FRONTISPIECE. Stereo-pair depicting the lower anterior teeth. Orthodontic bands are cemented onthe first bicuspid on each side with hollow tube welded on its outside surface. Removable wire frame inplace. Note stops on each vertical member.

HEINZ GRUNER*

Bausch & Lomb, Inc.].ZI·LQ.\R- AI andHELM'TA.ZANDER

Eastman Dental CenterRochester, N. Y. 14602

A Short-Range Systemfor Dental SurgeryQuantitative data permit positive conclusionsas to changes in time of teeth after surgery.

(Abstract on page 1243)

T HE SHORTAGE OF readily available equip­ment for the acquisi tion of photograms

in the field of short-range Photogrammetry isattribu ted to the great variety of condi tionsunder which photogrammetric surveys couldsolve many tasks in a most direct and eco­nomical manner. The frontal size and depth ofobjects of solid state or transient existence,

* Presented at the Annual Convention of theAmerican Society of Photogrammetry, Washing­ton, D. c., March 1967, under the title "A ShortRange Photogrammetric System for Dental Sur­gery."

their surface, light reRecting or emittingproperties, their environments (air, vacuum,water, temperature), and the accuracy re­quirements attached to each problem, posesevere obstacles to the design of universalphotogrammetric equipment for field andlaboratory use.

General design approaches are usuallybased on the so called Normal Case of terres­trial photogrammetry which is characterizedby parallelism of the two camera axes andtheir normali ty to the photo base, by metriccameras with adjustable principal distances,

1240

A SHORT-RA TGE SY TEM FOR DENT.\!. SURGERY 1241

by unsymmetric field formats to forestall theloss of stereo overlap, and by variable sepa­ration of their perspective centers along thebase bar. Evaluation of resulting stereograms,if done in the analog mode, requires specialplotting instrumentation, or conventionalheavy universal plotters. If done analytically,instruments of the stereocomparator typewi th electronic readou t and com pu ti ng ac­cessories are desirable.

The well known variety of means for map­ping from aerial photographs, which rangesfrom moderate to extravagant configurations,design, and price, has a similar counterpart inshort range photogrammetry. Here, too, wefind highly sophisticated instrumentations aswell as some poor-man's sol'/l.l'ions which servetheir purpose. The standard error of their re­sults, admittedly, is not quite the same asthat of the aristocratic approach, but accept­able results can be achieved in a most directmanner. The system described here is that ofsecond order. It makes economical use of com­mercially available components. The geom­etry of this short range system is built aroundthe "Convergent Case" of photogrammetry.As necessary, parameters are tailored tooptimize its use in dental research.

T HE PHOTOGRAPHiC OBJECT is the humanmouth. The area of interest in each stereo­gram is limited to about 30 mm in width andheight. The topographic relief seldom exceeds15 mm. Because of the organic instability:ofthe surfaces im·olved, a standard error in posi­tion and elevation of 0.1 m m is a realisticspecification. The clearance between the ob­ject and the camera equipment should not be

HEINZ GRU TER

less than 200 mm which is required to avoidinterference with ambulatory processes.

Figure 1 shows the exposure geometry con­forming to this environment. An isoscelesbasal triangle with a base/height ratio of1/2.8 is established by a photo base I-II. Thetwo photographic axes which intersect at theapex Co at a convergence angle 2a = 2 X 10°represent the two equal sides. Because of thesmall di mensions of the object located wi th itscenter at the point of com·ergence, the image­forming ray bundles are of narrow angles, andcameras wi th an angular field of 25° willamply co,·er the object space.

In the evaluation phase using direct projec­tion plotting equipment this basal triangle isreproduced at 4 times its original dimensions.Consequently, the model surface is generatedat a nominal projection distance of 800 mm.The model scale is equal to 4 times the objectphotographed and is considered most sui tablefor the purpose in mind. Commercially avail­able Balplex 760 projectors, which have aprincipal distance of 55 mm, can meet theseconditions without modification. Their dia­positi,·e frames are prepared to accept smallerplate formats. Their supporting brackets per­mit tilt angles up to 20° in all directions. Theconvergent case of 2 X 10° poses no problem ofprojector orientation. The projection lenseshave a depth of focus considerably in excess ofthe model configuration.

I" OUR CASE OF short-range photogram­metr)", we are concerned with a finite objectdistance, s = 200 m m (Figure 2). The conj u­gate image distance s' depends on the chosenfocal length of the camera lens. The ideal

HELMUT A. ZANDER, D.D.S.

1242 PHOTOGRMI'IMETRIC ENGINEERLNG

FIG. 1. Exposure/Projection Relationship-ac­quisition and evaluation geometry. The basal tri­angle is formed by the Photo (Projection) Baseline I-ll and the two exposure (projection) axes,which converge at the apex Co of the isosceles tri­angle.

image distance, that makes the negati ve orthe contact positive directly compatible foruse in the Balplex, is equal to the principaldistance of the projectors, i.e., 55 mm. The

focal equation l/F=l/S+l/s', then rendersthe desired focal length F=43 mm of thecamera lenses. The size of the negative Iresults from the ratio of the conjugates

1= (s'/s) XO=0.275 XO

where 0 is the object size. I t follows thatcamera wi ndows of 24 X 24 m m provideample image areas for objects that are cen­tered on each camera axis.

The great variety of commercially availablecameras, using 35 111m film with camera win­dows of 36X24 mm, offer a welcome source todraw from. The two prerequisites for eligibilityare: (1) a sufficiently rigid housing, and (2) awell defined focal plane in which fiducialmarks can be affixed. Desirable features are:(1) convertibility to the use of glass plates,and (2) parallax-free view-finding and focus­ing. We chose the Honeywell Pentax cameramodel HIa as meeti ng all req uired and de­sirable features including very reliable flashsynchronization. The use of focal plane sh ut­tel's is not objectionable, as objects andcameras remain stationary during the ex­posure.

The lens had to be especially designed byB&L with a maximum aperture F/2.5,optimized for the given object-image conju­gate ratio. The photographic resolution onaxis is 120 lines/mm; 15° off axis it drops to100 lines/mm. The radial and tangential dis­tortions, in the half-angular field of 15°, arewithin the limits of ±5 microns. The twolenses selected for the camera system arematched for equal focal length within 0.1 mm.They are barrel-mounted on the camerahousings to the given fixed image distance of55 mm. The location of the principal point,i.e., the foot of the perpendicular droppedfrom the interior node upon the image plane,is determined by a special centering micro-

1------------ ~.LOO

o .-.----- --.---~~ID~:~~=+~-·I ~"."-1

FIG. 2. The Photogrammetric Quadruplet. A special lens designed by B&L to give optimum per­formance at the conjugate distance ratio of 200/55. 1t is practically distortion free within the half angularfield of 15° and resolves in excess of 100 lines/mm.

A SHORT-HANGE SYSTEM FOR DENTAL S RGERY 1243

scope. I n this process, the four midside fidu­cialmarkers are also correctly positioned.

T HE CAMERAS ARE placed in a cradle (Figure3). The position of each camera body in thiscradle is rigidly fixed by alignment pads. Bythe release of three locking screws, eachcamera can be removed from the cradle forservicing in the photographic darkroom. Thepermanent relati"e orientation of the twocameras in the cradle is accomplished with acalibration attachment (Figure 4) which canbe fastened to the cradle base. The line cross

large orientation errors undetected, whichwould cause model deformations. Instead,the projector orientation uses a sequence ofopto-graphical steps.

Both projectors are set to an equal heightabove the tracing table platen (Figure 5). Thenadir point of each projector station is foundoptically, and marked in the mapping plane.The line connecting the nadir points is thehorizontal projection of the distance betweenthe projection cen ters, and expresses the baseof basal triangle. I ts correct length, i.e., fourtimes the photo base, is obtained by x-dis­placement of one projector along the support

ABSTRACT: A stereometric camera system comprised of two rigidly mounted 35­mm reflex cameras of metric properties is designed for an object distance of 200mm and an image distance of 55 mm. The camera axes converge at 2 XlO° andintersect in the object plane. The nominal baseldi~tance ratio of the resultingstereograms is 1/2.8. Restitu.tion and evaluation is accomphshed with a directprojection plotter at 4 X plotting scale. Standard Balplex projectors are used at800 mm projection distance. Three dimensional data are obtained with a pre­cision of 0.1 mm at the object scale. Projector relative and absolute orientation isaccomplished by a simple opto-graphical method supported by control data on themodel surface. This system applied to measurements in the human mouth per­mits for the first time quantitative data wMch permit positive conclusions as tochanges in time of teeth and gingival surfaces as a result of the natural healingprocess after surgery. This constitutes an important step towards reliable clinicalcase histories.

of its target plate establishes the apex of thebasal triangle. \Vhen the apex is imaged at theprincipal point of each camera, the basaltriangle is established. I ts base length is de­rived from the physical separation of the twoprincipal points. The orientation of the basaltriangle with regard to the plumb line is indi­cated by the cross levels on top of the cradle.

Although exposures are possible if thiscamera aggregate is held by hand, it is pre­ferred to mount the cradle on a firm supportand use the viewfinders for pinpointing andfocusing on the object. Simultaneous exposureis made with two Rash units, one attached toeach camera.

T HE EVALUATION PHASE of the resultingstereo pairs offers some interesting aspects.Qui te obviously, the orientation of thephotographs in the plotting instrument can­not be performed satisfactorily by using theconventional method of clearing the y-paral­lax from the model. I t would be a cumbersomeprocedure and, because of the small angularextent of the stereo area, it would leave rather

bar. The midpoint of the plotted line is thepoint of convergence. Each projector is tiltedand tipped so that the projection of its princi­pal point coincides with the measuring markof the tracing table placed over the point ofconvergence. This takes care of the </>- andw-orientation settings of the projectors. TheK- (Swing) settings are added, using the pro­jected images of the fiducial marks, or ofphotographic image detail nearby.

The resul ting stereo model is now essenti­ally parallax-free. Only very small residualy-parallax may be observed which can beeliminated easily. usually by a by-correction.As this process of projector orientation ob­serves and corrects image displacement in theprojection plane at a magnification of fourtimes, it is more precise and convenient thansetting the orientation angles by means ofangle measuring devices installed at the pro­jector movements.

THE SUBSEQ ENT ABSOLUTE orientation ofthe model, aimed at obtaining the desired cor­relation between the control points and the

1244 PHOTOGRAMMETRIC ENG I TEERING

FIG. 3. Cradle for Stereometric Camera Pair(rear view). The two 35-mm cameras are held inupright position side-by-side in a cradle, whichsecures their orientation in conformance with mid­side fiducial marks by which the camera principalpoint can be located. The cameras can be releasedfrom their calibrated position by sets of three lockscrews.

mapping plane, may be executed in the cOn­ventional manner of tipping and tilting theprojector support bar, or, if convenientmechanical means are provided, by tipping

• •~

FIG. 4. Calibration fixture attached to cameracradle. The basic camera orientation in the cradleis established and can be restored with the aid ofa center cross on the auxiliary target plate. Whenthis cross is imaged at the principal points of bothcameras the dimensions of the basal triangle canbe checked mechanically.

{

FIG. 5. Projector Orientation. The Balplex pro­jectors are oriented at the supporting bar in such amanner that the exposure geometry is restored atfour times the original scale. The tracing table islocated at the point of convergence of the projec­tion axes which form the sides of the isosceles basaltriangle.

and tilting the mapping table. If the cjJ-com­ponent of the required model rotation ex­ceeds 5°, one may resort to rotating the baseof projection by introducing bx- and bz-com­ponents as functions of the angle of base ro­tation. Again, the opto-graphical methodmay be used for the subsequent reorientationof the prcjectors (Figure 6). The methodproves particularly convenient if the basaltriangle is rotated about its midpoint, ill!.Then the orientation elements are as shownin Table 1.

In analogy to the ¢-rotation, the projectorbase may also be given a w-rotation, whichleads to the introduction of a third base com­ponent, by! and bYfl of the projector settings.

A change of model scale requires scaling upor down of the projection base, or its com­ponents, respectively, but does not changethe rotational orientation of the projectors.

T HE PRACTICAL EVALUATION of stereopairscarried out in the Eastman Dental Center of

.-\ SHORT-RANGE SYSTEM FOR DENTAL SURGERY 1245

TABLE 1. COMPONENTS or ABSOLUTE

ORIE'TATION

See Figure 6

try. It has panchromatic sensitivity and ex­tremely fll1e grain paired with high resolution.As it is not commercially available for 35-mmcameras, it has to be cut and perforated tothis size.

The exposure time for taking intraoral pic­tures in the described setup is that of an elec­tronic Rash of the order of magni tude of1/1,500 second. At a lens stop of f/ll theshutter setting is at 1/30 second. As we usethe double cable release, most likely theRashes from both units expose both pictures.After development and fixation, the negativesare transformed into diapositives by contactprinting on a standard sized aerographic posi­ti\"e plate. In this process, care is taken thatthe positive image has a properly centeredposition within the format of the glass plate.For proper centration in the Balplex projec­tors the standard centering device is used inconnection with the fiducial marks con­tained in the photographic images.

After the plates are placed in the Balplexprojectors, the three di mensional image is pro­jected on a grid consisting of 2X2-mmsquares which have been photographicallyprinted on dimensionally stable sensitizedCronar base drafting film. The grid sheet isthen oriented on the mapping table in such amanner that the abscissae and ordinate linesbecome parallel with the wire frame con­tained in the stereo model.

The wire frame fits into the patient'smouth by placement of orthodontic bands ontwo teeth on ei ther side of the area to be plot­ted (Frontispiece). This procedure allows usto replace the reference frame in an identicalposition in the patient's mouth at differenttime intervals. Obviously, future photographscontaining this reference frame can then besuperimposed upon the original plot in theidentical orientation. Measurements can thenbe made in X-, Y-, and Z-directions ofchanges that may have occurred with timein regard to the dental structures locatedwithin the reference frame.

FIG. 6. Exterior Orientation by Base Rotation.As an alternative to conventional levelling of thestereomodel (by tilting the base bar) the basaltriangle is rotated on the midpoint j\f of its base.Base components are introduced at the projectorsettings and the projection axes are reoriented toconverge at the offset apex CT.

Rochester has resulted in the following experi­ences.

Aerographic posi ti ve plates are not com­mercially available for the camera windowframe of 36x24 mm. It was found thatKodak spectroscopic plates type ]1- F ofsuitable size using ultraRat glass for the rightspeed and fineness of grain (better than 225lines per mm of resolution) were satisfactory.I t was soon found that the inconvenience ofreloading the cameras in the darkroom whentaking pictures of patients constituted ahandicap to the operator; Therefore, weturned to an Estar base film. RecOl"dakSpecial Micro-File AHU Film Type SO-291possesses the necessary photographic andphysical properties for microphotogram me-

bx,= -b:>;l/=b·sin cJ>

b~,= -bxl/=b·cos q,XcT=Dp'sin cJ>

ZcT=Dp(l-cosq,)

\\"ith cJ>=angle ofbase rota tion.X CT and ZcT=Coordinatesof displaced Apex CT of thebasal triangle.