N. BALASUBRAMANIANROBERT D. LEIGHTY

U. S. Army Engineer Topographic LaboratoriesFort Belvoir, VA 22060

Heterodyne Optical Correlation(HOC)The basic principles of operation are expressed, anexperimental system is described, and some photogrammetricapplications are considered.

INTRODUCTION

STEREO PERCEPTION results from the detec­tion of stereoscopic parallax, and photo­

grammetric data reduction is based mainlyon the measurement of this parallax differ­ence from stereo-photography. Automatedmeasurement of stereoscopic parallax withphotogrammetric instruments requires: (1)the ability to match corresponding imagesand (2) the ability to measure the parallaxautomatically. Over the last several decades

tern (HOC) is a generalized optical correla­tion system having significant advantages inits application to stereo-compilation. In theHOC, two transparencies forming a stereo­pair are relatively oriented and projectedonto a common image plane where the coin­cidence is detected. By means of heterodyneoptical techniques, the normalized correla­tion coefficient is determined at each ele­ment of a photo diode array detector in thecommon image plane. These correlation

ABSTRACT: A new image-correlation concept based upon opticalheterodyne detection is presented. In the Heterodyne Optical Cor­relator System (HOC), two transparencies are relatively orientedand projected onto a common image plane where coincidence is de­tected. By means of heterodyne optical techniques, the normalizedcorrelation coefficient is determined at each element of a photodiode array detector in the common image plane. These correlationvalues are used to define regions of corresponding image coinci­dence for a given x-parallax condition. The basic principle of theHOC operation is expressed and an experimental system described.Potential applications for stereocompilation and cartographic fea­ture extraction are briefly described and several other applicationsare listed. The unique features of the HOC as an area correlationsystem are included.

many techniques have been proposed anddemonstrated for matching correspondingimages. In electronic stereo-compilation sys­tems, the pictorial information is convertedto electrical signals and the correlation isperformed in the time domain. Thesetechniques are well documented in theliteraturel - 2 . The system described in thispaper is an optical correlation system thatachieves correlation in the space domain.

The Heterodyne Optical Correlation Sys-

values are then used to define regions of cor­responding image coincidence for a givenx-parallax condition.

The objective of this paper is to present asimple description of the HOC as it may beused in stereo-compilation. A brief descrip­tion of other applications of the HOC is alsoincluded. The discussion begins with thetheoretical basis for the determination of thenormalized correlation coefficient in theHOC. This is followed by a description of

1529PHOTOGRAMMETRIC ENGINEERING AND REMOTE SENSING,

Vo!. 42, No. 12, December 1976, pp. 1529-1537.

1530 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING, 1976

the basic HOC configuration compared witha double-projection direct-viewing photo­grammetric plotting instrument. The ex­perimental HOC is described and its opera­tional characteristics are outlined. The gen­erality of HOC is emphasized by specific po­tential applications. Finally, a summary ispresented of the HOC features that are un­ique to its applications for stereo­compilation. A detailed description of thehardware implementation of the entire sys­tem is not included in this paper.

For purposes of abridgement, no detailedreview of various optical correlationschemes based on coherent optical process­ing techniques is presented in this paper.Such reviews can be found in the litera­ture.3 - 5

PRINCIPLE OF OPERATION

The general two-dimensional functioncorrelating images on transparencies 1 and 2has the form:

PI2(XO, Yo) = fAfT1(x,Y) T2(x + xo, Y + Yo) dA

(1)

where Tlx,Y) and Tlx,Y) is the intensitytransmittance of the two transparencies andXo and Yo represent the relative displacementbetween the transparencies. The correlationprocess can be thought of as an integrationover a given region A containing the resultsof the multiplication of the two transmit­tance functions. This fundamental operationcan be accomplished by using either elec­tronic, digital, or optical systems. In theHOC, the multiplication is accomplishedduring detection by an element of the detec­tor array.

Let tlxbYl) be the amplitude transmit­tance of one of the photographs. Note thatthe intensity transmittance is simply thesquare ofthe amplitude transmittance. (xbyJis defined with respect to the photo­coordinates of transparency 1. Similarly theamplitude transmittance of transparency 2 ist 2(X2,Y2)' (X2,Y2) refers to the photo­coordinates of transparency 2. In the finalimage plane, the superimposed amplitudedistribution is given by

i(x,Y) = tl(~, JL)+ t2(~ + xo,JL + Yo)k 1 k 1 k 2 k 2 (2)

where

k1(X b Yl) = (x,Y)k2(X2-XO' Y2-YO) = (x,Y)

k 1 and k2 are the magnification factors as-

sociated with the two projectors, and (xo,Yo)represents a translation of the photo­coordinate system 2 with respect to theimage-coordinate system. For simplicity it isassumed that k 1 = k2 = 1. Hence i(x,y) =tlx,Y) + t£x+xo, Y+Yo). The photo detectorsenses the intensity rather than theamplitude. The intensity distribution isgiven by

I(x,y) = Itt(X,y)\2 + It2(x + xo, Y + YoW

+ 2t 1(x,Y) t2(x + xo, Y + Yo) cos 27T {A(X,y)} (3)A

where A is the wave length of the light andA(x,Y) is the optical path difference betweenthe two beams. Figure 1 illustrates the basicsystem configuration. By moving mirror M2

in a periodic manner, the optical path differ­ence A(x,y) can be made a time-dependentfunction.

A(x,y) = Ao(x,y) + cd (4)

Under these conditions the intensity func­tion becomes a time-varying function. Thisprinciple is called heterodyne detection.Equation 3 becomes.

I(x,y) = It 1(x,yW+ It 2(x +xo,Y +YoW+ 2 t1(x,y) t2(x +xo,Y +Yo) cos 27T {Ao(x+y )+at}

A(5)

When a detector senses intensity, it integ­rates the intensity distribution over its aper­ture area A. Hence the detector output atpoint P in the image plane is

S(P) = KfAfI(x,Y;P) dA

where K is a constant of proportionality de­pendent on the photo detector.

S(P) = K[IAfltl(X,Y)12 dA

+ fAflt2(X+XO, Y+Yo)1 2dA

+ 2fAftt(x,y) t2(x+xo,Y+Yo) cos (6)

27T{Ao(X,Y) + at}dA]A

The first two terms of the above equation ared.c. signals, whereas the third represents ana.c. signal at the frequency (alA).

If Aix,Y) is essentially constant over thedetector aperture area A, the maximumamplitude ofthe a.c. signal can be written as

HETERODY E OPTICAL CORRELATION (HOC) 1531

LASER

=t=:pTa IMAGEPLANE

"1'"2" ."IRRORS~,B2" .BEAM SPLITTER

1,L2•••B~;~~ANDIKG

T1 ,T2 ···TRANSPAREKCIESL) ••••••IKAGIHG LEKSP•••••••PHOTODETECTORD•••••••PIEZOELECTRIC DRIVE

FIG. 1. Optical system configuration for correlation coefficient measure­ment.

As shown in Equation 1 this form representsan amplitude correlation signal for the dis­placement (xo,Yo)' Existing correlationschemes rely on selection of the maximumvalue of S(P) to determine correspondingimage coincidence at point P. Selection of alocal maximum can lead to false correlation.For the HOC, however, two additional meas­urements permit normalization of the abovefunction and significantly reduce the possi­bility of false correlation. When only trans­parency 1 is illuminated, the d.c. signal isgiven by

Similarily, when transparency 2 is illumi­nated,

t1(X,y) = (a constant) (t2(x,Y))

Also the normalized correlation functionC I£Xo,YO) monotonically decreases when Xoand Yo are increased.

The derivative of the normalized correla­tion function depends upon the image struc­ture and contrast of the images being corre­lated, and it determines the accuracy ofparallax measurement. By determining thedisplacement (xo,Yo) necessary to achieve amaximum value for the normalized correla­tion coefficient, it is possible to determinethe parallax difference associated with theimage point P. By using a detector array inthe image plane, measurements can be madesimultaneously over a two-dimensional arrayof points P.

EXPERIMENTAL HOC

Consider a double-projection, direct­viewing photogrammetric plotting instru­ment. It represents a simple and direct solu­tion to the problem of forming an analogic,three-dimensional, accurate stereomodel ofthe earth's surface from two-dimensional ae­rial photographs exposed as stereopairs. Thebasic components of this system include apowerful illumination source, a precise pro­jection system, a discriminating viewing sys­tem for accurate observation of dual pro­jected images, and a system for precise meas­urement and delineation of the images. Inorder to form the stereomodel in the systemit is necessary to construct the same perspec­tive relationship between the pair of trans­parencies in the projectors as that existing inthe aerial cameras at the times of exposure.This process of relative orientation is fol­lowed by mutual adjustment of the projec-

(9)

(10)

[fAf It1(x,Y) 12dA fAf It 2(x+xo,Y +Yo) 1

2dA] y,

Sa(P)

c I2(Xo,Yo;P)

fAft1(x,y) t1(x+xo,Y+Yo) dA

With these three measurement values thenormalized correlation coefficient can becomputed for a given (xo,Yo) separation be­tween transparencies from

The two-dimensional function C llxo,Yo)has several important properties. For exam­ple, it is generally a symmetric figure withits maximum value equal to one when thecorresponding images are perfectlymatched. Ideally, then,

1532 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING, 1976

tors in order to bring the model to the correctscale and relationship to a datum plane.Measurement within the projectedstereomodel usually involves the determin­ing of coincidence or zero parallax for ag}ven point in the model by placing a float­ing mark in contact with a point on the appar­ent surface of the model as viewed on theplaten. The horizontal and vertical positionof the point can then be measured at thescale of the projected model.

Now consider the conceptual implementa­tion of the basic HOC as illustrated in Figure2 to be analogous to the double-projection,direct-viewing photogrammetric plottingsystem discussed above. The basic compo­nents of this system include a powerful il­lumination source, the laser; a precise pro­jection system consisting of two image pro­jectors; a discriminating sensing system foraccurate optoelectronic viewing of selectedaspects of the dual projected images; and anelectronic photo diode array detector servingas a precise measurement system. Astereomodel is not formed in the HOC, how­ever. Each projector system serves as a rec­tifier to correct for scale, tip, and tilt, andthe combined rectified images from both theprojectors are superimposed in the imageplane. Relative orientation of the trans­parencies in the projectors results in the re­moval of y-parallax. Then x-parallax as­sociated with each point in the image planeis determined by measuring the relative

x-displacement necessary to obtain themaximum value of the normalized correla­tion coefficients. The x-parallax values canthen be converted to represent terrain eleva­tions.

In order to satisfy the assumption as­sociated with Equation 3 dealing with mutu­ally coherent images over its correlationarea, the two projectors are illuminated in anoptical system configured as a Mach­Zehnder interferometer. The effect of thisarrangement, when the optical system isslightly detuned, is to create a stationaryfringe modulation of the superimposed im­ages. The fringe spacing should be largerthan the detector aperture to make t:.cf.x,Y)constant over the aperture so that, at pointswhere the correlation is maximum, thefringe modulation has a maximum value.This satisfies the assumption related to Equa­tion 7. Measurement of this fringe modula­tion is accomplished in the HOC by translat­ing a mirror in the Mach-Zehnder inter­ferometer, as shown in Figure I, and simul­taneously measuring the time-varying inten­sity function in the image plane. Detectionof the modulated signal at any point in thesuperimposed image plane forms the basisfor the heterodyne optical correlator and ef­fectively increases the signal-to-noise ratioin detection by several orders of magnitude.

Changes in the normalized correlationvalue are caused mainly by the image struc­ture associated with the two photographs,

DETECTORARRAY

PROJECTOR II

I rI I, J

PROJECTOR I

PHASEMODULATOR

TO ELECTRONICS

FIG. 2. Basic heterodyne optical correlation system.

HETERODYNE OPTICAL CORRELATION (HOC) 1533

whereas the average transmittance has aconstant bias level contribution to the corre­lation value. The ability to locate themaximum value of the normalized correla­tion coefficient can be enhanced by remov­ing this bias level contribution. In the elec­tronic correlation systems this is ac­complished by d.c. filtering of the video sig­nals. In the HOC the bias level is removedby placing a small, non-transmitting lightblock on the optical axis of the two projec­tion systems so as to remove the undiffractedlight from the transparencies. Then dif­fracted light, representing the image struc­ture, is allowed to pass through to the finalimage plane.

False correlation possibilities are signifi­cantly reduced in the HOC by computing thenonnalized correlation coefficient given byEquation 10. In order to accomplish this, themodulated intensity value defined by Equa­tion 7 is first measured. Values correspond­ing to Equations 8 and 9 are then deter­mined for the individual projectors bymeasuring the intensity distribution over theimage plane due to each projector whenlight from the other projector is blocked.Within the computer, the normalized corre­lation coefficient is then computed. Thiscoefficient has a maximum value of 1; how­ever, terrain slopes cause perspective differ­ences between stereoimages which can re­duce this value.6

The area of correlation can be determined

by projecting the elemental detector areabackwards through the optical system ontothe transparencies. This area is analogous tothat defined by the raster pattern in a con­ventional CRT-based electronic correlationsystem such as the UNAMACE or AACE.Resolution of the image at the commonimage plane (as defined by the transfer func­tion of the imaging optics) is analogous to thespot size of the flying spot CRT scanners inthe electronic correlation systems.

Actual implementation of the HOC prin­ciple to stereocompilation problems has re­sulted in an experimental system somewhatdifferent from that of Figure 2. The experi­mental system, shown schematically in Fig­ure 3, differs mainly in simplifications tothe optical system. For example, the basicoptical configuration remains that of aMach-Zehnder interferometer; however, thetwo-projector optical system has been re­placed by a single imaging system. Thischange is necessitated by the relative sizesof the illuminated transparencies and the de­tector array. The illuminating beam has adiameter of about 5 cm at the plane of thetransparencies, and the final image lens pro­jects the illuminated transparencies onto thedetector plane with a 5x reduction. TheRETICON photo diode array detector has amatrix of 50 by 50 elements and an overallsize of about 0.2 by 0.2 inches. Each transpar­ency is mounted on a photo-carriage capa­ble of translation along three axes, and the

""w

5

EXPERIMENTAL HOC SYSTEM

ILLUm NATI NGOPTICS

ILLUMINATINGOPTICS

Sl' S2······SHUTTERSTl' T2."". TRAflSPARENCIESM , PHASE MODULATORD ,.. ,., .DETECTOR ARRAYL3' L4 IMAGING LENSES

MICROSCOPE

FIG. 3. Schematic of experimental HOC system.

1534 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING, 1976

plane of the transparency can be rotatedabout its normal axis. The final beamsplitteris symmetric. Thus, any aberrations intro­duced by this element in the imaging pro­cess have the same effect in both projectedimages. Operation of the experimental HOCsystem is controlled by an HP-21MX mini­computer. The computer system sequen­tially operates the shutters in the two arms ofthe interferometer to permit selective il­lumination of the transparencies, and it re­cords the necessary array detector data andcomputes the nomlalized correlation coeffi­cient for each detector element.

The final beamsplitter has two outputbeam paths nOlmal to each other. One beampath, as described above, is directed to thearray detector. The other beam path permitsvisual examination of the common imageplane with a lOOx microscope mounted on athree-axis stage for initial relative orienta­tion of the two transparencies.

The system characteristics of the experi­mental HOC system are (a) The spatial res­olution of final imaging system at the planeof the transparency is approximately 25lines/mm. Empirically, it has been deter­mined that only the low spatial frequenciesare of importance in image matching. Thecontribution of the high spatial frequenciesis of the same order of magnitude as the sys­tem noise and, hence, is of no consequence.(This subject matter will be elaborated in asubsequent paper.) (b) Given the above spa­tial resolution, the depth of focus associatedwith the final imaging optics is such that thesystem can accommodate transparencies thathave 4X scale differences. (c) An individualdetector aperture is 60 by 90 micrometres.This represents a correlation area of 300 by450 micrometres on the transparency. (d)The least count of the translational stages is3.2 micrometres.

HOC ApPLICATIONS

APPLICATION I-STEREOCOMPILATION

Because of the extreme geometric fidelityof the detector array, each elemental area de­fines a precise location on the transparency.By using a grid plate for initialization, it ispossible to relate precisely the coordinatesystem of the array elements to that of thephoto stages. The procedure for compiling astereomodel is as follows: with the use of themicroscope, the two transparencies repre­senting the model are relatively orientedand the x-parallax direction is made to cor­respond to the x-axis of the translationalstages. During the relative orientation pro-

cedure the two transparencies are adjustedessentially for tilt, tip, and scale. In addition,the relative orientation of the array ori. thephoto-coordinate system is determined. Theinstrument is adjusted for the coincidence ofthe control imagery representing the datum.The x-parallax is introduced in incrementalsteps, and the normalized correlation valueat each element of the array for each step isdetermined. The resultant data can be rep­resented in a three-dimensional form shownin Figure 4. It is clear then that, by examin­ing the histogram of the normalized correla­tion coefficient as a function of x-parallaxsteps, it is possible to define uniquely thex-parallax associated with any given elementofthe array. The final output of the processoris a two-dimensional matrix of x-parallaxvalues representing two-dimensional ele­mental areas defined by the array (Figure 5).It is to be noted here that these x-parallaxvalues relate to the photo-coordinate systemof the stationary transparency, but they caneasily be transformed to elevation in theground coordinate system. The effects of re­sidual v-parallax and perspective slope(within limits) are to reduce the maximumvalue of the normalized correlation value;however, these do not introduce errors in thex-parallax measurement. By translating thecommon image plane with respect to the de­tector array, the compilation can be ac­complished over the entire stereomodelarea. This data reduction approach in theHOC not only enables one to overcome op­erational limitations such as slope effects

FIG. 4. Normalized correlation coefficient data inthree-dimensional fonn (shown here to have 8parallax submatrices).

HETERODYNE OPTICAL CORRELATION (HOC) 1535

3

FIG. 5. Find output data matrix. A two­dimensional matrix of values representingx-parallax wherein numbers for each matrix ele­ment represent parallax submatrix of Figure 4 atwhich maximum correlation was detected.

and residual y-parallax, but also permits po­t~ntially high speed of operation.

APPLICATION 2-CARTOGRAPHIC FEATURE

EXTRACTION

tion at the same time or in the same manneras the elevation image. Feature extractionprocessing can be accomplished sequentialto elevation extraction with the sameminicomputer or parallel to elevation extrac­tion with separate minicomputers operatingunder a master program.

The applications presented above repre­sent only a sample of the many potentialuses in photogrammetric and mapping oper­ations. For example, other applicationscould include change detection, photo­mission plotting, generalized feature extrac­tion in conjunction with an optical power­spectrum analyzer, and automatic pass-pointselection and measurement. Of particularvalue in mapping because of its simplicityand high speed of operation, the HOC sys­tem should have advantages as a correlationprescreener for an advanced digital photo­grammetric compilation systems. The HOCoutput can be used for a rapid first estimateof terrain elevations. By proper processing ofthe output, areas of weak or no correlationdue to shape distortion, poor image structureand quality, etc., can be delineated.

1 5 6

X-DISPLACEMEIIT (IN MILS)

FIG. 6. Variation of normalized correlation coef­ficient as a function of x-parallax betweenstereoaerial transparencies.

EXPERIMENTAL RESULTS

The performance of the HOC system hasbeen evaluated by using laboratory modelsas well as selected aerial transparencies. Fig­ure 6 shows the variation of the normalizedcorrelation coefficient as a function of paral­lax between conjugate images of stereoaerialtransparencies. The correlation area on thetransparency is about 1 millimetre square.

The experimental HOC system, describedin Application 1 above, can be adapted toprovide an experimental system for auto­mated cartographic feature extraction. Thisadaptation can be accomplished by placing aphoto-diode array detector in the imageplane of the projection system occupied bythe microscope in Figure 3. Call the HOCdetector array At and this second array A 2 •

When A2 is registered with A I> the systemhas the potential of providng photogrammet­ric elevations and a pseudoderivative imageof the stereotransparencies from AI; andfrom A2 an unprocessed gray scale imagefrom either of the stereotransparencies isavailable. The elevation image and the as­sociated gray scale image provide informa­tion similar to that available to a photo in­terpreter when studying corresponding im­ages with a stereoscope. With these datatypes, digital pattern recognition softwarecan be prepared to investigate extraction ofcartographic features for map symbolization.For example, vegetation, roads and railroads,structures, drainage, water, etc., can be clas­sified from the data ofAt andA2 and stored inmemory pages representing color-separationmanuscripts.

When the A2 gray scale image associatedwith the perspective elevation image on AIis used for pattern recognition processing,the extracted feature data can be geometri­cally corrected to an orthographic presenta-

"

1536 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING, 1976

The HOC system has been used in thestereocompilation mode with stereopairs ofalaboratory model and the results indicatethat parallax measurement accuracies of 5 to10 micrometres are possible in favorableimage areas. Difficulties were encounteredin areas without image structure and also inareas with steep slopes, as would be the casewith any automatic stereocompilation sys­tem.

The HOC system also has been evaluatedin the stereocompilation mode by usingidentical aerial transparencies, but with arti­ficially generated parallax. For a case involv­ing 1:30,000-scale imagery and a correlationarea of 300 by 450 micrometres, very goodand reproducible results were obtained.With a least count measurement of parallaxof 25 micrometres, correlation ambiguity re­sulted in only 15 out of 1,024 elemental areas(using a 32 by 32-element array).

Results with aerial stereotransparenciesare very encouraging but too preliminary toreport in this paper. In an intensive testingprogram, the instrument will be subjected toan extensive performance evaluation in thestereocompilation mode by comparing theresults obtained with manual stereocom­parator measurements made on an array ofgrid points on the transparencies. These re­sults will be presented in detail at the con­clusion of the tests.

UNIQUE FEATURES OF HOC

As an optical correlation system, the HOChas inherent advantages in higher signal­to-noise ratio, greater spatial resolution, andincreased speed of operation than other op­tical and electronic correlation systems usedin photogrammetric data reduction.

As a correlation system the HOC has sev­eral unique features that include:

(1) Similarity between different regions onthe two transparencies is determined onthe common image plane and not on theplane of the transparencies. This meansthat the two transparencies can be indi­vidually adjusted for changes in scale, tip,and tilt during the projection process sothat they are made to correspond at thecommon image plane. The two individualprojection systems can be thought of asconventional projection rectifiers involv­ing nothing but simple projection optics(no anamorphic correction optics re­quired).

(2) The output of the system is a normalizedcorrelation coefficient that is independentof the individual density levels of thetransparencies. This also avoids the prob­lems of spurious correlation peaks.

(3) The correlation between the two trans­parencies is detected as the amplitude ofasingle frequency a.c. signal. Because ofthis, measurement can be made with highsignal-to-noise ratios. The correlationoutput represents the correlation betweenthe amplitude transmittance rather thanthe intensity transmittance (square of theamplitude) of the transparencies. Hence,there is an increase in the effectivedynamic range of image structure infor­mation that can be utilized during the cor­relation process.

(4) Because of the system configuration, thetransparencies can be on film rolls orplates and require no liquid gates.

(5) The system can operate with partiallycoherent light sources such as high­pressure mercury arc lamps. The laser inthe HOC is being used only as a bright,monochromatic light source.

(6) Because the transparencies are imagedonto the array with only one imaging sys­tem, the geometric fidelity can be main­tained to meet photogrammetric stan­dards. No complex optical hardware isutilized in the system.

SUMMARY

In this paper a new correlation conceptbased on optical heterodyne detection ispresented. The basic principle of operationis expressed, an experimental HOC systemis described, and its system characteristicsare outlined. Potential applications of theHOC system for stereocompilation and car­tographic feature extraction are briefly de­scribed. Several other applications arelisted. The unique features of the HOC sys­tem as an area correlation system are in­cluded. Judging from the results obtainedfrom the experimental HOC system, the sys­tem appears to have great potential for pro­cessing aerial imagery. Detailed photo­grammetric investigation of the HOC systemconcept is being accomplished, and resultswill be presented later.

ACKNOWLEDGMENTS

The initial research was done at the Insti­tute of Optics, University of Rochester, byDr. N. Balasubramanian under a contractfrom the Research Institute, U. S. Army En­gineer Topographic Laboratories(USAETL)6. The bulk of the developmentwork has been carried out at the Center forCoherent Optics, Research Institute,USAETL, with Dr. N. Balasubramanian as acontractor-in-residence. Hardware andsoftware support for the minicomputer as­sociated with the HOC system was providedby Dr. W. Seemuller of the Research Insti-

HETERODYNE OPTICAL CORRELATION (HOC) 1537

tute. The initial photogrammetric analysis ofthe system has been conducted by Dr. E. M.Mikhail of Purdue University. Further de­velopmental work is continuing at the Re­search Institute.

REFERENCES

1. Thompson, M. M. (Ed), 1966, Manual ofPhotogrammetry, American Society of Photo­grammetry, Falls Church, VA, Chapter 15.

2. Kowalski, D. C., 1968, "A Comparison of Op­tical and Electronic Correlation Techniques",Bendix Technical Joumal, Summer 1968, pp.63-71.

3. Balasubramanian, N., and R. D. Leighty, (Ed),1974, Coherent Optics in Mapping, SPIEProceedings, Vol 45.

4. Bennett, V., 1974, Coherent OpticalTechniques in Stereo Photography, Ph.D.Thesis, University of Rochester.

5. Wertheimer, A., 1974, Optical ProcessingTechniques for Contour Generation fromStereo Photographs, Ph.D. Thesis, Universityof Rochester.

6. Balasubramanian, N., and V. Bennett, 1975,Investigation of Techniques to GenerateContours from Stereo Pairs, U.S. Army En­gineer Topographic Laboratories, ReportETL-0029.

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