Stereogram design for testing local stereopsis Gerald Westheimer and Suzanne P. McKee The basic ability to utilize disparity as a depth cue, local stereopsis, does not suffice to respond to random dot stereograms. They also demand complex perceptual processing to resolve the depth ambiguities which help mask their pattern from monocular recognition. This requirement may cause response failure in otherwise good stereo subjects and seems to account for the long durations of exposure required for target disparities which are still much larger than the best stereo thresholds. We have evaluated spatial stimuli that test local stereopsis and have found that targets need to be separated by at least 10 min arc to obtain good stereo thresholds. For targets with optimal separation of components and brief exposure duration (250 msec), thresh- olds fall in the range of 5 to 15 sec arc. Intertrial randomization of target lateral placement can effectively eliminate monocular cues and yet allow excellent stereoacuity. Stereoscopic acuity is less seriously affected by a small amount of optical defocus when target elements are widely, separated than when they are crowded, though in either case the performance decrement is higher than for ordinary visual acuity. Key words: stereoscopic acuity, local stereopsis, global stereopsis, optical defocus A subject is said to have stereopsis if he can are very low indeed, certainly under 10 sec detect binocular disparity of retinal images arc in a good observer, and such low values and associate the quality of depth with it. In can be attained with exposures of half a sec- its purest form this would manifest itself by ond or even less. the ability to identify a single feature, e.g., a It is sometimes thought that an observer line, as appearing in front of one or more can correctly call the direction of depth of a other features when it differs from them in feature by merely inspecting the two eyes' having crossed disparity of its retinal images views of a pattern containing disparity with- as compared with those of the other features. out truly experiencing the depth sensation Insofar as differing values of the "depth" that disparity normally engenders, although quality can be associated with single and in fact stereopsis can result from binocular quite small individual features, it is appro- pattern differences that are too small to be priate to use the term local stereopsis. Dis- detectable in one or the other monocular ret- parity thresholds under such circumstances inal image.' For that reason, random dot stereograms From the Department of Physiology-Anatomy, Univer- have been devised which have the property sity of California, Berkeley. of containing no depth clues that are accessi- This research was supported by the National Eye Insti- ble to monocular viewing. There are many tute, U. S. Public Health Service, through grant EY- identical feature elements which can have 00220. their retinal images associated in a variety of Submitted for publication March 29, 1979. Reprint requests: Dr. Gerald Westheimer, Depart- ways, each of which would yield a different ment of Physiology-Anatomy, University of California, disparity for each element. For a particular Berkeley, Calif. 94720. set of such associations, a pattern is seen in 802 0146-0404/80/070802+08$00.80/0 © 1980 Assoc. for Res. in Vis. and Ophthal., Inc. Downloaded from jov.arvojournals.org on 09/29/2021 Volume 19 Number 7 Stereogram design for testing local stereopsis 803 i RIGHT EYE LEFT EYE 8' 9' 10' 12' 13' 14' Fig. 1. Diagram of one line of a random dot stereogram. Central portion (elements 5 to 14) of the pattern of the left eye has been shifted one element to the right to create a disparity between the two eyes. For some elements, e.g., element 8', there is ambiguity about the direction of the disparity because that element could be associated with element 8 or element 10 of the pattern seen by the other eye. depth whose clues are not contained in the right eye has no counterpart in the left eye. It monocular views. This synthesis of a whole can be associated with element 8' or 10' in depth pattern from a particular set of dis- the left eye, each giving a binocular disparity parities of its constituent elements is called (in comparison with the reference regions 1 "global stereopsis." to 4, 5 to 18) but in opposite directions. The The very content of global stereopsis, global percept is attained by favoring the as- however, entails some disadvantages for ran- sociation 10 —» 10' because a similar associa- dom dot stereograms: some observers with tion of the other elements produces least normal local stereopsis have difficulties mak- overall dissonance. ing depth judgments in them2' 3; the struc- 2. There is crowding. For the purposes of ture of these patterns limits the minimum associating right and left eye features to de- disparity that can be presented to values termine the disparity, elements or clumps of considerably above the best stereoacuity elements must appear separate from their thresholds found with simpler patterns, and neighbors. The minimum separation is one unless the presented disparity is quite large element size, and this suffices if it is about 1 (>2 min arc), a long exposure duration is min arc or more. The average separation will usually required for a sensation of depth. depend on the element size and the statistics In Fig. 1 the structure of a small region of a generating the pattern; when the probability random dot stereogram is analyzed to illus- for black squares is 0.5, then if any separation trate how the need to scramble outlines of exists between elements, the mean separa- the global pattern imposes restrictions on the tion will be two elements. placement of elements. A line of 18 ele- 3. There is a restriction on stimulus dis- ments, each of which can be either white or parity. In the arrangement shown in Fig. 1, black, is shown in the views of both the right which is the most common one used, dispar- and left eye. Where no disparity is intended ity can be created only in modules of the size to be present, the patterns of the two eyes of each element. are in exact register (squares 1 to 4, 15 to 18). The essence of a random dot stereogram is A disparity equal to one square is produced not the irregular placement of elements. by displacing squares 5 to 14 to the right in Randomly placed features, each with a clear- the left eye—here exact register is attained ly and essentially unique disparity, can pro- only by association of each element in the duce excellent stereopsis, as has been shown right-eye view with the immediately adjacent by Frisby and Julesz4 and as will be demon- one to its right in the left-eye view. strated below. The task of making a depth The three important features of this ar- pattern inaccessible to monocular viewing by rangement are as follows: creating multiple ambiguities of element 1. There is ambiguity. Element 10 in the pairing, which is the hallmark of a true ran- Downloaded from jov.arvojournals.org on 09/29/2021 Invest. Ophthalmol.Vis. Sci. 804 Westheimer and McKee July 1980 VERTICAL HORIZONTAL Di GW s 40 40 DT • • D- --D • • 20 ill 20 10 20 30 0 10 20 30 T J 40 JS 40 SM 1 1 20 „ -O -0 -o 0 1 1 1 0 10 20 30 0 10 20 30 SEPARATION (S) MIN OF ARC SEPARATION (S) MIN OF ARC Fig. 2. Threshold disparity (sec arc) for stereoscopic depth discrimination as a function of edge-to-edge separation of two small squares, 2 min on a side. • •, Horizontal separation between the two squares; a a, vertical separation. Exposure duration 500 msec. Subjects G. W. and J. S. give consistently better thresholds for one direction than the other. dom dot stereogram, calls for the elaboration left eye and the other screen was seen only by the of a global percept, a facility which is not right eye. Target luminance was about 20 mil- necessarily the subject of a first examination lilamberts. During an experimental session, a of a patient's visual function. target was displayed every 3 sec for a duration, In this paper we point out some aspects of usually, of 500 msec. In the intervening period, there appeared a fixation square which was not stereoscopy that help account for the large visible during target presentations. The fixation differences in threshold parameters between square, outlined by four brackets 0.75° apart, random dot stereograms and more traditional permitted good binocular and foveal fixation. Sub- stereoacuity patterns. In the light of these we jects sat 2.5 m from the screens; observation was have designed stereograms that, like the ran- always binocular with natural pupils and with op- dom dot patterns, are inaccessible to purely timal correction for that distance of any refractive uniocular judgments while at the same time error. demonstrating stereoscopic acuity in the The target elements for all these experiments range of a few seconds of arc. were small bright squares, 2 min arc on a side. The "test" target elements were presented with one of Methods seven possible disparities, three equally spaced Targets were created under computer control positions (usually 8, 16, and 24 sec arc) behind or on two 602 Tektronix units with the P4 phosphor, in front of the fixation plane and one in the fixation whose screens were superimposed by a beam- plane. Reference elements were always presented splitting pellicle. Suitable placement of polaroid in the fixation plane.