1 " ", ",.11)" .. ",h tllA' K . ,k"o/", II., ",,,"he, of .1;'"";,, ~·h"'h 'h< height of ,he im'>go i> ,\i". !<ol .. hik /o.~ ,10001" ,I", "'''''"''' of ,li«o ""''''''pot" IIo''l:'o the i'Mg" ~,;.-lth. T he ".1" • .., K • • ,.1 K w 0;1 .. ,101 )., ,.,",,",,1 "",h 'h., K.· "w _ I'. I' IMinS tI", ""m)"" of 1"'-""""""'" Since 'ho; ;' ''''~, ~'id'h . • \ oml II", l"'i#'1. h •• r< ,lot ,,,",,,,,,",ril}· mul lipl""" of K. oml K. "-~"e<.i,,,I} ... he .;'" of ,he i,,,ol«' 0.1;"" "-""",,,""ling ,,, 1",,,,,,,,,0, P ,I •• ,kl)", "'''1''"",1 ".ing ,10" n,k ,!roc,;, •• I;" ~~I ( 16) ~'b"r< di,- ,k,,,~,,,

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·f h;' rulr ''''''",.,. tI", I>'Irt il"''';Uj( of II., ;"'''l!~ i" .J""'" 01 ,;",il., .;",-~. """ Ii", '0 0 MI .. ", ... ! _I of II", IM~_ ~;..d, i",'W' ,I"", <"" 10" ;'~"" ;fie<I'.,.. I>oi, of ,-.It.,. (p" . ",) ~-i.h (l ~ p, <: K. ","1 (l ~ p.. <: ,,~ ·n", P""""""" ,tc.l;,og w;lI, ,he ;"lAJ!< , I"" (P •. p~) will ,"'m",,""'O'c wilh 4 '''';&l'''''''' (;n ,!w: <_ of .. ,<0" N,'um."" ,"';&l,hotOOo<l) or ~'i'h 8 ''''i&l'''''''' (in ,I .. c_ of .. Moore ...-w,hotOOo<l). T ile .i"" of <l.,. ' 0 he "",,,,fer,,,! bcl~',." .. 1""'-''''''' ","I ; •• ~:fl ('egh') '>cis''''''';' < .h,. ,YS/1 '" c· hIK •. .vS/2 ~·hilc;" tI .. '''_ of 'o~ (1)01'01<1) "eiK)""" i, is < • u· •. N SI2 '" c· .,1 K • . NSI2 , Tile "i,. of ,I>\t. ' 0 h. tr~,,,,f<.r!'(11 I-.ct~""" • 1'''''' ''''''' .,,,1 i'" ,1i""",,,,1 ,"';g!,,,,,,,.,,, ;, " "",II .. ,,,,I.~ , <. NS'14. I" tI", """,-" 01 • hut< "",,,1 .. , of !.....-.-..... , I ... i"" of d.-.,. tr.",f.""j ill ,I", C""" of ~ "id·like '1lIil1ing of ,11. im.~ CA" he .iltllific.",I)' "",,1"--, ,hAll in ,I., """" of hori""".1 or n;";,,Al ' 1,1; " ' ''g. , 10, .. 1o.,-;,,&"u im).,,' .. ,,' ;"~,."",, on tIN: ollie.,,,,,)' of ,he 1'","11<;1 i'''pi<-t,,,-,,''';,,,, .

The I>'Ir.11<1 ,· .. ,ito", of (;I\FC~I .. '-er:\. ";, oil .. , . '-;,h the 1>'I...t1<1 FC~1 ~'i'h ""''''''' '0 ,he rot",n"nie.,;"', b".~',.-" , I""'''''''''''". bu' ;. ,~"Is . ~"O ""' .... 11,.001,,<. "All. , .. ..-....., tI", ;.,~".;,,, ]>rOC ..... fo. tI", <011«.-.;,,, rom_ ",,, ,,ion, of , he .",rAg< .,.1 of , I", '",;",Ke ",,,r , b •• nti re in_, A l"'rtieul.r <k''',,-",,'' of GKrG~1 "' ,he """1"""'"" o{ , )'" "",-"" )",,...-l '''''' ;,~, of 'ho; in;,;.1 I""W', inn",-i"g "''''Im'., """ "' ,,,,;g!,I-.,,I. ,,.1 0,,-.:1 In ""let- '0 A ,""1 ' be or.,,,,I,-,, of 1"",1", cle, ""''', h.t ~"«"I' p"""""""'. 0 """ it "'i'og ,,,,,,,,, I 0" ",,,,l1oppi,og . h""" w,," ".".-1. i.<", _h I~ """"",,,1. i" ",I<l it;"', '0 , he I~xel, 0111 .. roore;I"".li,og , ) ..... ,he loi,,~. of. 1"",1et- of .i"" (NS - 1)12.

.. ""',I, SI,~,';.. .. roo"", 2_ C"",,"""",.,'" of '_10" ""'.''''''''''1> , .. , .... ""'_" ''''~''''';'oo; J~'" ,,., ,_,..t." ""<i..,..,oJ "''"'''''& '" ,ho .. , .... (Irl\) ",.I " ~,;'_H"" .,~;,,;,,~ ~·;,h Kr • K. _ 3 ('~M)

AlltO,l,bm ~ The K"'le'AI "'ro""",,, of 11 .. 1*101.,] SFC.\! _!writh", ), RON) i,noge .Ii«: X(P) _ X •• s. 1e 1o,;".Ii« ,..., kx:~1 ,,,,,,,,l>=.h;1' ,,,,10.,. •• ,IP) J. "'IH'M ~, Oxn,nolc Cj(P) - LoU, "::i(P1 X,(P) ,.,. Compute Cj/p} - L.u. ":')(p) '" C.II KP I .... n ..... u <o 10 "'''pUI< Cj ~ Gjfl) + __ + C;(I') for ~Il j _ G 7, C.II IIPLlllr.:luco 10 ""'"PUle o:l ~ Cj( I) -+ ' .. -+ C]W) for ~Il j _ r.c 8, Co"'pul" I'j _ C,!C;r.,.. .. ,j _ I." 9: C.II KPI.s. 04 ", .. 11<1 t he oo..\cr ;"Im'n";"', to ,"" .. "i,ghl"",;,,~ I~

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4 . IM PLEMENTAT ION AND EXPE RJ lIIENT S

4.1 Com puting environm e nts a nd implementation de~"ils

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4.1.1 h,r •• (".';<1 CI".t~r

T toe I "f,.C,id d"",-~ is """ipl""i . 'i,h:

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• CPU: 1,,'01 Xeool 2.OGhz CPU .. 4 (""-~ per CPU (6-1 );i,. """,Ie):

• I\A~L 1.2;,(;11 1 rot,,,

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4.1.2 lIJM DI""GcJ>ej l' Snp"I"<X>,,,pn',,<

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• Col..""" i",,,,COl"""''' r.:JGh).ti t:.. .. l"'i,h (~!" ""I'"'''''' ,i" .. lor ~I I'I oo",,,,,,,u"'.t ioo,) ........ 100- ",,,,,',,"~I l ooon,,,,,,,"'" iot, .,,,1 ""10""",,,, """",ion> f",,,,, ""\Ali',"

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4.1.3 CO"'"ik .... ,,,,01 nhrm'i""

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.".h~'" "d ... ".ni"." ",~; m'ZA' '''' ' , h'gh_'-"'In- """"~"'""' .... , ".x'ul< An.! ;,,,....-_""',"",,'" A''''')'''' ( ft'hi<h iml'''''''' ink' """""",.. ""''''Or)' =hanu p"'~,.,''''n,,~j. T) ... ~_ ",,,, ill 'Il<> """-""'", "I"imi,.,ion "All" ft",,· ' _03 -<Iho. -<l ipAm""'cl~2 -<1',,,d,. ,I5OoI- Th .. "'~;"';""ion J"" 'O'n i"""",~"o,,' of U .. P""O""'.' "", ft',, 1<

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• "n ,II 'IBIS low .1, ;,,,,,,, "-'., high """Ul"'" im'lge ~-ilh a I"OV ,nno'"" of ,,"""ral "",." (ZZ I) .,.1 1087x61~ ,';;«'" (.",iIAI>Ie in the NASA c.,.q, .. · h"p: II.,·i,i.jpl." ..... ~·/h'ml/ .. ,i, .. .f.."",-l .... lttml)

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4.3 Implemented varia"t~

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IZI 1I""l<k,J ,C .. " I'>"ern r<ropo;, .... , . ';<1, f""y ohjrt';w fo,oct"'" .. tp;tI,,"."'. 1'1..,,,,,,,. Nc .. · Yo,k. 1!IIli. [al Ch ..... '~, I\ .S .. ' [""tg, 11.1... <., .. ", S" "",,, J.. "'., C"",,,, "[' ,J.. "F",,"}' ".,,""'''' d ... t<"l'i,,, ~' i <l, .""h.,

;"~"'RA'"'' I". ;m"V "'lI"",,"A''''''" . C,.nl"""n,,,1 ~1,,'kAI '''>Ag;'" "'., C'"l'ho.., :10. 11-15 (1000) . PI YA'". US. "'., T .. i. II.S .. ",I CA''''';''" 1..,,""_10 .... 1 lu"y "'''.'''''' 'W--i<lu" . ';,h .. '1"";""." """,-d ;'n,".

p .. ll .. ..., Il eoogni'joo I ... ,,,,,,, 2'), 1713-ln~ (2008), [51 L;.-.·.,\. W. C .• !"-"ns. S. II .• "., I ... ". W. II .. " t·",,), i~'"V d";'vins i"''''I,o"''''i"g "",,;"1 """ i,,,,;,y".

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Fuzzy Clustering of Large Satellite Images usmg High Performance Computing

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