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A comparison of stereo and vernier acuity within spatial channels as a function of distance from fixation
~‘ision Res. Vol. ‘5. No. 8. pp. Ill&1119. 1985 Pnnwd ,n Grw Briram. hll r.ghts rrsened
Copyright c
0042-6989 85 S3.00 + 0.00 1985 Pergamon Press Ltd
A COMPARISON OF STEREO AND VERNIER ACUITY WITHIN SPATIAL CHANNELS AS A FUNCTION OF DISTANCE FROM FIXATION CLIFTON M. SCHOR and DAVID R. BADCOCK* University of California. School of Optometry, Berkeley, CA 94720, U.S.A.
(Received 3 October 1984; in revised form 8 January 1985) Abstract-We have used DOG stimuli in order to investigate the relationship
to selectively stimulate size tuned channels within the visual system between stereo and vernier acuity. We measured these acuities as a function of spatial frequency. retinal eccentricity and distance from the fixation point in depth. Both hyperacuities are poorer with low spatial frequencies but vernier was effected to a smaller extent. Vernier acuity deteriorated to a much greater degree than stereo acuity as retinal eccentricity increased up to 10 arc min. Stereo acuity was more dependent upon distance from the fixation point in depth than would be expected from the dependence of vernier acuity on retinal eccentricity. We conclude that there must be different limiting factors for the two hyperacuity tasks. Horouter Loc&ed
Stereopsis Vernier alignment Hyperacuity Parafovea Blur Spatial channels pedestal
INTRODUCIION
Stereopsis and vernier alignment are two forms of hyperacuity that respond to relative spatial localization within the visual field. Relative spatial displacements within the retinal image as small as several seconds of arc can stimulate the perception of stereoscopic depth when presented dichoptically and of spatial misalignment when the perception presented monocularly. The similarity of retinal stimuli for these two forms of hyperacuity has led to the suggestion that sensitivity to vernier offset maybe a precursor for stereo-sensitivity (Wheatstone, 1838). This suggestion implies that the binocular stereoscopic threshold would equal the sum of the two monocular vernier thresholds. Contrary to this however, most studies report that the binocular stereo threshold equals a single monocular vernier threshold (Berry, 1948; Stigmar, 1970; Westheimer and McKee, 1979). Differences in stereo and vernier sensitivity become exaggerated under specific test conditions. As vernier like targets are blurred, stereoacuity falls off more rapidly than vernier acuity (Berry, 1948; Stigmar, 1971). The relationships between these two hyperacuities as a function of the vertical separation or gap size between upper and lower line segments has been examined by Berry (1948) who reports that vernier sensitivity falls off more rapidly than stereo sensitivity as gap width increases. However, Stigmar (1970) comes to the opposite conclusion. Part of the
*Present address: Department of Psychology, University of Melbourne, Parkville, Victoria 3052, Australia.
Depth increment threshold frequency analysis
Disparity
effect of gap separation may be due to reduced sensitivity in the retinal periphery. Both vernier acuity (Westheimer, 1982; Enoch ef al., 1984) and stereoacuity (Blakemore, 1970) become poorer with increased retinal eccentricity, however, these effects have never been directly compared. To make this comparison we must also consider the spatial channels that are potentially responding to the stimulus. Recent work suggests that the visual system is composed of multiple channels with luminance weighting functions that can be described by a difference of two Gaussians (Wilson, 1978). Several sizes of these channels exist at each retinal eccentricity (Wilson and Bergen, 1979; Graham et a/., 1978). As eccentricity increases, the size of all channels increases so that the range of spatial frequencies processed moves to lower frequencies. It is possible that the above changes in vernier and stereoacuity reflect this progressive change of channel size. To address this possibility we have employed difference-of-Gaussian (DOG) luminance distributions of various widths as stimuli which allow us to examine the effects of retinal eccentricity upon vernier and stereo acuity, within a channel having a DOG receptive field profile. The effects of blur upon hyperacuity may also be better understood by examining the frequency spectrum. Blurring stimuli causes a reduction in the high spatial frequency content (the changes are somewhat more complex than this as we will discuss below but this does not matter to the current argument). This change will modify the distribution of channel sizes effectively stimulated. This raises the possibility that the effects of blur are also related to changes in the population of stimulated detectors. Examining be-
III3
IllI
CLFTOU
M.
SCHOR
and
ha\lor within DOG channels of different sizes and at different retinal eccentricities may help compare stereo and vernier sensitivity under equivalent stimulus conditions. METHODS We have compared stereoacuity with vernier resolution using a ‘*stereo-vernier target” suggested by Walls (1943). The classic target consists of two vertical rods. one above the other. We have replaced the rods with DOGS. Vernier acuity was investigated by presenting two DOGS, one above the other, to one eye. The upper DOG was displaced laterally to produce a vernier offset. Stereopsis was investigated by presenting these vernier targets haploscopically to each eye but with lateral displacements in opposite directions to produce disparity. A computer controlled the magnitude of the offset during each stimulus presentation. The upper and lower halves of the DOG were each two degrees long. They were separated by a 3 arc min gap. This gap produces good vernier acuity (Westheimer, 1952) and was produced with a black horizontal line placed across the display screens. These stimuli were presented on two 603 Tekrronix oscilloscopes (subtending 8 deg x I2 deg) that were viewed haploscopicaliy at a distance of 57cm from two front surface mirrors placed before the eyes at angles of I35 and 45 deg. The test stimuli were DOGS that were produced from look up tables and passed through 8 bit Digital to Analogue converters. The luminance profile of the DOGS had the form
DOG(X)
= 3 expf -x1/a’)
- 2 exp(-xz/2.25az).
The spatial extent of the negative Gaussian function was I .5 times wider than that of the positive gaussian. The net sum of their areas equaled the mean background luminance (40 cd/m?). DOGS had bandwidths of 1.75 octaves at half height and center spatial frequencies of 0.15, 0.6, 2.4 and 9.6 c/deg. Effects of retinal eccentricity upon stereo and vernier acuity were investigated with comparable stimuli. Extra fovea1 vernier acuity was measured by placing the vernier DOG stimulus to the left of a central fixation point before the left eye while the right eye viewed a black felt patch. During the study of stereopsis a second vernier DOG was presented to the right eye at the same retinal eccentricity in the same or in the opposite half of the visual field as the DOG vernier stimulus seen by the left eye. When presented in the same hemifield, the stereovernier target produced a disparity increment between the upper and lower DOG in the frontoparallel plane. When presented in the opposite hemifieid the stereo-vernier target produced an extrahoropteral or disparity pedestal stimulus, that appeared either in front of or behind the fixation point. The subject’s task was to discriminate between the presence and absence of depth differences between
DAVID R. BAUCOCK
the upper and lower vernier DOGS subtended from the disparity pedestal. Both of these conditions are comparable to the monocular vernier experiment since closing either eye during the stereo depth increment threshold task yielded a monocular I-srnier judgement task at a fixed retinal eccentricity. Any influence of vernier resolution upon disparity processing should be reflected in the fronto-parallel and extra-horopterai measures of stereo-increment threshold. During vernier and fronto-parallel stereo tests, DOGS were placed at the fixation point and to the left at retinal eccentricities of 5, IO, IO and 40 arc min. We selected this range of retinal eccentricities to produce a range of disparity pedestals within the scope of quantitative stereopsis when the vernier targets were presented to opposite hemifieids. During extra horopteral stereo tests DOGS were placed at the same retinal locations but in opposite halves of the visual field to produce disparity pedestals of 0, IO, 20, 40 and 80 arc min in either the crossed or uncrossed direction. Stereo and vernier increment thresholds were determined at these retinal eccentricities using DOGS whose center spatial frequencies ranged from 0. I5 to 9.6 c/deg (center widths ranging from 6.7 to 0. I deg respectively). Vergence eye movements were controlled with a small central fixation spot surrounded by two other spots. These three spots provided a fronto-parallel reference plane. Nonius lines were placed below the left and above the right eyes’ central fixation point. Sensitivity to vergence errors was approximately I arc min. Trials were rejected when noticeabie vergence errors occurred. Specific details for vergence control are presented elsewhere (Schor PI al., 1984b). Thresholds were measured with a two alternative forced choice staircase with 9 reversals that converged in approximately 50 trials upon a ?I”,; “correct” performance ievei (Levitt, 1971). The pedestal and pedestal plus test disparity combinations were presented in randomized order, each for 750 msec. A tone preceded each test stimulus and it also provided feedback for incorrect responses. Subjects indicated in which of the two intervals that they perceived the relative depth offset by pressing one of two buttons. The computer evaluated their response and in the next trial presented a smaller offset if two consecutive responses were correct and a larger offset if one response was incorrect. Step size was varied with an 8 bit logarithmic attenuator such that steps became smaller as the threshold was approached. The smallest step size was 0.8 arc set for stereopsis and 0.4 arc set for vernier acuity. The magnitude and direction of disparity pedestals were randomized for a given DOG during a given test session although they were not varied during a staircase. The size of a DOG was ~ISO randomized between test sessions. Each session consisted of ten test pedestals for a given size DOG and each of these sessions were repeated three times. The entire procedure was under computer control. Tests
1115
Relationship between stereo and vernier acuity svere conducted on three subjects who had normal binocular vision and fully corrected refractive states. RESULTS The results obtained for vernier and stereo acuity are plotted for 3 subjects in the upper and lower halves of Figs l-3 respectively. We have multiplied a/f monocular vernier thresholds by a factor of two in order to compare them with the monocular precision required for stereo processing which by definition is the sum of :wo monocular components. The reciprocal of these doubled vernier thresholds are plotted both as a function of DOG center spatial frequency and retinal eccentricity in arc min. Stereo sensitivity is plotted both as a function of DOG center spatial frequency and disparity pedestal size. The results obtained with crossed and uncrossed disparity pedestals were indistinguishable, and have therefore been pooled as a mean of 6 threshold measures in this presentation. Vernier sensitivity for ail observers decreased markedly as spatial frequency was reduced. Fovea1 thresholds increased by a factor of 4 for two subjects (C.S. and D.B.) and by a factor of 2 for the third subject (M.M.) as spatial frequency decreased from 9.6c/deg to 0.15 c/deg. Similar reductions of sensitivity occurred with retinal eccentricity. Vernier thresholds at high spatial frequencies decreased by factors of 29 and 3 for the three subjects (C.S., D.B., and M.M. respectively) as stimuli were moved from the fovea to an eccentricity of 40 arc min. The changes with eccentricity were greater with narrow (high frequency) DOGS for one subject (D.B.) (Fig. 2) and they were equal to those obtained at lower frequencies for the two other subjects (Figs 1 and 3). Stereosensitivity underwent similar changes with decreasing spatial frequency. As the center spatial frequency of DOGS decreased, stereo threshold for the zero disparity pedestal increased by factors of IO, 6 and 5 for the three subjects. These increases were much greater than those observed with vernier acuity and they were similar to the changes in stereothreshold as a function of spatial frequency observed by Schor, Wood and Ogawa (1984). Stereosensitivity was also reduced by factors of 7, 8 and 5 for subjects C.S., D.3. and M.M. respectively as disparity pedestal increased to 80 arc min. This increase in stereothreshold with disparity pedestal was greater with DOGS having high than low center spatial frequencies in one subject (C.S.) and increase was approximately the same for ail center spatial frequencies in the other two subjects. Interestingly, stereosensitivity measured in the fronto-parallel plane was unaffected by retinal eccentricity in all three subjects. Stereosensitivity at various eccentricities in the fronto-parallel plane is represented by the mixed dashed line plotted in Figs 4-6. This measure of stereopsis remained at its peak level for ail spatial frequencies (high and low frequencies shown in top
and bottom plots of Figs 4-6) over the entire range of retinal eccentricities (O-40 arc min) in contrast to the 10 fold change of stereoacuity with an 80 arc min disparity pedestal produced by two 40 arc min retinal image displacements. Figures 4-6 compare for three observers the effects of retinal eccentricity and comparable disparity pedestals upon vernier acuity and stereopsis respectively. Results obtained with a high (9.6cideg) and low (0.15 c/degf center spatial frequency are shown in the upper and lower halves of the figure. For all three observers and for all spatial frequency targets, extrahoropteral stereothresholds increased markedly with the magnitude of disparity pedestal or offset from the horopter. In contrast, fronto-parallel stereothresholds changed little if at all when tested at retinal eccentricities that were equivalent to the extrahoropteral disparity pedestals. The same figures illustrate that vernier thresholds tested away from the fovea with high spatial frequencies (upper plots) were lower than extra-horopteral stereo thresholds and they were higher than fronto-parallel stereothresholds. Vernier thresholds tested with low spatial frequencies were usually lower than extra-horopteral stereothresholds and they were both lower and higher than fronto-parallel stereothresholds. Vernier thresholds were lower than fronto-parallel stereothreshoids at small retinal eccentricities, and a reverse relationship occurred at larger retinal eccentricities. In two observers (D.B. and M.M.) vernier threshold, stereoalthough lower than extra-horopteral thresholds, increased at a similar rate. These results are plotted on a log scale so that the constant separation in the vernier and extra-horopteral stereo functions shown in Figs 5 and 6 represents a fixed multiple. If they were transformed to a linear scale the two functions would diverge. For example in the top of Fig. 5, vernier and extra-horopteral stereo thresholds differ by 2 arc set at the fovea whereas they differ by 5 arc set when tested at 40 arc min retinal eccentricity and the corresponding 80 arc min disparity pedestal respectively. DISCUSSION
The major impetus for this study was to investigate differential sensitivity of spatial channels to relative position. We examined these channels with DOG stimuli to isolate a narrow range of continuous widths or spatial frequencies. Previously this problem was addressed with blurred stimuli (Stigmar, 1971; Westheimer and McKee, 1980; Williams er ai., 1984). Blur changes the relative contribution of channels tuned to different spatial widths but it does not provide the precise control of spatial stimulus components that can be obtained with DOG stimuli. Westheimer and McKee (1980) describe the effects of spectacle blur (see their Fig. 3) which reduces the transfer of higher spatial frequencies. The function is not monotonic, however, since it has regions of
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energ) in higher frequency bands (for a discussion see Goodman. 1968). Ground glass blurring [see Stigmar t 19il), Westheimer and McKee / 1980). Fig. 4 and LViliiams ri (II. (19%). Fig. l] attenuates high frequencies more than low frequencies, however it does not allow band pass selection of intermediate spatial frequencies. To achieve a narrou’ band stimulus. Westheimer and McKee (1980) used B narrow DOG to produce a stimulus with only high spatial frequencies. They found that reducing the high frequency content of stimuli caused a deterioration of stereoacuity. However a DOG centered on a high frequency (22 c;deg) resulted in a greater reduction of stereoacuity than found with the elimination of high frequencies. They concluded that the entire frequency spectrum was required for optimal steroperformance. The current study shows that good stereopsis requires frequency information above 2.4c/deg up to 9.6 cideg both on and olT the horopter even though only small segments of the frequency spectrum are presented with our DOG stimuli. This result is consistent with the report by Westheimer and McKee ( 1980) provided that stereo-performance deteriorates at higher spatial frequencies than those presented in the current study. Both studies agree that detectable amounts of energy in the range of 2.4 cfdeg up to but less than 22c/deg (the upper limit has not been precisely determined) are required for good stereoperformance. Stereo performance is poorer for channels that respond to frequencies lower than 2.4 c/deg. Vernier ircuity is also reduced with lower spatial frequency stimuli (Stigmar. 1971; Williams et al., 1984) bl*t good vernier acuity depends less upon high spatial frequency information that does stereoacuity. All of our subjects had Larger reductions in stereo than vernier acuity as spatial frequency decreased (when measured at the fixation point). These results indicate that different mechanisms may be involved in these two forms of hyperacuity. Our results confirm previous observations (Blakemore. 1970; Westheimer and McKee, 1978) that stereo increment threshold and stereothresholds of moving targets increase more quickly with distance away from the horopter than with eccentricity along the horopter, even though the same size retinal eccentricities are involved in both stimulus conditions, Recently McKee (1983) has observed a decline of fronto-parallel stereothreshold when tested at 20 arc min retinal eccentricity. Perhaps reductions of stereothreshold are only apparent if the stereoacuity of the central fovea is very good or perhaps reductions of stereoacuity are greater at eccentric retinal sites along the vertical meridian tested by McKee (1983) than those we have observed along the horizontal meridian. In spite of these subtle differences, it is clear that functions describing extra-horopteral stereopsis and fronto-parallel stereopsis are very different. Interestingly, *when tested at large retinal
eccentricities 130 arc mini rernier xuitk fails betbkm these two measures of stsreopsis. These three d~~r~‘pant functions provide a clear demonstration oi the independence of vernier and stereoacuitb. At the fovea or on the horopter all three measures were nearly equal (i.e. the doubled monocular vernier threshold equals the stereothreshold) in two of our subjects (D.B. and M.&i.). It has not escaped our attention that our third subject (C.S.), ivho had tht: best stereoacuity and was the onl) case in ivhich stereoacuity at the fovea could not be accounted for by doubling the vernier threshold. ~~3s also the most experienced with the stereo task. Przctice effects on these tasks are well known (McKee and Westhelmer. 1975: Fendick and Westheimer. 1983) and it appears that il sufficiently experienced subject can produce stereo thresholds that are not limited by monocul:\r vernier acuity (e.g. Berry, 1938: Berry e! ~1.. 1950; Westheimer and McKee. 1979). Thus xc could not make a clear comparison of stereo and vernier ilcuity at the fovea due to practice etTects which were greater than the difTerences we were seeking. We were able however to compare these two hyperacuities in the parafovea where our observers had not >er had extensive experience. In the parafovea, high spatial frequency measures of stereoacuity exceeded vernier acuity by a Pactor of 3 before doubling the vernier threshold. This result is not produced by practice effects since our subjects had more experience with peripheral vernier than peripheral stereo tasks (peripheral stereo was done last). Hence even greater differences between the two hyperacuities than reported here might exist in the parafovea. It appears that the falloff in vernier acuity with increasing eccentricity and the similar falloff in stereoacuity with distance from the horopter was not due to a progressive change in channel size since eccentric stereoacuity on the horopter did not falloff to the same extent. Ciearly the decline of t’,strahoropteral stereoacuity was not due to any limitation of retinal eccentricities that were required of each eye to produce the disparity pedestal. These results can be explained however by factors inflencing information processing after the early stages represented by the spatial channels currently postulated. Differences in the t\vo measures of stereopsis may reflect the differences in increment sensitivity of tuned cortical detectors sensitive to small disparities near the horopter and near-far neurones sensitive to large disparities proximal and distal to the horopter (Poggio and Fischer, 1977; Poggio and Talbot. 198 i 1. Since the parafoveal retina seems to be capable of encoding extremely small offsets to be used for stereopsis that are unavailable to the vernier system it is apparent that different factors, which are prssumably not retinal, limit performance on the two tasks (Westheimer and McKee. 1979: Geisler. 1984).
Relationship between stereo and vernier acuity
Schor C. AM.,Wood I. C. and Ogawa J. (I984a) Spatial tuning of static and dynamic local stereopsis. Vision Rex
RElXRENCES Berry R. (1948) Quantitative relations among vernier, real depth. and stereoscopic depth acuities. J. e.rp. Psvchol. 38, 708-72 I. Berry R. N.. Riggs L. A. and Richards W. (1950) The relation of vernier and depth discrimination to width of test rod. J. e.up. Psychoi. lo, 520-522. Blakemore C. (1970) The range and scope of binocular depth discrimination in man. J. Physiof. Zfl, 599-622. Enoch J. .M.. Williams R. A., Essock E. A. and Barricks M. (1984) Hyperacuity perimetry. Archs Ophthalmol. 102, 1164-l 168. Fendick M. J. and Westheimer G. (1983) Effects of practice and the separation of test targets on fovea1 and peripheral stereoacuity. Visian Rrs. 23, 145-150. Grisler W. S. (1984) Physical limits of acuity and hyperacuity. J. opt. Sot. Am. A 1, 775-782. Goodman J. W. t 1968) introduction to Fourier Optics: ,McGral~-Hill
Ph)*sicai
and Quanatum
1119
Electronic
Series
(Edited by Terman F. E.). McGraw-Hill, New York. Graham N.. Robson J. G. and Nachmias J. (1978) Grating summation in fovea and periphery. Visian Res. 18, 8 15-m. Levitt H. (t97I) Transformed up/down methods in psycho acoustics. J. acousi. Sot. Am. 49, 461-477. McKee S. and Westheimer G. (1978) Improvement in vernier acuity with practice. Percept. Psychophys. 24, 358-262. ,McKee S. (1983) The spatial requirements for fine stereoacuity. V&IZ Res. 23, 191-198. Poggio G. F. and Fischer B. (1977) Binocular interaction and depth sensitivity of striate and prestriate cortical neurones of the behaving rhesus monkey. J. Neurophysiol 40, 1392-140s.
Poggio G. F. and Talbot W. H. (1981) Mechanisms of static and dynamic stereopsis in fovea1 cortex of the rhesus monkey. J. fhysiol. 315, 469-492.
24, 573-578.
Schor C. M.. Wood I. C. and Ogawa J. (1981b) Binocular sensory fusion is limited by spatial resolution. Vision Res. 24, 661-665.
Stigmar G. (1970) Observations on vernier and stereo acuity with special reference to their relationship. ilcta ophrhaf. 48, 979-799. Stigmar G. (1971) Blurred visual stimuli: The effect of blurred visual stimuli on vernier and stereoacuity. Acra ophrhal.
49, 364-379.
Walls G. L. (1943) Factors in human visual resolution. J. opl Sac. Am. 33, 487-505. Westheimer G. and Mckee S. (1978) Stereoscopic acuity for moving retinal images. J. opr. Sot. Am. 68, 4D-455. Westheimer G. and &McKeeS. (1979) What prior uniocular processing is necessary for stereopsis. Inaesl. Ophfhaf. visual Sci. 18, 6 14-62 I. Westheimer G. and McKee S. (1980) Stereoscopic acuity with defocused and spatially filtered retinal images. J. opt. Sot.
Am. 70, 772-787.
Westheimer G. (1982) The spatial grain of the perifoveal visual field. Yirion Rex 22, t57-162. Wheatstone C. (1838) Contributions to the physiology of vision: I. On some remarkable and hitherto unobserved, phenomena of binocular vision. Trans. Phil. R. Sot., Land. 128, 371-394. Williams R. A., Enoch J. M. and Essock E. A. (1984) The resistance of selected hyperacuity configurations to retinal image degradation. ftraest. Oph~ha~. visuai Sci. 25, 389-399.
Wilson H. (1978) Quantitative characterization of two types of line spread function near the fovea. Vision Res. 18, 971-981.’ Wilson H. and Bergen H. R. (1979) A four mechanism model for threshold spatial vision. Vision Rex 19, 19-32.
Copyright c
0042-6989 85 S3.00 + 0.00 1985 Pergamon Press Ltd
A COMPARISON OF STEREO AND VERNIER ACUITY WITHIN SPATIAL CHANNELS AS A FUNCTION OF DISTANCE FROM FIXATION CLIFTON M. SCHOR and DAVID R. BADCOCK* University of California. School of Optometry, Berkeley, CA 94720, U.S.A.
(Received 3 October 1984; in revised form 8 January 1985) Abstract-We have used DOG stimuli in order to investigate the relationship
to selectively stimulate size tuned channels within the visual system between stereo and vernier acuity. We measured these acuities as a function of spatial frequency. retinal eccentricity and distance from the fixation point in depth. Both hyperacuities are poorer with low spatial frequencies but vernier was effected to a smaller extent. Vernier acuity deteriorated to a much greater degree than stereo acuity as retinal eccentricity increased up to 10 arc min. Stereo acuity was more dependent upon distance from the fixation point in depth than would be expected from the dependence of vernier acuity on retinal eccentricity. We conclude that there must be different limiting factors for the two hyperacuity tasks. Horouter Loc&ed
Stereopsis Vernier alignment Hyperacuity Parafovea Blur Spatial channels pedestal
INTRODUCIION
Stereopsis and vernier alignment are two forms of hyperacuity that respond to relative spatial localization within the visual field. Relative spatial displacements within the retinal image as small as several seconds of arc can stimulate the perception of stereoscopic depth when presented dichoptically and of spatial misalignment when the perception presented monocularly. The similarity of retinal stimuli for these two forms of hyperacuity has led to the suggestion that sensitivity to vernier offset maybe a precursor for stereo-sensitivity (Wheatstone, 1838). This suggestion implies that the binocular stereoscopic threshold would equal the sum of the two monocular vernier thresholds. Contrary to this however, most studies report that the binocular stereo threshold equals a single monocular vernier threshold (Berry, 1948; Stigmar, 1970; Westheimer and McKee, 1979). Differences in stereo and vernier sensitivity become exaggerated under specific test conditions. As vernier like targets are blurred, stereoacuity falls off more rapidly than vernier acuity (Berry, 1948; Stigmar, 1971). The relationships between these two hyperacuities as a function of the vertical separation or gap size between upper and lower line segments has been examined by Berry (1948) who reports that vernier sensitivity falls off more rapidly than stereo sensitivity as gap width increases. However, Stigmar (1970) comes to the opposite conclusion. Part of the
*Present address: Department of Psychology, University of Melbourne, Parkville, Victoria 3052, Australia.
Depth increment threshold frequency analysis
Disparity
effect of gap separation may be due to reduced sensitivity in the retinal periphery. Both vernier acuity (Westheimer, 1982; Enoch ef al., 1984) and stereoacuity (Blakemore, 1970) become poorer with increased retinal eccentricity, however, these effects have never been directly compared. To make this comparison we must also consider the spatial channels that are potentially responding to the stimulus. Recent work suggests that the visual system is composed of multiple channels with luminance weighting functions that can be described by a difference of two Gaussians (Wilson, 1978). Several sizes of these channels exist at each retinal eccentricity (Wilson and Bergen, 1979; Graham et a/., 1978). As eccentricity increases, the size of all channels increases so that the range of spatial frequencies processed moves to lower frequencies. It is possible that the above changes in vernier and stereoacuity reflect this progressive change of channel size. To address this possibility we have employed difference-of-Gaussian (DOG) luminance distributions of various widths as stimuli which allow us to examine the effects of retinal eccentricity upon vernier and stereo acuity, within a channel having a DOG receptive field profile. The effects of blur upon hyperacuity may also be better understood by examining the frequency spectrum. Blurring stimuli causes a reduction in the high spatial frequency content (the changes are somewhat more complex than this as we will discuss below but this does not matter to the current argument). This change will modify the distribution of channel sizes effectively stimulated. This raises the possibility that the effects of blur are also related to changes in the population of stimulated detectors. Examining be-
III3
IllI
CLFTOU
M.
SCHOR
and
ha\lor within DOG channels of different sizes and at different retinal eccentricities may help compare stereo and vernier sensitivity under equivalent stimulus conditions. METHODS We have compared stereoacuity with vernier resolution using a ‘*stereo-vernier target” suggested by Walls (1943). The classic target consists of two vertical rods. one above the other. We have replaced the rods with DOGS. Vernier acuity was investigated by presenting two DOGS, one above the other, to one eye. The upper DOG was displaced laterally to produce a vernier offset. Stereopsis was investigated by presenting these vernier targets haploscopically to each eye but with lateral displacements in opposite directions to produce disparity. A computer controlled the magnitude of the offset during each stimulus presentation. The upper and lower halves of the DOG were each two degrees long. They were separated by a 3 arc min gap. This gap produces good vernier acuity (Westheimer, 1952) and was produced with a black horizontal line placed across the display screens. These stimuli were presented on two 603 Tekrronix oscilloscopes (subtending 8 deg x I2 deg) that were viewed haploscopicaliy at a distance of 57cm from two front surface mirrors placed before the eyes at angles of I35 and 45 deg. The test stimuli were DOGS that were produced from look up tables and passed through 8 bit Digital to Analogue converters. The luminance profile of the DOGS had the form
DOG(X)
= 3 expf -x1/a’)
- 2 exp(-xz/2.25az).
The spatial extent of the negative Gaussian function was I .5 times wider than that of the positive gaussian. The net sum of their areas equaled the mean background luminance (40 cd/m?). DOGS had bandwidths of 1.75 octaves at half height and center spatial frequencies of 0.15, 0.6, 2.4 and 9.6 c/deg. Effects of retinal eccentricity upon stereo and vernier acuity were investigated with comparable stimuli. Extra fovea1 vernier acuity was measured by placing the vernier DOG stimulus to the left of a central fixation point before the left eye while the right eye viewed a black felt patch. During the study of stereopsis a second vernier DOG was presented to the right eye at the same retinal eccentricity in the same or in the opposite half of the visual field as the DOG vernier stimulus seen by the left eye. When presented in the same hemifield, the stereovernier target produced a disparity increment between the upper and lower DOG in the frontoparallel plane. When presented in the opposite hemifieid the stereo-vernier target produced an extrahoropteral or disparity pedestal stimulus, that appeared either in front of or behind the fixation point. The subject’s task was to discriminate between the presence and absence of depth differences between
DAVID R. BAUCOCK
the upper and lower vernier DOGS subtended from the disparity pedestal. Both of these conditions are comparable to the monocular vernier experiment since closing either eye during the stereo depth increment threshold task yielded a monocular I-srnier judgement task at a fixed retinal eccentricity. Any influence of vernier resolution upon disparity processing should be reflected in the fronto-parallel and extra-horopterai measures of stereo-increment threshold. During vernier and fronto-parallel stereo tests, DOGS were placed at the fixation point and to the left at retinal eccentricities of 5, IO, IO and 40 arc min. We selected this range of retinal eccentricities to produce a range of disparity pedestals within the scope of quantitative stereopsis when the vernier targets were presented to opposite hemifieids. During extra horopteral stereo tests DOGS were placed at the same retinal locations but in opposite halves of the visual field to produce disparity pedestals of 0, IO, 20, 40 and 80 arc min in either the crossed or uncrossed direction. Stereo and vernier increment thresholds were determined at these retinal eccentricities using DOGS whose center spatial frequencies ranged from 0. I5 to 9.6 c/deg (center widths ranging from 6.7 to 0. I deg respectively). Vergence eye movements were controlled with a small central fixation spot surrounded by two other spots. These three spots provided a fronto-parallel reference plane. Nonius lines were placed below the left and above the right eyes’ central fixation point. Sensitivity to vergence errors was approximately I arc min. Trials were rejected when noticeabie vergence errors occurred. Specific details for vergence control are presented elsewhere (Schor PI al., 1984b). Thresholds were measured with a two alternative forced choice staircase with 9 reversals that converged in approximately 50 trials upon a ?I”,; “correct” performance ievei (Levitt, 1971). The pedestal and pedestal plus test disparity combinations were presented in randomized order, each for 750 msec. A tone preceded each test stimulus and it also provided feedback for incorrect responses. Subjects indicated in which of the two intervals that they perceived the relative depth offset by pressing one of two buttons. The computer evaluated their response and in the next trial presented a smaller offset if two consecutive responses were correct and a larger offset if one response was incorrect. Step size was varied with an 8 bit logarithmic attenuator such that steps became smaller as the threshold was approached. The smallest step size was 0.8 arc set for stereopsis and 0.4 arc set for vernier acuity. The magnitude and direction of disparity pedestals were randomized for a given DOG during a given test session although they were not varied during a staircase. The size of a DOG was ~ISO randomized between test sessions. Each session consisted of ten test pedestals for a given size DOG and each of these sessions were repeated three times. The entire procedure was under computer control. Tests
1115
Relationship between stereo and vernier acuity svere conducted on three subjects who had normal binocular vision and fully corrected refractive states. RESULTS The results obtained for vernier and stereo acuity are plotted for 3 subjects in the upper and lower halves of Figs l-3 respectively. We have multiplied a/f monocular vernier thresholds by a factor of two in order to compare them with the monocular precision required for stereo processing which by definition is the sum of :wo monocular components. The reciprocal of these doubled vernier thresholds are plotted both as a function of DOG center spatial frequency and retinal eccentricity in arc min. Stereo sensitivity is plotted both as a function of DOG center spatial frequency and disparity pedestal size. The results obtained with crossed and uncrossed disparity pedestals were indistinguishable, and have therefore been pooled as a mean of 6 threshold measures in this presentation. Vernier sensitivity for ail observers decreased markedly as spatial frequency was reduced. Fovea1 thresholds increased by a factor of 4 for two subjects (C.S. and D.B.) and by a factor of 2 for the third subject (M.M.) as spatial frequency decreased from 9.6c/deg to 0.15 c/deg. Similar reductions of sensitivity occurred with retinal eccentricity. Vernier thresholds at high spatial frequencies decreased by factors of 29 and 3 for the three subjects (C.S., D.B., and M.M. respectively) as stimuli were moved from the fovea to an eccentricity of 40 arc min. The changes with eccentricity were greater with narrow (high frequency) DOGS for one subject (D.B.) (Fig. 2) and they were equal to those obtained at lower frequencies for the two other subjects (Figs 1 and 3). Stereosensitivity underwent similar changes with decreasing spatial frequency. As the center spatial frequency of DOGS decreased, stereo threshold for the zero disparity pedestal increased by factors of IO, 6 and 5 for the three subjects. These increases were much greater than those observed with vernier acuity and they were similar to the changes in stereothreshold as a function of spatial frequency observed by Schor, Wood and Ogawa (1984). Stereosensitivity was also reduced by factors of 7, 8 and 5 for subjects C.S., D.3. and M.M. respectively as disparity pedestal increased to 80 arc min. This increase in stereothreshold with disparity pedestal was greater with DOGS having high than low center spatial frequencies in one subject (C.S.) and increase was approximately the same for ail center spatial frequencies in the other two subjects. Interestingly, stereosensitivity measured in the fronto-parallel plane was unaffected by retinal eccentricity in all three subjects. Stereosensitivity at various eccentricities in the fronto-parallel plane is represented by the mixed dashed line plotted in Figs 4-6. This measure of stereopsis remained at its peak level for ail spatial frequencies (high and low frequencies shown in top
and bottom plots of Figs 4-6) over the entire range of retinal eccentricities (O-40 arc min) in contrast to the 10 fold change of stereoacuity with an 80 arc min disparity pedestal produced by two 40 arc min retinal image displacements. Figures 4-6 compare for three observers the effects of retinal eccentricity and comparable disparity pedestals upon vernier acuity and stereopsis respectively. Results obtained with a high (9.6cideg) and low (0.15 c/degf center spatial frequency are shown in the upper and lower halves of the figure. For all three observers and for all spatial frequency targets, extrahoropteral stereothresholds increased markedly with the magnitude of disparity pedestal or offset from the horopter. In contrast, fronto-parallel stereothresholds changed little if at all when tested at retinal eccentricities that were equivalent to the extrahoropteral disparity pedestals. The same figures illustrate that vernier thresholds tested away from the fovea with high spatial frequencies (upper plots) were lower than extra-horopteral stereo thresholds and they were higher than fronto-parallel stereothresholds. Vernier thresholds tested with low spatial frequencies were usually lower than extra-horopteral stereothresholds and they were both lower and higher than fronto-parallel stereothresholds. Vernier thresholds were lower than fronto-parallel stereothreshoids at small retinal eccentricities, and a reverse relationship occurred at larger retinal eccentricities. In two observers (D.B. and M.M.) vernier threshold, stereoalthough lower than extra-horopteral thresholds, increased at a similar rate. These results are plotted on a log scale so that the constant separation in the vernier and extra-horopteral stereo functions shown in Figs 5 and 6 represents a fixed multiple. If they were transformed to a linear scale the two functions would diverge. For example in the top of Fig. 5, vernier and extra-horopteral stereo thresholds differ by 2 arc set at the fovea whereas they differ by 5 arc set when tested at 40 arc min retinal eccentricity and the corresponding 80 arc min disparity pedestal respectively. DISCUSSION
The major impetus for this study was to investigate differential sensitivity of spatial channels to relative position. We examined these channels with DOG stimuli to isolate a narrow range of continuous widths or spatial frequencies. Previously this problem was addressed with blurred stimuli (Stigmar, 1971; Westheimer and McKee, 1980; Williams er ai., 1984). Blur changes the relative contribution of channels tuned to different spatial widths but it does not provide the precise control of spatial stimulus components that can be obtained with DOG stimuli. Westheimer and McKee (1980) describe the effects of spectacle blur (see their Fig. 3) which reduces the transfer of higher spatial frequencies. The function is not monotonic, however, since it has regions of
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energ) in higher frequency bands (for a discussion see Goodman. 1968). Ground glass blurring [see Stigmar t 19il), Westheimer and McKee / 1980). Fig. 4 and LViliiams ri (II. (19%). Fig. l] attenuates high frequencies more than low frequencies, however it does not allow band pass selection of intermediate spatial frequencies. To achieve a narrou’ band stimulus. Westheimer and McKee (1980) used B narrow DOG to produce a stimulus with only high spatial frequencies. They found that reducing the high frequency content of stimuli caused a deterioration of stereoacuity. However a DOG centered on a high frequency (22 c;deg) resulted in a greater reduction of stereoacuity than found with the elimination of high frequencies. They concluded that the entire frequency spectrum was required for optimal steroperformance. The current study shows that good stereopsis requires frequency information above 2.4c/deg up to 9.6 cideg both on and olT the horopter even though only small segments of the frequency spectrum are presented with our DOG stimuli. This result is consistent with the report by Westheimer and McKee ( 1980) provided that stereo-performance deteriorates at higher spatial frequencies than those presented in the current study. Both studies agree that detectable amounts of energy in the range of 2.4 cfdeg up to but less than 22c/deg (the upper limit has not been precisely determined) are required for good stereoperformance. Stereo performance is poorer for channels that respond to frequencies lower than 2.4 c/deg. Vernier ircuity is also reduced with lower spatial frequency stimuli (Stigmar. 1971; Williams et al., 1984) bl*t good vernier acuity depends less upon high spatial frequency information that does stereoacuity. All of our subjects had Larger reductions in stereo than vernier acuity as spatial frequency decreased (when measured at the fixation point). These results indicate that different mechanisms may be involved in these two forms of hyperacuity. Our results confirm previous observations (Blakemore. 1970; Westheimer and McKee, 1978) that stereo increment threshold and stereothresholds of moving targets increase more quickly with distance away from the horopter than with eccentricity along the horopter, even though the same size retinal eccentricities are involved in both stimulus conditions, Recently McKee (1983) has observed a decline of fronto-parallel stereothreshold when tested at 20 arc min retinal eccentricity. Perhaps reductions of stereothreshold are only apparent if the stereoacuity of the central fovea is very good or perhaps reductions of stereoacuity are greater at eccentric retinal sites along the vertical meridian tested by McKee (1983) than those we have observed along the horizontal meridian. In spite of these subtle differences, it is clear that functions describing extra-horopteral stereopsis and fronto-parallel stereopsis are very different. Interestingly, *when tested at large retinal
eccentricities 130 arc mini rernier xuitk fails betbkm these two measures of stsreopsis. These three d~~r~‘pant functions provide a clear demonstration oi the independence of vernier and stereoacuitb. At the fovea or on the horopter all three measures were nearly equal (i.e. the doubled monocular vernier threshold equals the stereothreshold) in two of our subjects (D.B. and M.&i.). It has not escaped our attention that our third subject (C.S.), ivho had tht: best stereoacuity and was the onl) case in ivhich stereoacuity at the fovea could not be accounted for by doubling the vernier threshold. ~~3s also the most experienced with the stereo task. Przctice effects on these tasks are well known (McKee and Westhelmer. 1975: Fendick and Westheimer. 1983) and it appears that il sufficiently experienced subject can produce stereo thresholds that are not limited by monocul:\r vernier acuity (e.g. Berry, 1938: Berry e! ~1.. 1950; Westheimer and McKee. 1979). Thus xc could not make a clear comparison of stereo and vernier ilcuity at the fovea due to practice etTects which were greater than the difTerences we were seeking. We were able however to compare these two hyperacuities in the parafovea where our observers had not >er had extensive experience. In the parafovea, high spatial frequency measures of stereoacuity exceeded vernier acuity by a Pactor of 3 before doubling the vernier threshold. This result is not produced by practice effects since our subjects had more experience with peripheral vernier than peripheral stereo tasks (peripheral stereo was done last). Hence even greater differences between the two hyperacuities than reported here might exist in the parafovea. It appears that the falloff in vernier acuity with increasing eccentricity and the similar falloff in stereoacuity with distance from the horopter was not due to a progressive change in channel size since eccentric stereoacuity on the horopter did not falloff to the same extent. Ciearly the decline of t’,strahoropteral stereoacuity was not due to any limitation of retinal eccentricities that were required of each eye to produce the disparity pedestal. These results can be explained however by factors inflencing information processing after the early stages represented by the spatial channels currently postulated. Differences in the t\vo measures of stereopsis may reflect the differences in increment sensitivity of tuned cortical detectors sensitive to small disparities near the horopter and near-far neurones sensitive to large disparities proximal and distal to the horopter (Poggio and Fischer, 1977; Poggio and Talbot. 198 i 1. Since the parafoveal retina seems to be capable of encoding extremely small offsets to be used for stereopsis that are unavailable to the vernier system it is apparent that different factors, which are prssumably not retinal, limit performance on the two tasks (Westheimer and McKee. 1979: Geisler. 1984).
Relationship between stereo and vernier acuity
Schor C. AM.,Wood I. C. and Ogawa J. (I984a) Spatial tuning of static and dynamic local stereopsis. Vision Rex
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