Download - Development and evaluation of a new 3-D digitization and computer graphic system to study the anatomic tissue and restoration surfaces

Journal of Oral Rehabilitation 1996 23; 25-34

Development and evaluation of a new 3-D digitization andcomputer graphic system to study the anatomic tissue andrestoration surfaces '\A. DASTANE, T.K. VAIDYANATHAN, J. VAIDYANATHAN, R. MEHRA & R. HESBYDepartment of Prosthodontics and Biomaterials, NJ Dental School, UMDNJ, New Jersey's University of Health Sciences, NJ, U.S.A.

SUMMARY It is necessary to visualize and reconstructtissue anatomic surfaces accurately for a variety oforal rehabilitation applications such as surface wearcharacterization and automated fabrication of den-tal restorations, accuracy of reproduction of impres-sion and die materials, etc. In this investigation, a 3-Ddigitization and computer-graphic system was devel-oped for surface characterization. The hardware con-sists of a profiler assembly for digitization in an MTSbiomechanical test system with an artificial mouth,an IBM PS/2 computer model 70 for data processingand a Hewlett-Packard laser printer for hardcopyoutputs. The software used includes a commerciallyavailable Surfer 3-D graphics package, a public do-main data-fitting alignment software and an inhousePascal program for intercommunication plus someother limited tasks. Surfaces were digitized before

and after rotation by angular displacement, thedigital data were interpolated by Surfer to providea data grid and the surfaces were computer graphi-cally reconstructed: Misaligned surfaces were alignedby the data-fitting alignment software under differ-ent choices of parameters. The effect of differentinterpolation parameters (e.g. grid size, method ofinterpolation) and extent of rotation on the align-ment accuracy was determined. The results indicatethat improved alignment accuracy results fromoptimization of interpolation parameters andminimization of the initial misorientation betweenthe digitized surfaces. The method provides impor-tant advantages for surface reconstruction andvisualization, such as overlay of sequentially generatedsurfaces and accurate alignment of pairs of surfaceswith small misalignment.

Introduction

There has been growing interest in recent years indeveloping the ability to reconstruct anatomic tissuesurfaces by digitization and computer graphic processingof the digital data. Such tissue surface reconstruction hasa variety of potential applications in oral rehabilitationand these include the following:

(1) in vitro and clinical determination of wear parametersof restorative materials (DeLong et al, 1985; DeLong,Pintado & Douglas, 1985; Sakaguchi etal, 1986; McDowelletal, 1988; DeLong & Douglas, 1990; Dastane etal, 1991).(2) quantitative estimation of sealant volume (Pintado,Conry & Douglas, 1988).(3) evaluation of the accuracy of reproduction ofimpression and die materials (Bloem etal, 1991).

(4) fabrication of restorations using CAD-CAM tech-niques (Rekow, 1987; Duret, Blouin & Duret, 1988).

Traditionally, clinical follow-up of anatomic surfacechanges relied primarily on ordinal or interval scale ofdata measurements based on visual rankings and visualcomparison with calibrated standards. In contrast, com-puter graphic processing of digital surface co-ordinatedata provide ratio scale of accuracy in surface represen-tation in addition to the 3-D visuahzation capabilitiesavailable in computer graphic data processing. Theseadvantages are valuable in the determination of the lossof surface material as in wear characterization, thevolume of material incorporated into the surface as insealant volume measurements, as well as the ability ofimpression and die materials to accurately reproducesurface features, and last but not least, in automating

1996 Blackwell Science Ltd 25

26 A. DASTANE etal.

the fabrication of dental restorations by CAD-CAM tech-niques. While these are important advantages, computersoftware systems available for surface data processingbave largely been proprietary and it is advantageous todevelop a system for tissue surface reconstruction fromcommercially available 3-D graphic packages.

The objectives of this investigation were:

(1) to utilize the hardware capabilities of an MTSbiomechanical test system with an oral environmentalchamber (artificial mouth) and profiler assembly, and anIBM computer system interfaced to it to generate surfaceco-ordinate data of anatomic surfaces of tissues.(2) to combine a commercial 3-D graphic softwarepackage and a public domain surface alignment softwaresystem to visualize, reconstruct, overlay and align thetissue surfaces with a view to characterizing the surfacechanges in clinical and laboratory studies of wear.

(3) to evaluate the different interpolation options in thecommercial software with a view to improving the align-ment accuracy of 'before' and processed 'after' surfaces,where the 'before' surface is an initial surface, the 'after'surface is the same surface after limited misalignmentthrough angular or axial displacement (i.e. rotation ortranslation along the x -, y -, and z-axes) and the proc-essed 'after' surface is the 'after' surface aligned to the'before' surface by an iterative data-fitting procedure ofthe alignment software. Potential misalignment of atissue surface may occur during chewing and/or due tothe minor variations in the mounting of the specimensfor digitization. Similar misalignment may also occur incasts from clinical impressions of the same tissue surfaceobtained at different time intervals of a longitudinalclinical study. The effect of different levels of misorientationon the accuracy of alignment by the alignment softwarewas also investigated.

Materials and methods

Figure 1 shows the MTS biomechanical test systemincorporating,an oral environmental chamber. The testsystem, similar but somewhat modified from that describedby DeLong & Douglas (1983), is capable of controlledmasticatory motions using a servo-hydraulic system of twoactuators whose motions are synchronized to simulatechewing cycles. One actuator operates vertically and theother operates in a horizontal direction. By rotating theplanes of motion so that straight line motion of thehorizontal plane lies parallel to the long axis of thehorizontal actuator, tbe three-dimensional motion of

Fig. 1. MTS biaxial mechanical system with the artificial mouth.

mastication can be reproduced by two-dimensionalcontrol (DeLong & Douglas, 1983). The testing systemalso has the capability of spraying the specimens with asalivary fluid or water at the desired temperature undercontrolled continuous or pulse modes.

A second feature of the test system is the hardwarefor surface digitization. Figure 2 shows an extensometer(model MTS 632-06B-93*) and stylus probe assemblyattached to tbe vertical actuator, and also the tooth(whose occlusal surface is to be digitized), which issupported by stone in a teflon ring and attached to thehorizontal actuator. A molar tooth was used as shownin the figure. To collect surface co-ordinate data, thestylus is scribed across the tooth surface by moving thehorizontal actuator under stroke control along its axis(i.e. the x-axis) and the co-ordinates of 200 points alonga line of approximately 2 cm span along the x-axis ofthe tooth surface are fed into a computer. Figure 3 shows

*MTS Systems Corporation, Minneapolis, MN, U.S.A.

1996 Blackwell Science Ltd, Journal of Oral Rehabilitation 23; 25-34

3-D STUDY OF ANATOMIC SURFACES 27

Fig. 2. Scanning arrangement for digitization of surface co-ordinate data.

Oscilloacope

Microconsolewith

A.C/D.CControllers

1. DCI controllerZ. Vertvaal Aat-uaior3. ExtensorriBier4. Stylvs5. Sample

e. Horizontal Act-uaior 11. To HP 74757. Slide TableB. UTS Control Unit9. A/D Terminal Box

10. IBU 80386 computer viith A/D board

Fig. 3. Schematic diagram of the hardware assembly for collectingdigital surface co-ordinate data.

a schematic diagram of the scanning arrangement forgenerating surface co-ordinate digital data. The purposeof the extensometer is to provide a feedback signal tothe MTS system control console so as to activate thehydraulic circuit in the appropriate direction of thecross-head movement to ensure that the stylus is incontact with the tooth surface. The command centreactivates the hydraulic circuit appropriately by compar-ing the extensometer signal with a pre-programmedlevel of the signal needed to ensure stylus contact withthe tooth. The points generated by a single scandescribed above constitute a 'line profile'. Every pointon the profile is determined by the signals from the hori-zontal actuator (i.e. the x-co-ordinate) and the signalsfrom the vertical actuator (i.e. the z-co-ordinate). Aftereach profile, the stylus is displaced 400 jim in the di-rection perpendicular to the axis of the horizontal ac-tuator (i.e. the y-axis) by a DCI stepper motor controller.

Thus, a series of line profiles are generated. The dataacquisition system consists of a Metrabyte |i-DAS16GA/D board (12 bit, 16 channel) and ASYST softwareversion 3-0*. An IBM PS/2 model 70 with 4MB RAMwas used for data processing. The acquired data areused to reconstruct the tissue surfaces by computerdata processing and selected pairs of surfaces are thenaligned by a data-fitting programi. In order to simplifythe overall data processing procedures involved, twoseparate software programs were used for surfacereconstruction and alignment routines. The Surfer 3-Dgraphic package. Version 4+ was used for the originalsurface reconstruction (i.e. the 'before' surface) andthe mis-oriented surfaces (i.e. the 'after' surface or sur-faces). The acquired digital data may be randomly spaceddue to an electronic or other delay in data acquisition.For proper surface visualization, reconstruction andalignment of misaligned surfaces, matched sets ofuniformly spaced data points are required. This wasacquired from the raw data by Grid routine in the Surfersoftware. Gridding creates a regularly spaced grid fromirregularly spaced data by interpolation. A regularlyspaced grid is a rectangular grid made up of rows andcolumns of data and the Surfer grid routine, in effect,interpolates the z-value for every (x, y) point at the in-tersection of each row and column. Data interpolationcan be performed by three different algorithms and choiceof grid sizes (limited only by the maximum number of14 400 grid points that can be processed in Surfer). Allsurface co-ordinate data were interpolated within al -4cmx 1-4 cm area using four different grid sizes(39 X 39, 51x51 , 63 x 63 or 81 x 81, corresponding to175, 225, 280 and 370 fim grid spacing, respectively)using all three available algorithms of inverse distance,minimum curvature and Kriging methods. In the inversedistance method, the elevation (i.e. the z-coordinate) ofthe interpolated point P (i.e. Z ) is determined by theequation:

z,, =P n

d

where z.s are the elevations of raw data points within apredefined search radius, d.s are the distances of these

* ASYST Inc., Rochester, NY, U.S.A.

+ Golden Software Inc., Golden, Co, U.S.A.

© 1996 Blackwell Science Ltd, Journal of Oral Rehabilitation 23; 25-34

28 A. DASTANE etal - -

points from the interpolated point, p, and n is tbe numberof points witbin tbe search area. Note tbat tbe data pointsused in tbe inverse distance method are weighted witbtbe exponent 2 so tbat the influence of eacb data pointis determined by tbe square of its distance from tbeestimated point. In otber words, the neighboring pointswill have more than a proportional influence on tbe eleva-tion of tbe interpolated point tban points away from it.In tbe minimum curvature method, grid interpolationuses an algorithm based on the principle of minimumcurvature (Briggs, 1974). This is an iterative procedureto solve a system of linear algebraic equations obtainedby using finite difference metbods. Kriging is a methoddeveloped in geopbysics to make contour maps from sam-pled data consisting of elevations, as is also tbe case inour investigation. Tbe value of elevation at an unsampledpoint p is predicted from a set of sampled values of nnearby points by a weighted equation:

Zp-

where W.s are tbe weight factors to be optimized, so as

to minimize tbe estimation error e^, given by.

where Zp is tbe estimated value, and Zp is tbe true value.Optimum values for tbe W.s can be found by solvinga set of simultaneous equations and the resultingestimates are unbiased and have minimum estimationvariance. A detailed review of tbe procedure by Jones,Hamilton & Carlton (1986) provides a full descriptionof Kriging method.

Tbe interpolated 'before' and 'after' surfaces are nowaligned by a public domain software*. Tbis program, cur-rently used to align surfaces using optical microstructuralimages, uses Simplex algorithm whicb minimizes tbe sumof tbe squared residuals (SSR) between tbe 'before' and'after' surfaces by rotating and translating the 'after' sur-face on tbe X-, y-, and z- axes by an iterative procedure(Caceci & Cacberis, 1984). Tbe value of RMS/pointdefined mathematically by:

/=!

* CRA alignment program from the Clinical Research Associates, Provo,Utah, U.S.A.

where iVis tbe number of points, z.. and z. are the eleva-^ w la

tions, (i.e. tbe z-co-ordinates of tbe i"'point in the 'be-fore' and 'after' surfaces, respectively), calculated by tbeCRA program, was used as a measure of tbe accuracy oftbe alignment. Intercommunication between differentsoftware programs used an inbouse Pascal program. Tbisarrangement was very convenient because data files couldbe exported from one software to anotber for dataprocessing and computer graphic routines in a conven-ient way. Tbe Surfer software also facilitated the overlayof tbe reconstructed surfaces for better visualization. AHewlett-Packard laser printer was used to obtain abardcopy of tbe reconstructed surfaces.

Results

Figure 4 shows tbe reconstructed 'before' surface of tbemolar tooth, obtained by our digitizing procedure. Fig-ure 5 shows two surfaces, one of wbicb is tbe 'before'surface as before and the second surface (i.e. the 'after'surface) was generated by rotating the 'before' surfaceby 1 degree around tbe x-, y- and z-axes. The effect oftbe rotation is tbe misorientation between tbe surfacesmanifest in tbe overlapped surfaces. Figure 6 also sbowstwo surfaces, one of whicb is again tbe 'before' surfaceand tbe second surface is tbe 'aligned after' surface wbicbwas obtained by subjecting tbe 'after' surface tbrougbtbe CRA alignment routine after interpolation using a81x81 grid size and tbe minimum curvature metbod.Note tbat tbe 'aligned after surface' is closely matched totbe 'before' surface, indicating tbe effectiveness of tbealignment. Tbe calculated RMS/point after tbe alignmentis 9-49 |j.m. Figure 7 represents two surfaces reconstructedusing the minimum curvature metbod witb 81x81 gridsize at a misorientation of 5 degree rotation around alltbree axes between tbe surfaces. Figure 8 gives tbese sur-faces after alignment by the CRA software. The RMS/point as a result of tbis alignment is 12-2 |j,m. Figures 9and 10 show two surfaces after CRA alignment of sur-faces witb a relative 1 degree rotation around tbe tbreeaxes after interpolation of tbe scanned data using theKriging and inverse distance metbods (witb 81x81 gridsize), and yielded RMS/point values of 13-42 and22-94 )a.m, respectively. Figures 11 and 12 sbowtbe tootbsurface with initial relative rotations of 1° and 5° aroundtbe X-, y-, and z- axes, respectively, and subsequentlyaligned after interpolation by minimum curvaturemetbod using 39 x 39 grid size. Tbe RMS/point values(after alignment as seen in Figs 12 & 13) were 22-84 and



Fig. 4. A reconstructed 'before' surface of the molar tooth studied, using minimum curvature interpolation method with 81x81 grid size.

Fig. 5. Two surfaces of the molar tooth reconstructed with a 1° relative misorientation around the x-, y-, and z-, i.e. the 'before' and'after'surfaces superposed. Minimum curvature method of data interpolation with 81 X 81 grid size. • , , ;.

31-45 |j,m, respectively. These results illustrate typicalalignment accuracies as a function of the method ofinterpolation, degree of misorientation and grid size.Table 1 lists the mean and (s.d.) values of RMS/point fordifferent levels of initial misorientation of the surfacesand grid sizes used in interpolation. The data clearlyindicate that the initial misorientation, the interpolationmethod and the grid size used for interpolation may affectthe accuracy of alignment. A three-way ANOVA wascarried out to test the hypothesis that these differences arestatistically significant. The summary of ANOVA results are

presented in Table 2. Note that the alignment accuracy isstrongly influenced by the main effects of initialmisorientation, choice of the miethod of interpolationand the grid size used in the interpolation and, in addi-tion, selected interaction effects (two-way interactioneffects of method* grid size, and grid size* misorientation)are significant at P < 0-02. Duncan contrasts of the meanRMS/point values, as a function of the different inde-pendent variables (method of interpolation, degree ofmisorientation and grid size) are presented in Table 3.Figures 13, 14 and 15 are bar graphs which show the


30 A. DASTANE etal

Fig. 6. The two surfaces in Fig, 6 after alignment by the CRA program, i.e., the 'before' and 'aligned after' surfaces superposed.

Fig. 7. Surfaces reconstructed with a 5° relative misorientationaround thex-, y- and e-axes, using minimum curvature interpola-tion with 81x81 grid size.

Fig. 8. Surfaces in Fig. 8 after alignment with CRA program, i,e,the 'before'and 'aligned after' surfaces superposed.

influence of grid size and level of initial misorientationon tbe RMS/point in tbe different metbods used in tbestudy. For best accuracy of alignment, tbe initialmisorientation must be low and a finer grid size ispreferred. In addition, tbe minimum curvature methodof interpolation provides superior alignment accuracy,especially when using finer grid sizes. While Kriging

interpolation provides good alignment at finer grid sizes,caution may be needed in using tbe inverse distancemetbod of interpolation prior to alignment.

Discussion

In tbis investigation, we have combined a commercial 3-D



Fig. 9. 'Before' and 'aligned after' surfaces generated by Kriging interpolation with 81x81 grid size and aligned by the CRA programafter a relative misorientation of 1° around the x-, y-, and z-axes.

Fig. 10. 'Before' and 'aligned after' surfaces generated by the inverse distance method of interpolation with 81x81 grid size andaligned by the CRA program after a relative misorientation of 1° around the x-, y-, and z-axes.

graphic software package with a public domain data-fittingprocedure to visualize, reconstruct, align and overlay anatomicsurfaces of tissues. A Pascal program written inhouse helpedto communicate between the 3-D graphic softwarepackage and the data-fitting program in a user friendlyway, and also facilitated data transformation resultingfrom controlled translation and rotation of the surface. Thevisualization, reconstruction and overlay capabilities ofthe 3-D graphic package and the surface alignment capa-bility of the data-fitting program have been combined veryefficiently. The procedure developed in this investigationmay be an effective model for future surface reconstruc-tion, visualization, alignment and overlay of tooth surfaces.

The mathematical algorithms used for interpolation tocreate a grid of uniformly spaced data points appear toinfluence the accuracy of subsequent alignment usingthe simplex algorithm. These differences may arise fromthe characteristics and/or limitations of the interpola-tion techniques used for surface reconstruction in thealgorithms and the role of grid size in determining theselimitations in eacb of the methods. In addition, tbeextent of initial misorientation may influence tbesolution wben using the simplex algorithm for align-ment. The grid size* misorientation interaction effect alsoappears to be significant (?< 0-0001), indicating tbattbe influence of grid size is not uniform at all levels of


32 A. DASTANE etal

Fig. 11. 'Before' and 'aligned after' surfaces generated by the mini-mum curvature method of interpolation with 39 x 39 grid size andaligned by the CRA program after a relative misorientation of 1°around the x-, y-, and z-axes.

Fig. 12. 'Before' and 'aligned after' surfaces generated by the mini-mum curvature method of interpolation with 39 x 39 grid size andaligned by the CRA program after a relative misorientation of 5°around the x-, y-, and z-axes.

misorientation. Similarly, the influence of grid size is notuniform in the different methods used because thereappears to be significant grid size* method interactioneffect (P<0-02).

50

40

•E 30o

a .

to

on20

10 -

Interpolation Method: Inverse Distance

Grid Sin

51x51V///////A 63x63Y///A 81x81

I1 degree 3 degrees

Level of Misorientation5 degrees

Fig. 13. Bar graph of RMS/Point as a function of level of initialmisorientation and grid size using the minimum curvature method.

It is also important to assess the effectiveness of thenew system to follow surface changes in a clinicalsituation. In reconstructing tissue surfaces from castsprepared from impressions of teeth in 50 clinical cases,only a maximum misorientation of about 0-017 radian(approximately 1 degree) around the three axes has beenreported by other authors (DeLong & Douglas, 1990).At this level of misorientation, the accuracy of align-ment (RMS/point) in the minimum curvature method,for example, was as low as 9-49 |im at a grid spacingof 175 jimand as high as 21-04)i.m at a grid spacing of370|Ltm. Improved accuracy associated with smaller gridsize comes unfortunately at the expense of dataprocessing of time. A finer grid size increases the timeof interpolation. However, in the case where initialmisorientation is low (as is the case with clinicalreconstructions), the time needed for sufficientlyaccurate software alignment is not an overridingconsideration. While we have not studied the effect ofthe number of interpolated points used for alignment,a minimum of 500 points was used in this study. Inorder to keep the initial misalignment relatively low,a mechanical alignment using reference recess pointshave been used in the past. Such mechanical align-ment can presumably be further improved by softwarealignment.

Conclusions

Three-dimensional digitization using a MTS biome-chanical test system with an artificial mouth and profilerassembly have been combined with commercial and



Table 1. Mean and (s.d.) values ofRMS/point (in |j.m) for different levelsof misorientation and grid sizes

Table 2. Summary of ANOVA resultsfor the defined classes

Gridsize

1° misorientation

MC

mean(s.d.)

KG

mean(s.d.)

ID

mean(s.d.)

3° misorientation

MC

mean(s.d.)

KG

mean(s.d.)

ID

mean(s.d.)

5° misorientation

MC

mean(s.d.)

KG

mean(s.d.)

ID

mean(s.d.)

81 x81

63x63

51 x51

39x39

Source

9-47(0-24)11-83(0-77)14-37(0-90)21-05(1-38)

12-59(0-85)16-32(0-82)19-21(0-79)23-13(1-51)

23-81(0-87)27-60(1-93)27-16(1-12)32-72(2-83)

11-88(1-09)14-62(0-54)16-43(1-25)28-63(1-46)

13-64(0-53)16-08( M l )20-59(1-77)31-26(1-27)

23-62(0-49)29-30(1-69)29-93(3-07)42-10(2-24)

12-21(0-13)17-45(0-90)20-33(1-12)30-65(1-26)

15-44(1-15)19-59(1-61)23-99(1-49)31-03(1-51)

24-24(0-78)31-93(1-78)34-74(1-51)44-60(2-69)

Degree ofFreedom Mean square F value Pr >F

MethodGrid sizeMisorientationMisorientation*grid sizeMethod*grid sizeMisorientation*method*grid sizeMisorientation*method

23266

12

1844-791134-79282-46

36-945-762-35

1-98

876-84539-37134-2517-562-741-12

0-00010-00010-00010-00010-01880-3605

0-94 0-4458

Table 3. Duncan's contrast forRMS/point value as a function ofmisorientation, method and grid size

Misorientation

Misorientation

n1

3

5

Samplesize

36

3636

Mean(l^m)

19-9423-1725-52

Methoc

MC

KGID

Method

Sample1 size

36

36

36

Mean(^m)

17-4120-2430-98

Gridsize

81 x8163x6351 x5139x39

Grid size

Samplesize

27

27

27

27

Mean(M-m)

16-3220-5322-9731-69

public domain software systems to visualize and recon-struct the anatomic surfaces of dental tissues. In thisinvestigation, the overall system was assembled andtested for accurate reconstruction and alignment ofsurfaces after a small relative misalignment. The resultsof this study suggest that the method of interpolationused to obtain a uniformly spaced grid of data points fromraw data and the extent of misalignment of surfaces maysignificantly influence the accuracy of alignment, but the

accuracy obtained under optimized choice of conditionsis remarkably high.

Acknowledgments

This study was supported by grant nos ROl DE08024-06and S10RR04216-01 from the Dental and ResearchResources Divisions, respectively, of the NationalInstitutes of Health, Bethesda, Maryland, U.S.A.


34 A. DASTANE etal

50

40

.E 30o

Q_

CO20

10

1 degree

Interpolation Method: Kriging

Grid St»

3 9 x 3 9 ,.,.,: ..,: .-,

51x51 •' ^ 'V///////A 63x63

81x81

3 degrees


Fig. 14. Bar graph of RMS/Point as a function of level of ini-

tial misorientation and grid size, using the Kriging method of

interpolation.

50

40

.E 30o

Q_

20

10

Interpolation Method: Minimum Curvature

Odd Sin

39x395 1 x 5 1 •• ' ' •

63x6381x81

1 degree 3 degrees


Fig. 15. Bar graph of RMS/Point as a function of level of initial

misorientation and grid size, using the inverse distance method.

References

BLOEM, T.J., CZERNIAWKSI, B., LUKE, J. & LANG, B.R. (1991) Determination of

the accuracy of three die systems. Journal of Prosthetic Dentistry, 65, 758.

BRIGGS, LC. (1974) Machine contouring using minimum curvature.

Geophysics, 39, 39.

CACECI, S. & CACHERIS, W.P. (1984) Fitting curves to data. BYTE, 340-

62.

DAVIS, J.C. (1986) Statistics and Data Analysis in Geology. John Wiley

and Sons, New York.

D A S T A N E , A . , VAIDYANATHAN, J . , VAIDYANATHAN, T . K . & H E S B Y , R . ( 1 9 9 1 )

Application of commercial software packages for 3-D surface re-

construction. Journal of Dental Research, 60 (Special Issue), Abstract

no. 1677.

DELONG, R. & DOUGLAS, W.H. (1983) Development of an artificial

oral environment for the testing of dental restoratives: hi-axial

and movement control. Journal of Dental Research, 62, 32.

DELONG, R. & DOUGLAS, W.H. (1990) Quantitative assessment of ana-

tomical change in human dentition. Proceedings of the 12th Annual

International Conference of the IEEE Engineering in Medicine and Biology

Society, 12 (Part 5), 2054.

DELONG, R. , PINTADO, M . & DOUGLAS, W.H. (1985) Measurement of

change in surface contour by computer graphics. Dental Materi-

als, 1, 27.

\

DELONG, R. , SAKAGUCHI, R.L., DOUGLAS, W.H. & PINTADO, M . R . (1985)

The wear of dental amalgam in an artificial mouth: a clinical

correlation. Dental Materials, 1, 238.

DURET, E , BLOUIN, J.L. & DURET, B . (1988) CAD-CAM in dentistry.

Journal of American Dental Association, 17, 715.

JONES, T.A., HAMILTON, D.E. & CRALTON, R.J. (1986) Contouring

Geologic Surfaces with the Computer. Von Nostrand Rheinhold Co.,

New York.

MCDOWELL, G.C., BLOEM, T.J., LANG, B.R. & ASGAR, K. (1988) In vivo

wear. Part 1. The Michigan computer graphic measuring system.

Journal of Prosthetic Dentistry, 60, 112.

PINTADO, M.R., CONRY, J.P. & DOUGLAS, W.H. (1988) Measurement

of sealant volume in vivo using image processing technology.

Quintessence International, 19, 613.1.

REKOW, D . (1987) Computer-aided design and manufacturing in den-

tistry: a review of the state of the art. Journal of Prosthetic Dentistry,

58, 512.

SAKAGUCHI, R.L., DOUGLAS, W.H., DELONG, R. & PINTADO, M.R. (1986)

The wear of dental composite in an artificial mouth: a clinical

correlation. Dental Materials, 2, 35.

Correspondence: Dr T.K. Vaidyanathan, Department of Prosthodontics

and Biomaterials NJ Dental School, UMDNJ, New Jersey's University of

Health Sciences, 110 Bergen Street, Newark, NJ 07103, U.S.A.
