S. A. VERESSJ. N. HATZOPOULOS

University of WashingtonSeattle, WA 98195

A Plotting Instrument forClose-Range PhotogrammetryThe design, calibration, and operation of a stereo plotteremploying Balplex projectors and suitable for close-rangestereo and mirror photography is described.

I"TRODUCTIO:-i

M ANY ARTICLES have been published inprofessional literature which report

the development and application of close­range photogrammetry to the bio-medicalfield. In 1974 a Bio-photogrammetricLaboratory was established at the Universityof Washington as a result of a grant given bythe National Science Foundation for bio­medical research. In this Bio photo­gram metric Laboratorv, the camera s\'s­tem has been estahlish~d. The description

There are different types of instrumentsavailable at the University of Washingtonwhich can be used for measurement andplotting of photographs taken bv these men­tioned cameras. Thesc instruments are theOMIAP/C analytical plotter, the Zeiss 1818stereocomparator, a Kclsh plotter, se\'eralBalplex plotters, etc. Of these, the AP/Canalytical plotter and Zeiss 1818 stereo­comparator are used basically for hio­medic,\1 purposes when high accurac\' inmeasurement is required. These instru-

ABSTRACT: A Biomedical Laboratory was established at the Univer­sity of Washington with a grant from the National Science Founda­tion. During research conducted in this laboratory, there was a needfor graphical plottingfor facial studies andfor amputees. To proVidethe most economical means for such mapping, a new plotter wasdesigned and fabricated from available parts of a Balplex plotter.The instrument is an affine restitution plotter. The calibration pm­cess and the achievable relative accuracy are described. The instru­ment is capable of mapping, using close-range stereo-photographswith fixed orientation elements as well as variable orientation ele­ments. Mirror photographs also can be accommodated. Thus a com­plete three-dimensional mapping of the subject can be ac­complished.

and the application of such a system has al­ready been reported (Veress and Tiwnri,1976).

In this article one of the instruments con­structed at the Universitv ofvVashington forbio-medical purposes will be described. Thecamera system consists of three metric MK70 mm Hasselblad cameras, two of whichhave been blctory matched, having the samefocal length and nearly the same characteris­tics of distortion.

ments, of course, can be used only in con­nection with analytical photogrammetricmethods and the~' provide graphical or nu­merical data output showing one or moreviews of the object photographed, but the~'

take more time and cost more than the clas­sical photogrammetric method. vVhen loweraccuracy is acceptable, as is often the case,the time and cost can be considerably re­duced by employing the stereo-plottingmethod which uses another group of instru-

273PHOTOGRAMMETRIC ENGINEERIl'G AND HEMOTE SENSING,

Vol. 44, No.3, March 1978, pp. 273-283.

274 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING, 1978

ments, such as the Balplex plotter. There areman~' such applications in the bio-medicalfield lor graphical plotting. Among others arethe mapping of the human stump for below­the-knee amputees ("erces, Tiwari, andI-latzopoulos, 1976) and a number of Elcialstudies when the required accuracy need nothe more than ± 2 mm. These graphical datawere necessary to evaluate the effect of theshape of the stump for physiological supportof the prosthesis or for the various types ofElcial studies which will be presented laterin this article.

In so many cases the object has to be map­ped, not only from one view but also in all ofthe three-dimensional views. Therefore, athree-dimensional map of the stump or thehuman Elce has to be compiled. For thisreason, a system of mirror photography wasdesigned and used in connection with themodified stereo-plotter to be described.

The laborator~' could not afford thepurchase of a complex camera and plotters"stem that would accommodate all of thesetasks. It was, therefore, necessary to design aplotter around the available material and toElbricate it, using the minimum amount ofresources aqlilable, in order to be able toundertake the studies of motions of thehuman body and to solve the problems al­read~' mentioned.

CO:\'SIDERATIOi\'S FOR THE DESIGi\'

The Bio-photogrammetric Laboratory hasto accommodate and thereby producephotographs from various sizes of objects,ranging from 2 or 3 inches to the full lengthof the human body. Provisions thereforewere made for the taking of stereo photo­graphs. The base length of these stereocameras also varied. However, the one mostused was the one which has 0.6 meterlength. The focal length of the cameras is61.34 mm. However, when they are focusedfor the finite distance, the principal distanceis 63.89 mm for each camera.

The following are the design criteria usedfor the reconstruction of the photographstaken h,' these cameras:

• ~Iake the plotting for the Biophoto­gram metric Laboratory as ('1st as possiblehy using fixed orientation elements.

• Assure an accuracy between ± 2 mm.• Perform the plotting from mirror photog­

raph. without making changes in theorientation of the projectors.

• se optical projection systems withBalplex equipment which is available atthe University of Washington. This equip­ment is composed oftwo Balplex projectors

of 760 mm, a diapositive centering device,and a metallic bar for the accommodation ofthe base of the projectors. The Balplex pro­jectors were preferred because they have aprincipal distance close to the cameras'focal length. They also have efficient mag­nilkation and depth offield, thus giving theleast amount of affinity.

If one wants to construct the spatial modelofthe object to be photographed by these cam­eras in a Balplex projector, the construction ofsuch a model can he onl,' an affine restitutionbecause the principal distance of the instru­ment (f;) is different from that of the camerafocal length (n. Therefore, the ratio is

(1)

The am ne factor, therefore, is

a = 63.89 = I.l6 (2)55

As was mentioned earlier, a criterion forthe new design was that it should be able toreconstruct mirror photography. The princi­ple of mirror photography was first de­veloped by Dr. Kratky of the National Re­search Council of Canada and was used inconnection with bio-medical photogram­metry (Kratky, 1975). He used an analyticaltransformation and an analytical approach tosolve the bio-medical problems. In this arti­cle, a graphical transformation will be usedto obtain the mapping from the mirrorphotographs.

GEOMETRY OF THE MIRROR PHOTOGRAPHY

AND PLOTTER ARRAi\'GEMENT

The general geometry of the mirrors isshown in Figure 1. The optimum objectspace is about 0.32 meter by 0.15 meter.The angle between each mirror and the re­spective camera axes as shown in this figureis 53°. Due to the mirror images, there arethree objects as shown in the figure. The firstis the middle object which is the actual sub­ject. The second one is regarded as theL-object and is a mirror reflection of the ob­ject and the third is regarded as the R-objectand is also a mirror reflection of the object.The expression of M-, L-, and R-object usedin this paper will stand, furthermore, forsi mpl ification of these minor objects or,more precisely, mirror images. In the case ofthe instrument, similar expressions will beused in connection with the establishedstereo model of M, L, and R. The mirrorcoverage ol'the actual object is shown in Fig­ure 2. It is apparent hum these figures that

PLOTTING INSTRUiVIENT FOR CLOSE-RANGE PHOTOGRAMMETRY 275

SCALEzoo 400 600 800 1000 mm

111/16 (lII'1lRA ... '"6 CAMERA

EFT MIRROIf

F,G. 1.

f~63.B'",ma---+--4) - -- -- - - --

Geometry of' mirror photography.

a target on the double overlap area gives twoimages on the same photograph. This con­cept is usehI1 for the coordinate transfOl'lna­tion of L- and R-models to the M-model.This coordinate transformation can be donein two ways. One, for instance, given by Dr.Kratky, is an analytical method and the sec­ond is a graphical or instrumental transfor­mation (Hatzopoulos, 1976). Furthermore,

Figure 1 is a section of the instrument with avertical plane, which means that 1\1-, L-, andR-models in this figure are cross sections ofthe actual plotting. The actual plotting is anorthogonal projection of the three sub­models to a horizontal plane. (See E, or E 2 inFigure 3 and the plotting in Figure 6.) Dueto the fact that Figure 6 is a three­dimensional map, it is always feasible to

Stereo VfeW

FIG. 2. Photographic coverage of'the object.

276 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING, 1978

left pnJi'ec/ar Right pr,!jeetor

blawY" plot/inq lewl ,

£1 er

r--0. imlUT/ (ovtrdge of trdJ:.lng tahlt in [2 position """"

I

FIG. 3. Projection of photographs by the instrument.

make a cross section and create a situationsimilar to Figure l.

Figure 1 shows that the L-object is thesymmetrical of M object with respect to theaxis of symmetry QQ', where QQ' is the in­tersection between the plane of the left mir­ror and the horizontal plane in the objectspace. It becomes the intersection with thevertical plane in the model space. Similarly,the R-object is the symmetrical of M-objectwith respect to the axis of symmetry QQ",where QQ" is the intersection between theright mirror plane and the horizontal planein the object space. The interrelation be­tween the M- and L- objects is that AA' is astraight line perpendicular to the QQ' axis ofsymmetry and IAI I= IA'I I where I is the in­tersection between the AA' and QQ' lines.This interrelation exists between all pointsof M- and L-objects. Similar interrelationexists between M- and R- mirror objects withrespect to the axis of symmetry QQ".

The geometric arrangement of Figure 1 al­lows each camera to "see" all three M-, L-,and R-objects. This is shown in Figure 5.

In conclusion, the assumption can bemade that the cameras are the projectors in aplotting instrument. (Compare Figures 1 and3.) The graphical transformation will be per­formed in the following steps:

(1) Perform the stereo-plotting (Figure 6)(2) Make a cross section similar to Figure l.

This cross section will difler from Figure1 by showing only the mutual visiblepoints from both cameras. More precisely(Figure 2) the cross section of M-modelwill be the "stereo view" line, the crosssection of L-model will be the "left mirrorview" line, and finally the cross section ofR-model will be the "right mirror view"line.

(3) Reconstruct all points of M-model bytransforming graphically the correspond­ing points fi·om Lor R models. This trans­formation can be done as follows: Assum­ing that point A' appears on L model, itscorresponding point A does not appear on1'1 model. To determine point A, draw aline A'A perpendicular to QQ' so thatIA'I I= IAI I where I is the intersectionbetween the lines A'A and QQ' where

PLOTTING INSTRUMENT FOR CLOSE-RANGE PHOTOGRAMMETRY 277

pel

FIG. 4. The plotting instrument.

QQ' is the intersection between the planeof the left mirror and the vertical plane(that vertical plane creates the cross sec­tion). The line QQ' can be located eitherfrom the calibration data of the Bio­photogrammetric Laboratory or by usingthe common points between L-model andM-model. Those points are located in thedouble overlapped areas (Figure 2). Inthis way the point A is determined on theM-model cross section. Similarly allpoints of M-model can be determined.Analogically the entire cross section of Mmodel can directly plot this by a specialinstrument, but this is beyond the scopeof this article.

The new plotter operates the mirrorphotographs in the manner shown in Figure3 by using Balplex 760 projectors. TheBalplex projectors are capable of providingthe maximum accuracy of 1/10,000 at the

photographic distance. This distance in theBio-photogrammetric Laboratory corre­sponds to approximately 2 meters, assumingthe illustrated geometry. In this case, there­fore, the expected accuracy is 0.2 mm, whichceltainly fulfills the design critelia set for thenew Balplex type of instrument. It can beseen in Figure 1 as well as in Figure 3 thatthe general arrangement of the instrument isas follows:

The scale bctor of 2.9 was found to be agood one for plotting mirror photography.Using this scale bctor, the models M, L, andR can be established into an acceptablefocus in the instrument. Assuming that thedistances in the model space are d

"d2 , el,

and pd, the corresponding distances in theobject space are D I , D 2 , D, and PD, as shownin Figure 1. The values of the d" el2 , d, andpd in the model space using the scale of1:2.9 are-

. 150el, = el 2 = = 45 mm

1.16 x 2.9

el 700 = 208 mm approximately1.16 x 2.9

1888---- = 561 mm1.16 x 2.9

where the 1.16 is the previously mentionedaffine bctor and the pel is equal to 561 mm,which is the minimum projection distancefor the projector. The pel plus D equals 769mm, which is about the same as themaximum projection distance tor the project­or. The tracing table optimum vetical cover­age is called dt and is approximately 100mm. The conclusion from these analyses isthat the tracing table cannot cover the total

FIG. 5. Stereo pair of mirror photography for facial study.

278 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING, 1978

L_

L

H_lotJ 111m

lIomm M R

~ ~ ~ ~ {mm]L----'---'_'L----'------'_-i'&:ALE

Th~ wr;lt~n (Ol1lotV-IIf1e niJ.mOer.5 ~hoa/tl he mtJ/lp/itd by j

to "~pr~5ef1t acluLJ.! e/t'Ydt/on" in mm.

FIG. 6. Maps of mirror photography of Figlll'e 5.

depth of the model since the dt is smallerthan d. It can cover only one model, eitherthe M- or the L- and R-models, but not allthree models at the same time. In order,therefore, to satisfy the requirement of plot­ting all three models, it was necessary toseparate the plotting into two plotting levels.These two plotting levels are very well incli­cated in Figure 3 by E I as the upper plottinglevel and E 2 as the lower plotting level.These separate plotting levels are parallel toeach other.

The upper or E 1 plotting level permits theplotting of the M-model. The second plot­ting level is located 200 mm lower whichprovides for the plotting of the L- and theR-models. This vertical arrangement canreadily be seen b'om Figure 3. In this ar­rangement, the model remains within theacceptable depth of focus of the instrument.As a consequence, an optimum accuracy canbe obtained in the reconstruction of thephotograph.

The tracing table is set tlrst on the E 1 plot­ting surhlce which is constructed b'om glassone-half inch thick. In this position the~'I-model is plotted and then after finishingthe M-model, it is moved down to the E 2

plotting surhlce on which the models LandR are plotted. The Ez plotting surhlce con­sists of one-half~inch-thickglass like the E I

plotting surhlce.

SOME PLOTTING EXAMPLES

The plotting instrument is shown in Fig­ure 4 with the actual hame ,md with the

plotting levels. Up to the present time, theinstrument has been used basically for hlcialstudies and for stump studies. For example,the procedure of plotting for mirror photog­raph~1 in general is the same as the proce­dure generally used for conventional photog­raphv. The M-model is plotted at the uppersurbce and since the cameras are in a fixedposition and only use the fixed orientationelements, the base component in theX-direction and the two rotations are neededto orient the model. The scale is set at 1:3position. After plotting the middle model M,two points on the metal bar, where the pro­jectors are located, are marked on the plot­ting paper using a plumb bob. These pointsare used as registers to connect the plottingof the M-model with the plotting of the L­and R-models. The L- and R-models are plot­ted on the E 2 lower plotting surface as fol­lows:

The upper plotting surface or glass ismoved out from its position in order to giveaccess to the lower plotting surbce and theglass plate is moved into the back of the in­strument. The two points on the metal bar, aspreviously mentioned, are marked on theplotting paper which is attached to the lowerplotting surbce. Then the KL and the KII

orientation elements are moved. These tworotations eliminate the very small parallaxexisting in the L- and R-models when com­pared to the M-model. This parallax is due tothe auto collimation effect which will be dis­cussed in a later section. The next step is thescale correction which is done with the Bx ,

PLOTTING INSTRU"IENT FOR CLOSE-RANGE PHOTOGRAM~IETRY 279

base eomponent. The scale correction alsoneeds to be done due to the t~lct of the autocollimation effect. Then the plotting of theL- and R-models on the second surblce isperformed exactly the same wa~' as it is donein a conventional plotter. J\'eedless to sa", allof these models also can be digitized. As aconsequence, therefore, using XY coordi­nates measured on a coordinatogmph, thesemi-analytical method can also be used inconnection with this mirror photogmphv. Afew examples along this line are shown inFigures 5 through 8. Figure 5 shows thephotography of an individual for facialstudies and Figure 6 shows the plotti ng ofthe same individual using that photograph. Aphotograph is shown in Figure 7 of a humanstump and the corresponding plotting of it isshown in Figure 8. The hlcial study wasdone by conventional plotting while thestump study was done by digitizing themodels.

CALIBRATIOi\ OF THE PLOTTli\G I/\,sTRUME:-':T

The reader realizes that this plotting in­strument is a modified Balplex Plotter pro-

viding affine restitution and it is capable ofplotting at two different levels in order toaccomocbte the mirror photographs. Thecalibration process of this instrument is,therefore, roughly the same as a com-en­tional Balplex Plotter which is described indetail in the USGS booklet in the followingsteps:

(1) Calibrating and adjusting the centeringde,·icc,

(2) Positioning the reflector,(3) Positioning the projector bulb,(4) Adjusting the tracing table measuring

mark,(5) Checking the verticality of the tracing

table columns,(6) Checking and calibrating the principal

distance of each projector, and(7) Checking and calibrating the principal

point of each projector.

Steps 1, 2, 3, 4, and ,5 h,lve been performedin exactlv the same wav as described bv theUSGS m·anual. As a co'nsequence, the': willbe omitted here. However, steps 6 ,Ind 7 arediscussed,

Step 6 is the calihration of the principal

­I

+

1~

+ -..AiFIG. 7. Stereo pair for stump study.

280 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING, 1978

FIG. 8. Map from photographs of Figure 7.

FIG. 9. Determining the principal distances.

principal distance modilles the afline hlctorto be equal to 1.1598 instead of the previ­ously mentioned 1.16.

Finally, step 7 is the calibration of the pro­jective center. The principal point of eachprojector was checked and cal ibrated in thewa)' described in the USGS manual.

x

THE ~ID PLATE

--+-4='smm

I

I + 2 ~mm2

y

where

distance for the projector. A grid plate ob­tained hom the Bausch and Lomb Companyis put into the projector and this grid plate isgraduated in 5 mm intervals. The projector isoriented so that the grid plate is parallel tothe plotting surhlce. Points were selected onthe grid plate, two in x and two in y directionwhich are located on the same lines that passthrough the principal point or center inter­section of the grid so that they are located ina symmetrical pattern. The tracing table isset at its lower position with the elevationcounter pointing at h,; the measuring mark iscentered on one of the grid intersections,which is marked on a plotting paper (point1L in Figure 9). Then the next point is mea­sured in the same way (point 2L). After thismeasurement the tracing table is set at itsupper elevation and a new set of points ismeasured (lU, 2U respectively). Using thisnew set of points and similar triangles, theprincipal distance of each projector can bedetermined according to the geometrv of Fig­ure 9:

This equation gives the principal distance ofthe projectors. In this particular instrument,it was found that for the left projector theprincipal distance was 55.086 mill and forthe right projector it was 55.085 111111. This

PLOTTING INSTRUMENT FOR CLOSE-RANGE PHOTOGRAMMETRY 281

ACHIEVED ACCURACY

A desirable test to obtain data on theachievable accuracy would be to photographa controlled test area and compare the coor­dinates of the surveyed points against thosemeasured in the spatial model of the plotter.There are a number of difficulties with thismethod. The first one is to establish the con­trol field with sufficient accuracy in the ob­ject space. Second is the expense involved inestablishing such a control field. There are anumber of articles in professional literaturewhich point out the difficulty of achievingthe desirable accuracy in the ground mea­surements of the control field (Karara, 1966;Veress and Tiwari, 1976). Even if this accu­racy is achieved, there is considerable ex­pense im'olved in the establishment of sucha project with a significant number of pointsto be used for the statistical analysis. Be­cause of this fact and because the plotter willmostly be used for graphical evaluation, itwas decided to evaluate its relative ratherthan its absolute accuracy. The relative accu­racy was obtained by comparing the resultsof the new plotter with those obtained by theAP/C. For this purpose five models withpremarked poi nts were digitized on the newplotter as well as observed on the AP/C. Be­sides these premarked points, observationswere made on unmarked points so that thetotal of 407 points were evaluated on both.

The object space coordinates ofthe pointsobserved by the AP/C were determined byspace resection/intersection. The samepoints were observed on the new plotter andtheir model coordinates were digitized andtransformed to the object space system bythree-dimensional transformation. The con­trol points for space resection were deter­mined by classical "ground" method. Thethree-dimensional transformations of thecoordinates of the Balplex model resulted ina system determined by the coordinates ofthe AP/C. The standard errors obtained fromthe differences between the two systems are

given in Table 1. It can be seen (i'om the testof the five models and li'om the aveage stan­dard errors that the results are acceptableand adequate for nearly all of the bio­medical photogrammetric projects.

CONCLL:SIO,,"S

The analysis of the results indicates thatthe accuracy is adequate for mapping ofstump, for hlcial measurements, for mO\'e­ment studies, and for many other quantita­tive analyses of the human body.

The procedure for stereo-plotting is hlsterand more economical when compared tolnalytical photogrammetry in connectionwith computer graphics.

The major sources of errors of the newplotter are-

• The affine restitution.• The auto collimation point determination.• The degree of non-flatness of the mirrors.

This last effect can be discounted if relati\'emotion of points is studied, that is, themovement of certain points is required. Thisis obtained by comparing two positions ofthe same point where the distortion is thesame in both positions. Thus, its effect isnullified.

The eHect of the auto collimation pointsare described in detail in the USGS manualwhere its model deformation effect is alsoillustrated. This effect could be overcome by"drawing" two additional crosses on the cen­tering device as illustrated by Figure 10. Inthis figure the #146 and #148 refer to theserial number of the cameras by which thephotographs are taken. At present this cor­rection does not exist because of the cost in­vo Ived.

ACK,,"OWLEDG~IE,,"TS

The authors would like to express theirsincere appreciation to the National ScienceFoundation for providing the grant.

The would also like to express their ap-

TABLE l. STANDARD ERRORS OBTAINED FROM AP/C AND NEW PLOTTER IVIEASUREMENTS

Model Model Scale Plotting Level (J.r (mm) (Jy (mm) (J: (mm)

1 1: 1.878 Lower ±0.25 ±0.39 ±1.072 1: 1.864 Lower ±0.43 ±0.59 ±0.983 1: 1.877 Lower ±0.38 ±0.55 ±1.264 1: 1,878 Lower ±0.29 ±0.44 ±0.74

1:3.00 Upper ±0.69 ±0.49 ±1.505 1:3.10 Lower (L) ±0.58 ±0.53 ±1.13

1:3.08 Lower (r) ±0.76 ±0.69 ±2.05Average ±0.41 ±0.51 ±1.l2

282 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING, 1978

iThe '" IQfj didpos'live franl .5ide

(ross /ine~ for lh~ :Ji. 1t/8 dia/7OSitiY!wh,t.h I!. 1d.ced into the ri hi "a.tor

A b5!1 of Ire l"'-e _ball(;)@'"',_I"..c'ry..-....:::I< _

(ra~s Imes of the 'enfer/n device

~ T!Je .. 146 d'apas!f iye front side

FIG. 10. Design for allto-collimation points correction.

prcciation to Dr. Ernest M. Burgess, r-.1. D.,head of Prosthetics Research and his staff atthe Swedish ~Iedical Center for providingpntients and material assistance to executepractical experimentation on the describedpi otter.

This paper is only a part of the larger re­scarch project and the follo\Ving personsha\'e had responsibilities on the project:

Dr. F. G. Lippert, ~d.D., Ph.D., super­\'ised the medical procedures and executionof the research. The major emphasis \Vas onthe surgical technique of implementation ofpermanent land marks into the skeleton sys­tem. Further, he has selected patients, per­formed the required surgery, and evaluatedthe results.

Dr. S. A. Veress, D.Sc., supervised the en­gi neering part of the research. The majoremphasis was on the establishment of theBiomedical Laboratory for general studies,cmphasizing motion studies. Further, hesupen'ised and formulated the process ofx-ray photogrammetrv.

Dr. T. Takamoto, Ph.D., \Vas responsiblefor developing methodology and computerprograms. He executed the experimentationII)]' analvtical and stereo x-ra\' photogram­metJy.

~Ir. R. S. Tiwari was responsible for de­\'eloping computer programs for the analyti­cal process of external photogrammetry.Further, he has performed the calibration ofthe camera b'ame \Vork.

;"Ir. S. A. Feher \Vas responsible for the

design and installation of the c,lmera Ii·ames.r-.'!r. C. H. Schuch \Vas responsible for

further refinements to the x-ray photogram­metn' considering programs and auxiliaryequipment.

:\Ir. J. N. Hatzopoulos was responsible forthe calibration and recalibration of the ex­ternal photogrammetry lab. He designed aspecial plotter for the graphical evaluation.(The plotter was not manuhlctured out ofgrant funds.)

r-.lr. G. A. Spolek, ;"1. S. was from Or­thopaedic Services, Veterans AdministrationHospital, Seattle. (He was not on the grantbudget, but his time was donated by theV.A.H.) He was responsible for the designand manufilcture of auxiliary equipment forsurgical and x-ray purposes.

Finally, the authors would like to thankthe Aerial Mappi ng Company of Oregon andits President, Bela Kalotay, for donating theBalplex projectors which made possible theconstruction of the described instrument.

REFERENCES

1. Hatzopoulos,.J. N., Design and Calibration ofa Plotting Instrument for Close-RangePhotogrammetry, Thesis, University ofWashington, 1976.

2. Herron, R. E., "Close Range stereo­photogrammetr~'-A Bridge Between :\Ied­icine and Photogrammetric Engineering,"Proceedings of A.S.P., 1959 Convention.

3. Karara, H. ~I., "Stereometric Svstems of HighPrecision," Proceedings of InternationalSymposium I.S.P., 1966.

PLOTTINC INSTHUMENT FOH CLOSE-HANCE PHOTOCRAM~·"IETHY 283

4. Kratk~', V., "Photogrammetric Digital ~Iodel­

ing of Limbs in Orthopaedics," Photogram­metric Engineering and Remote Sensing, Vol.41, 1\0. 6, 1975.

5. Lippert, F. C., "The Three DimensionalMeasurements of the Tibia Fracture Motionby Photogrammetr~':'Clillical Orthopaedics,1974.

6. Lippert, F. C., ~1. Hussain, and S. A. Veress,"Measurement of Spatial jVlotion UsingClose-Hange Analytical PhotogrammetricPrinciples," Proceedings ASP-ASCM, 1970.

7. U.S.C.S. Topographic Instructions, ER-55Plotter Procedures, Book 3, Chapter 4F4,Washington, D. C., 1960.

8. Veress, S. A., "The Use and Adoption of Con­ventional Stereo-Plotting Instruments forBridging and Plotting of Super Wide AnglePhotographv, The Canadian Surveyor, Vol.23:359-376, 1969.

9. Veress, S. A., and R. S. Tiwari, "Fixed-Frame~Iultiple-Camera System for Close-RangePhotogrammetry," Phologr(lmmelric En­gilleering (I lid Remote Sensing, Vol. 42, 1\'0. 9,September 1976.

10. Veress, S. A., H. S. Tiwari, and J. N. Hat­zopoulos, "~Iapping of Stump sing Close­Hange Photogrammctry," Proceedings of theASP Fall Conventioll, Seattle, Washington,1976.

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