The Effect of the Disparity on Photogrammetric Processes

SANDOR A. VERES, Asst. Proj., Surveying and Mapping, Purdue University

ABSTRACT: This paper reviews the function oj the human eyes in photogram­ metry, and discusses its limitations. The correction of the observation error is presented by mathematical derivations and practical examples. The paper points out the need for continued development of techniques in view of con­ stantly increasing requirements.

INTRODUCTION study of coincidence is most important from the photogrammetric point of view. For a HOTOGRAMMETRIC instrumentation has undergone a revolutionary development study of this kind an instrument called a P has been used. since the second World War. A precision photogrammetric instrument today is able to The horopter designed by Tschermak con­ provide measurement to within a precision of sists of thirteen steel channels mounted so as ± 3 microns. By using these precision in­ to converge to the midpoint of the inter­ struments the compensation of errors in­ pupillary base line of the two eyes of an volved in the measurements becomes of pri­ observer. The central channel lies in a median mary importance. The compensation of errors plane, perpendicular to the eyebase of the is based upon the geometrical knowledge of observer, and the others make angles of 1, 2. the source of errors. The human eye is in­ 4, 8, 12, and 16 degrees on each side of the volved in every photogrammetric measure­ central channel. A small vertical steel rod can ment; consequently the geometrical knowl­ slide smoothly in each channel and the rods edge of the errors due to the limi tation of the are mounted for use at visual distances of 20, human eye is very important. Because the 40, and 75 cm. from the interpupillary base orientation procedure is one of the most im­ line. The rods in the channels are movable portant parts in the reproduction of the toward and away from the observer except photographic bundle of rays, in which the for the central one which is representing the human eyes are directly or indirectly in­ point of fixation. volved, the limitation of the human eyes The motion is controlled by handles and is defines the accuracy obtainable in photo­ adjusted by the observer so that all the rods grammetric data. should be placed in a line parallel to the eye LIMITATION OF HUMAN EYES base at the distance of the point of fixation. The discrepancies of the individual rods from The function of the human eyes in photo­ the correct line can be measured on a measur­ grammetry can be classified into two catego­ ing device. A screen located in front of the ries; a, observation and b, orientation. observer's eyes permits him to see only the a. [n photogrammetric observation both eyes lower part of the left-side rods with the left are directed to a point on the photogram­ metric model, which can be called the point eye, and only the upper part of the right-side of fixation. The image of this point should rods by the right eye. (This is the case in fall on a corresponding retinal element. The photogrammetry, when the left eye is ob­ measuring mark of a photogrammetric in­ serving the left picture and the right eye the strument has to be adjusted until it coin­ cides with the point of fixation or, physiologi­ right picture. The images are not the same cally, the images of the measuring mark fall since the pictures are taken at different air on the same retinal elements as the images stations.) The results published by Dr. K. N. of the fixation point. Ogle are given in Figure 1. The error of observation is represented as It can be seen from the Figure 1 that the the non-coincidence of the measuring mark connecting line of the corresponding rods and the point of fixation. Consequently the yield a hyperbolic line which is called the 148 THE EFFECT OF THE FIXATION DfSPARITY 149

'1_ be general agreement that the training cannot L. Channels R. Channels reduce the area beyond a certain limit. 16° .- This phenomenon can be represented on a .- horopter diagram. The diagram is given in 0 Figure 2 after Fischer (5). -<.rom In his experiment the observation distance was 40 cm. It can be seen that the limits are ---I_ near the point of fixation and they are spaced further apart on both sides away from the fixation point. Experiment has also shown that the size of the Punum area is larger in the case of iden­ tical target patterns and smaller in the case of dissimilar target patterns. ~ "" These limits are of primary importance L.E. R.E. from the photogrammetric point of view, FIG. 1. Spatial representation of because if the limits could be determined the longitudinal horopter. correction and the point of fixation could b~ computed. longitudinal horopter. Therefore, the images CORRECTION OF PHOl'OGRAMMETRIC of the fixation point must be disparate. The COORDINATES FOR FIXATION DISPARITY magnitude of the angular disparity at the point of fixation as determined by Dr. K. The limits of the region are given by the Ogle (1) is as follows: surface of a normal-stereo and pseudo-stereo model. The situation is presented in Figure 3, Llb 7J = - 2a­ (1) where 0 1 and O2 are the left and right eye b2 respectively, and O. is the perspective stereo where center. P is a point on the surface of the 71 is the disparity normal-stereo model and the corresponding a is one-half of interpupillarity distance point on the pseudo-stereo model is P'. The and corresponding rays intersect the reference plane R at PI and P • An approximate par­ b is the observation dista nee. 2 allelogram is given by P, Ph P 2, pI, which This disparity is the observation error in can be called the error parallelogram. This photogrammetry due to the limitation of the parallelogram is developed into an error human eyes. Similar results have been ob­ double cone or more precisely into an ellipsoid tained by Fischer, Ames, and others (2; 3). when taking into account the X and Y direc­ tional errors or the longitudinal and lateral b. The second and more important function of the human eyes in photogrammetry is in disparity. In a three dimensional observation orientation. It was pointed out in the analy­ inside this error ellipsoid, it is possible to sis of photogrammetric observation above obtain a parallax-free orientation although that the images of a point should fall on the the corresponding rays do not intersect each corresponding point of the . If this condition is fulfilled the images will fuse and other. will be seen as a single image. Singleness was the criterion for determining the horopter curve. Punum (4) studied this problem and showed that an image on a retinal point of one eye would fuse with an image falling within a small area of other . This means a certain region exists where only one image is seen; that is, within this region the two images are fused, although disparate. Photogrammetrically speaking, the parallax­ free orientation of a model is possible within this region although the corresponding light rays are not necesiarily intersecting each other. The limit of this region determines the accuracy of the orientation. Experiment has shown that the size of this region,-or some­ times called Punum area-can be decreased FIG. 2. Region of binocular single vision on somewhat with training, but there seems to the longitudinal horopter. 150 PHOTOGRAMMETRIC ENGINEERING

In order to prove that the limits of the fh",c.) ·Y(",.) ,,'...... fixation disparity are given by the surface of a 40 40 normal-stereo and pseudo-stereo model an / \. experiment has been executed. The experi­ 30 30 \\" !\ 20 20 " , ment was based upon the assumption that if ~, ~/' A \, an area is photographed in such a way that 10 10 ---\,/ v ~ the coordi nate axes of the ground control +--_---'_4.-_':--'---'_4.---+----'_4.- Polntso points are parallel to the model coordinate 28 29 30 31 33 34 35 38 axes, the standard error of observation (If a poin t is related to the distance between PX(rnico) eX(CIll.) points P and P' (Figure 3). It should show a high similarity to the residual error of the same 40 J.O point, because the point has been observed at 30 30 the upper and lower limits of the region. 20 20

The camera testing area of U.S.c.&G.S. 10 10 1---1---1-_'---1---1-_1---1-- Points. in northern Ohio was photographed by the 28 29 )0 31 33 34 :3 5 38 Ohio State Highway Department with a Fairchild F-501 (j=6") camera, at the scale of 1/12,000. The control points were pre­ FIG. 4. Relation between the residual error of signalized and their coordinate values were coordinates (da~hed lines) and the standard error of observations (solid lines). A is normal stereo and obtained from U.s.c.&G.s. in the State B normal plus pseudo stereo. Plane Coordinate System of Ohio. The obser­ vation of control points were made with the The model coordinates of the control points Wild A-7 Autograph of the Ohio State were transformed into the ground coordinate University. The orientation of the models was system by using the following well known accomplished using the optical-mechanical coordinate transformation formulas. orien tation method in the usual man ner. y = - bx + ay + elf Two groups of observations were made. X = ax+by+e' (2) One consisted of four series of observations on Three points out of the given eleven were the normal-stereo model, the second was used for coordinate transformation, as well as composed of two series of observations on the for the numerical absolute orientation. The normal-stereo model and two series of observa­ residual coordinate error for the remaining tions on the pseudo-stereo model. From these eight points were computed and compared to observations the standard error of observa­ the standard error of observation. The resul t tions has been computed in the usual man ner. is given in Figure 4, where No. 4-A presents the result of the first group. On the abscissa the poi nts are gi ven and the errors are plotted as ordinates. The standard errors of observa­ 7 tions (J.l.y) are given in microns and presented / as the solid line. The residual errors (e y ) are / / given in centimeters and plotted as the / dashed line. As can be seen, no relation exists / between the two kinds of errors because the / standard errors of observation refer to the sur­ / face of the normal-stereo model. / / The Figure 4-B concerns the second group, / and a high si milari ty exists between the ~ /_ Normal Stereo Model standard error of observations and the re­ sidual error of coordinates. This result clearly /P --~-4-~-'lL-...:!o...----EQOl indicates the two surfaces, namely the nor­ \/ mal-stereo and the pseudo-stereo model, \/ coincide with the limits of the region of ...... _ ___\ / -- Pseudo Stereo Model fusion. The results also indicate that, if the - limits are known, the corrections needed to pI obtain the correct position of a point of FIG. 3. Correction of fixation disparity_ fixation can be computed. THE EFFECT or THE FIXATION DISPARITY 151

1 .,-,.:;--"'n--­ errors due to the fixation disparity in the left f and in the right photograph can be called LiXl and LiX2 respecti\'ely. The incorrect position b , pI of the examined point P can be constructed ,, by using the picture coordinates of x,+Lixi / / / . and X2+Lix2 and is given by dashed lines in , / Figure 5. This is the location of the poin t in ". ,,/ "'. " the case of normal-stereo obsen·ation. If the "'. " h -"" ,," photographic plates are interchanged, in­ \ "'." \ )< cluding the picture coordinates, the pseudo­ \pt//px stereoscopic position P" of the P point can be obtained. as is presented hy dotted lines in Ah Figure 5. 1

+-----...!...... '---.!-----_ X The model coordinates of the point are XI' and Y 1" in the case of normal-stereo observa­ FIG. 5. Correction of X Moclel coorclina te. tion and XI''' and Yp" in the case of pseudo­ stereo observations. As can be seen from A correction method involving the Z co­ Figure 5, a tJ.h elevation error exists between ordinate only has been published by Mr. H. points P and pI which can be computed in Yzerman (6) as follows: "'vVe see that (Figure the following manner: 3) 0 1, Oz, PI, P z are points of a complete quadrangle of which the t\\·o sides Ot, Oz and PI, P 2 are parallel. \Ve know therefore that or the cross ratio 01020,E~= -1 and thus that It' 0,0,= -0,02", This means that the inter­ D.1t = bj (D.X, - D.X,) (3) change of stereoscopies results in equal in\'er­ sion of the model with respect to the refer­ The correction for XI" coordinate can be ence plane. Or in other \\'ords, if, due to ex pressed as Fixation disparity or Fertch-effect. the t::uYP' = )(p - ...X pI parallax of Jf (measuring mark) with the (4) in \\'hich model point P seems to be nil, then the inter­ change of stereoscopies \\'ould make the latent parallax visible in the order of t\\'ice of its value. This could not only be compared \\'ith Substituting the (3) formula into the above an increase of B/H (Base-Height) ratio or equation magnification of two times. Still more chal­ It lenging is that a true zero-method is available Xp' = - (x, + D.X,) instead of an approximation method with all f its su bjective aberrations." It' - bj2 (x,D.X, + D.~·,D.X, - ~',D.XI - D.X,') (5) This correction method for the Z coordi­ and nate is certainly correct with the assumption /l X,> = -~', (6) that the two limits are located symmetrically f with respect to the point of fixation or refer­ ence plane. Since the X and Y model coordi­ Substituting (5) and (6) into Equation (4), nates are also affected by this fixation dispar­ the correction becomes ity, further investigation was undertaken It' 2 (10). D.Xp' = bj2 (X,D.X, + D.x,D.:r, - XID.X, - D.XI )

It The correction for the X model coordinate -- 11,1', (7) can be deri"ed from the follo\\'ing conception. f In a stereoscopic model an arbitrary point A similar equation can be derived for the "P" is given (Figure 5). The corresponding correction of XI''' coordinate such as picture coordinates are XI for the left and X2 It' for the right camera. If one assumes that D.Xp" = ~f' (x,D.X, - x,l1x, - D.X,D.X, + D.X,2) these picture coordinates are theoretically correct, then the model coordinates XI' and II + --:- !h, (8) YI' are also correct. The X componen ts of the J 152 PHOTOGRAMMETRIC ENGINEERING

By knowing the Xp', b.Xp', Xp" and b.Xp" Substituting equations (12), (13) and (14) the correct model coordinate of the point can into equation (11), the final formulas are: be expressed with the following formula XP = 0.5(Xp' + X p") = XP' + XP" + !lXp' + !lXp" X p 2 2 (9) +0.5 -XP' (XP" - XP') [ b 2 (15) Substituting the corresponding equations for Equation (9), the final formula is

XP = 0.5(Xp' + Xp") and 0.5 [:' (:rl!lx, - XI!lXI - !lXI' x 2!lx, (10) + + Yp = 0.5(Yp' + YP")

~ - X,!lXI !lx,') (!lx, - !lXI)] +0.5 Y, (Y p "- YP ') + + ; [ b 2 (16) or simply YP" (YP" - YP') YP" - YP'J XP = 0.5(Xp' + Xp") +!lX (11) + b 2 + 2 Four unknowns exist in Equation (10); In the Equations (15) and (16) every term consequently the equation in this form can­ is known. Therefore these formulas can now not be used for any practical purpose in be used for a practical purpose. order to solve the unknowns, three more The test of these formulas was performed equations would be required. The equations by using the model described earlier. The cannot be established; consequently it is ground coordinates were computed from necessary to introduce certain approxima­ model coordinates with and without correc­ tions in order to obtain a useful correction. It tion and compared to the given coordinates can be assumed that: of corresponding points. Eleven control points were given on the model and three were used h' h' - !lXI' = - !lx,' = 0 (12) for absolute orientation and coordinate trans­ bf' bI' formation. The residual standard position errors have been computed and the result is and if t::.h=O compared to hand b.XI=O com­ given in Figure 6. The dashed line represents pared to Xl it can be written: the residual standard position error obtained from the uncorrected coordinates and the iX' d i (13) x, = h p an x, = h x p " solid line represents the residual standard position error computed from the corrected A further approximation can be introduced coordinates. As can be seen, the correction that the provides about 40 per cent increase in accu­ racy of position. Eight different models were It X '+X" - (!lx - !lx) = p p - X' examined (10) about 45 per cent in X and Y 2 (14) coordinates as well as in Z. The average residual elevation error was found to be 1/7,000 of the flying height without correc-

f'p (em.) R ,, /" \ I\ 50 I\ : \ I \ 40 / , I , I \ I , 30 / \ / \ I \ 20 I /

10

1-----+--1---1---"1-----1---1--+---"1-----1--.+---1--- Points. 28 29 30 31 32 33 34 35 38 39 46 FIG. 6. Comparison of standard residual position errors. For uncorrected coordinates (dashed line) and corrected coordinate (solid line). THE EFFECT OF THE FIXATION DISPARITY 153 tion and 1/13,000 using the correction for­ REFERENCES mulas. 1. Dr. K. N. Ogle: , \Y. B. Saunders Co., Philadelphia and London, 1950. CONCLUSION 2. A. Ames, Jr., K. N. Ogle and G. H. Gildon, Size and Shape of Ocular Images. Method of The analysis of the above correction Determination and Physiologic Significance. method led to the conclusion that the correc­ Arch. Opth. (April) 1932. tion formulas have a very significant effect on 3. A. Ames, Jr., K. N. Ogle and G. H. Gildon: "Corresponding Retinal Points, the Horopter the improvement of accuracy. But one has to and Size and Shape of Ocular Images." Optic. realize that the correction formulas were Soc. America, Vol. 22, 1932. derived only to improve the observations and 4. P. L. P. Punum: Uber die Einheitliche Ver­ do not improve the orientation. It is also schmelzung Versch iedenartiger Netzhou tein­ drUcke beim Sehen mit zwei Augen," Arch. f­ emphasized that a close relation exists be­ A nat. ·und. Physiol. 1861. tween the orientation of a stereo-model and 5. F. D. Fischer: "Fortgesetzte St\l.dien Uber the fixation disparity and also between the Binokularsehen (Tschermak): 11 Uber Asyi­ measured Y parallaxes and the fixation dis­ metrien des Gesichtssinnes Speziell des Raum­ sinner beider Augen." Arch. f. d. des Physiol. parity. Therefore these correction formulas 1924. are effective only as far as the observation is 6. H. Yzerman: "The S. D. I. A New Method for concerned. Consequently, a large amount of Stereoscopic Measurements and Plotting," the residual errors after the correction are due IntemationalArch. of Photogrammetry. Vol. XII, 1956. to the uncorrected orientation. Further in­ 7. S. A. Veres: "Physical Aspects of Aerial Photo­ vestigation must be undertaken in order to grammetry," Unpublished PhD Dissertation, obtain correction method or methods for The Ohio State University, 1962. orientation, which is highly important in any Additional References aerial triangulation Dr. A. J. Brandenberger: Fehlertheorie der Aus­ seren, Orientierung von Steilaufnahmen." Tech. Hochschule Zurich, 1947. ACKNOWLEDGMENT Dr. A. ]. Brandenberger: "Aerial Triangulation The author wishes to express his gratitude by Least Squares." Mapping and Charting Research Laboratory. The Ohio State Univer­ to Dr. A. ]. Brandenberger for his valuable sity, 1956. advice and of making possible the use of the Dr. A. J. Brandenberger: "Theorie und Praxis der instrumentation of the Ohio State University, Gegenseitigen Orientierung von Steilaufnah­ and also to Mr. L. O. Herd, Chief Engineer men." Zeitschrift fUr Vermessung und Kultur­ technik. Heft 4,5, 1948. of Aero Survey Section of the Ohio State D. R. Dwyer: "Visual Factors in Stereoscopic Highway Department for providing the Plotting." PHOTOGRAMMETRIC EKGINEERING, material needs of this study. Vol. XXVI, No.4, September 1960.

Book Review

Proceedings of the Fifth National Surveying by Professor Wilfred H. Baker. I n the review Teachers Conference-August 1962. Spon­ it was noted that the discussion was primarily sored by Committee VIII, Surveying & concerned with methods and procedures used Mapping of the American Society Engi­ for teaching students in the field of photo­ neering Education. Conference held at grammetry, the fundamental principles rather Georgia Institute of Technology, Dah­ than technical aspects. To most of our mem­ lonega, Georgia. Published by Committee bers, information of this nature is more VII, Surveying & Mapping, American readily available from other sources in various Society Engineering Education. 98 pages textbooks, manuals and publications. In most with illustrations. Obtainable from Mr. D. instances the reference books will explain the H. Harkness, Secretary. Address W. & subject matter in greater detail than is dis­ L. E. Gurley, Troy, New York. cussed in the Proceedings. However, for those instructors who have little or no acquaintance The Publications Committee has reviewed with the field of photogrammetry, this publi­ the Proceedings at the request of Mr. Hark­ cation will be of some assistance. ness. Particular emphasis of the review was placed on the portion titled "A Course in ABRAHAM ANSON, Chairman Basic Photogrammetry, pp 13-32, presented Publications Committee