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The Effect of the Fixation Disparity on Photogrammetric Processes

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The Effect of the Fixation Disparity on Photogrammetric Processes The Effect of the Fixation 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 horopter 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 retinas. 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 retina. 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.
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