THE INFLUENCE
OF PERSPECTIVE
CUES ON THE PERCEPTION
AND DISPARITY OF SLANT
WILLLAM M. YOUKGS’ Dartmouth College. Department of Psychology. Hanover. NH 03755. U.S.A. (Rrceiced 4 ~Vocembrr 1974; in recisedform
14 March 1975)
Abstract-A rectangle rotated about its vertical axis provides many cues regarding its slant relative to the frontoparallel plane including linear perspective and binocular disparity. In thisexperiment, five OS estimated the slant of stereoscopictargets containing one, both, or neither of these cues. Data analysis indicated for figures with vertical contours separated by 3.80” horizontally that perspective was the most effective cue to slant. The results are discussed in relation to Freeman’s theory of slant perception. Further quantitative work concerning the functional relationship between contour separation and the effectiveness of the disparity code is suggested.
basis of Freeman’s work that line and surface targets would be equally effective in perceptually defining slant.
began as an attempt to make a target rectangle presented in a stereoscope appear slanted with respect to the frontoparallel plane using the horizontal disparity cue alone. Specifically, we wanted to make a rectangle appear rotated about its vertical axis. In pilot work, it turned out to be surprisingly difficult to create an impression of slant in the target rectangle using the horizontal disparity cue. We reasoned that either some other cue was compromising the disparity manipulation, or that the disparity manipulation itself was ineffective. For a rectangle slanted with respect to the frontoparallel plane, Freeman (1966; 1970) has argued that the effective retinal stimulus for slant is the difference in the visual angles subtended by the near and far edges of the rectangle. Adopting this angular difference as our working definition of linear perspective, we hypothesized that the relative ineffectiveness of the disparity manipulation in our pilot work may have been due to the absence of linear perspective in the target rectangle, an absence suggestive of a rectangle oriented in a frontoparallel plane. -l-he present investigation was designed to determine the separate and combined influences of linear perspective and binocular disparity cues on the perception of slant and to test Freeman’s assertion that the difference in angular subtense between the near and far edges of a rectangle, in the absence ofother cues, is the effective retinal stimulus for slant. In our study, we employed two main types of targets, surface targets and line targets. Surface targets were either rectangles or trapezoids, the latter designed to represent the appearance of rectangle slanted 45’ relative to an objective frontoparallel plane. Line targets resembled surface targets stripped of everything but their two parallel vertical contours. Line targets contained only those components of a rectangle that Freeman has asserted are used to evaluate slant. Therefore, we hypothesized on the This investigation
METHOD Targets
Four of the eight pairs of target half-images were surfaces, either rectangles or trapezoids. and the remaining four pairs consisted of half-images with two parallel vertical lines having lengths and center-to-center separations identical to the vertical edges of analogous surface targets. Vertical lines were constructed from a black matte contact tape (Chartpak cat. No. 3101 M) which was 08 mm wide. The background for all targets was vellum paper (Aquabee Bristol Pad 1171) which had a luminance of 85 ft-L under lighting conditiohs of the experiment. as contrasted with black matte lines and surfaces which had a luminance of 3 ft-L. Both the background and the targets had a uniform, textureless appearance under conditions of this experiment. The four surface targets in the experiment had either disp$y and perspective (DP), no disparity but perspective (DP), disparity but no perspective (DP), or no disparity and no perspective (m). Line targets were completely analogous. Illustrative examples of surface and line half-image pairs from the DP condition are shown in Fie. 1. The table in the lower portion of Fig. I provides the dkensions (in cm) of the target half-images used in .the experiment. Note that the same target dimensions apply to the four surface condit&ns as a& to the analogous iour line conditions (DP. DP. DF. DP). Vie&d through the stereoscope. the lengths of the left and right vertical contours in each ha[f-image of a stereo-
gram with perspective (P) were 2” (2.90cm) and 2.1’ (3.10cm), respectively, whereas the lengths were both 2’ for the vertical contours in no perspective conditions (p). The horizontal separations of the vertical contours for the left and right stereoscopic half-images in all stereograms with disparity (D) was 3.95” (5.80 cm) and 3.65’ (5.35 cm) visual angle, respectively. For targets without disparity @), the horizontal separation of the vertical contours for both left and right half-images was 3.80” (5.55 cm) visual angle. The horizontal separation of the vertical contours in all experimental stereograms appeared constant inasmuch as the mean separation of the vertical contours for all halfimage pairs was always 3.80. (i.e. D: (3.95 + $65)/2 = 3.80:b: (3.80 -t 3.80)/2 = 3.80). Thus. apparent foreshort-
’ Present address: The Worcester Foundation for Experimental Biology, 222 Maple Avenue, Shrewsbury, MA 01545, U.S.A. 79
TARGET Surfac.
DIMENSIONS Targer Target
t
f
AL
8,
I
holder
1 -c,
-
-c,
-
(b)
Headr
Fig. I. The dimensions of surface and line targets in the experiment. Values in the table apply to both surface and line target half-images. Sample stereograms in the top portion of the figure are from the DP condition of the experiment.
Fig. 2. Schematic diagram of the Wheatstone-style stereoscope used in the experiment as seen in perspective view (a) and from above (b). Dashed lines in Part (b) refer to o’s lines of sight from left and right eyes to the target plane.
ening along the horizontal axis. which normally accompanies slant when rigid bodies are rotated about the vertical axis in physical space, was eliminated as a cue to slant in the present experiment. Both perspective and disparity were calculated to accurately represent surface and line targets in physical space which were rotated 45’ with respect to an objective frontoparallel plane such that the right vertical contour was nearest to 0. Alternatively. we could have placed a meridional afocal magnification lens in front of one eye to introduce horizontal disparity in the targets of this experiment (see Ogle, 1950). However, we elected to use the present target construction technique because a meridional lens would have magnified ecer);thirtg along the horizontal meridian. Thus, in the case of line targets with disparity (DP, D’ii), a meridional lens would have increased effectively not only the horizontal separation of the two vertical lines but would have increased also the apparent width of the vertical lines seen by one eye. Increasing line width to one ey-e would have provided stimulus conditions appropriate for the rotation ofeachICte itself about a vertical axis, a potential cue to the roration of the plane of the pair of lines which we sought to eliminate.
less than 96% on the Fry-Shepard Scale. In addition. OS demonstrated normal near lateral and vertical phoria scores. All OS were naive to the experimental hypotheses.
A Wheatstone-style stereoscope with first surface mirrors was employed (see Fig. 2). The viewing distance from the bisector of the interpupillary axis to the center of the target field was S4cm. A padded forehead rest served to limit head movement and to maintain O’s interocular axis parallel to the front of the stereoscope. Square viewing apertures I.1 cm on a side located approx 4 cm forward of O’s cornea were adjustable to individual pupillary separation. Room lights were off and each target half-image was front illummated by two vertically oriented 15-W fluorescent lights (not shown in Fig. 2) sufIiciently lateral to O’s restricted field of view so as to be out of sight. Obsrrcers
Five undergraduates (two men. three women) enrolled in introductory psychology participated in the experiment. A preliminary vision test conducted with a Bausch and Lomb IMaster Ortho-Rater (cat. No. 71-21-40-65) indicated that all OS had visual acuities corresponding to a Snellen fraction of 20:22 or better and stereoscopic acuities of not
Trairling
During training OS were seated in a chair facing the training apparatus which consisted of a dark rectangle on a light background. The dark rectangle was hinged about its left vertical edge and could be swung toward the 0 and fixed at any desired angle relative to the background. The OS were trained to judge the angle formed by the plane of the dark rectangle relative to the light background which remained in an objective frontoparallel plane. Training was carried out in a semidarkened room with only the training apparatus illuminated. The rectangle, viewed from a distance of I m, had a height and width of 2” and 4” visual angle, respectively, when in the frontoparallel plane. The OS were given a minimum of IO training trials with feedback about their performance after every judgment. Each 0 was required to make five consecutive judgments correct to within 5’ of the actual angle set by E. During training, angles of the rectangle relative to the background were varied between 0” and 5.5”.Each training series consisted of a random series of angles with each 0 seeing a different random series. All OS trained to criterion in fewer than 20 trials. Experimental
task
Immediately following training, each 0 saw the set of eight stereoscopic target pairs five times in random order. Trial order was randomized across conditions and repetitions such that a given target could, and sometimes did, follow itself. The OS were asked to close their eyes between trials while targets were being changed and, just as in training, they were asked to judge the angle formed between the surface and the background but were given no feedback about their performance. In the case of the line targets, OS were told to imagine a plane passing through the two vertical lines and to report the angle formed with the background by that plane. The OS were allowed to report angles which indicated that the right edge or line appeared further away than the left edge or line even though target conditions were inappropriate for such reports.
Perspective and disparity cues RESLZTS
Mean judged slant for each of the eight experimental stereograms are shown in Fig. 3. For data collapsed over repetitions. an analysis of variance (disparity level x perspective condition x target type x observers) revealed a significant main effect of perspective (F = 78.4: d.f. = I. 4; P < O-002). No other significant main effect or interaction was found. The mean judged slant for targets with perspective (P) was 24.3”, whereas the mean judged slant for targets without perspective (P) was only 8.2”Aative to the frontoparallel plane. Analysis of the DP data alone indicates that OS reported a small but significant slant for surface and line targets in the absence of perspective and disparity (t = 364; d.f. = 9: P < O-005). As can be seen in Fig. 3, OS underestimated the 45” slant predicted by the perspective and disparity cues. DISCUSSION
Results of the present study are consistent with the assertion that a visual angle difference between the near and far edges of a rectangle (perspective) is an effective retinal stimulus for slant. The data reveal that. as a group, surface and line targets with perspective were judged to have significantly more slant than targets without perspective. Failure to find significant differences between the slants reported for surface and line targets suggests that perspective is just as effective a cue to slant for line targets as it is for rectangles. This experiment raises some questions. It is not clear. for example, why OS in this experiment underes50
45
40
DP
6P
Di
ET;
Condition
Fig. 3. Mean judged slants relative to the frontoparallel plane (fpp) for each of the eight experimental stereograms. Inset shows the summary table for the analysis of variance. The analysis revealed that surface and line targets with perspective (P) were judged to have significantly more slant than surface and line targets without perspective. The type of target (T = surface or lines) and the presence of disparity (D) had no significant effect on the amount of slant
reported.
81
timated the slant of surface and line targets even in the presence of perspective and disparity cues. Judgments of slant, on the average, were less than half the amount expected on the bases of the perspective and disparity cues. Smith (1967) reports similar underestimations by OS viewing trapezoids under monocular and binocular viewing conditions. In addition. Beck and Gibson (1955) report that, “the presumption of frontal position wins out in a striking way over the presumption of rectangular shape” when OS are required to judge both the shape and orientation of quadrilateral forms viewed under reduced cues. Whether the underestimation of slant represents the influence of a similar presumption by OS in the present experiment, or is attributable to the loss of such cues as foreshortening or texture gradients. remains to be determined. Whatever the causes of underestimation. it is clear from the training procedure that 0s in a full cue situation given feedback about their performance rapidly acquire an ability to judge slant with high accuracy. Reports of small but significant slants in the absence of experimentally defined appropriate perspective and disparity cues has precedence but is nonetheless curious. While determining slant thresholds for 14 sizes of textureless rectangles. Freeman (1966) found that the median subjective frontoparallel plane for OS in his experiment deviated from the objective frontoparallel plane by 3.55’. He proposed that the bias shown by his subjects may have been a simple response tendency related to the button pushing experimental task or that the bias may have reflected an adaptation to retinal perspective brought about by long-term, extraexperimental experience with slanted surface in the visual environment. Given the difference in the axis of rotation of our targets and the difference in our experimental task relative to Freeman’s, neither of these explanations of the bias seems applicable to the present case. Ogle (1938; 1939a; 1939b) has demonstrated that meridional differences in the size of ocular images can result in an apparent tilt of the visual field. If naturally occurring meridional differences in the size of ocular images (i.e. aniseikonia) are responsible for the tendency of OS in this experiment to report small slants in the absence of appropriate target cues, then why are similar experimentally imposed manipulations so ineffective in enhancing th_e impression of slant? Compare, for e.xample, the DP and DP conditions for surface targets. A full understanding of this response tendency awaits further study. Finally, the results of this experiment demonstrate a clear need to understand better the limits of the disparity coding mechanism in the human visual system. Much psychophysical and electrophysiological evidence has emerged over the years to suggest highly sophisticated and sensitive disparity coding mechanisms in mammalian visual systems including man (for representative psychophysical data, see Lawson and Gulick. 1967; Foley, 1968; Foley and Richards. 1971; an article by Bishop, 1973, summarizes much of the electrophsyiological evidence gathered over the last decade). Why the mechanism for disparity coding fails so miserably in the present case needs CIarification. Specifically, we need to understand more fully the functional relationship between
2
WfLL1A.M
the effectiveness of disparity coding and the horizontal separation of disparate contours. Acl;nowledgemenr--The author wishes to thank Professor W. L. &lick for his helpful comments offered during the preparation of this manuscript.
REFERESCE!3
Beck J. and Gibson J. J. (19%) The relation of apparent shape to apparent slant in the perception of objects. 1. up: Psychbi. 50. 1X-133. Bishoo P. 0. (1973) \ , Neuroohvsioloev ., *_ of binocular single vision and stereopsis. In Handbook of Srrisory Ph.&ology. Vol. VII’3A (Edited by Jung R.) chap. 4. Springer, Berlin. Foley J. M. (1968) Depth. size and distance in stereoscopic vision. Prrcepr. Ps!~chophys. 3. 265-274. Foley J. M. and Richards W. (1972) Effects of voluntary eye movement and convergence on the binocular appreciation of depth. Percept. Psychophn. 11. 423-437.
hit
:OUNGS
F mnnn. R. B. (1966) Absolute
threshold for visual slant: the effect of stimulus size and retinal perspective J. e?cp. Psvchol.
71. 170--176.
Freeman R. B. (1970) Theory of cues and the psychophysics of visual space perception. Psychon. Monogr. Suppl. 3(13). Whole No. 45. 171-181. Lawson R. B. and Gulick W. L. (1967) Stereopsis and ano_?qlous contour. Vision Res. 7. 271-297. Ogle K. N. (1938) Induced size effect--I: A new phenomenon in binocular space perception associated with relative sizes of the images of the two eyes. Archs Ophthal.. .V.Y 20. 604-623. Ogle K. N. (1939a) Induced size effect-II: An experimental study of the phenomenon with restricted fusion stimuli. Archs Ophrhal., N.E 21. 605-625. Ogle K. N. (l939b) Induced size effect-III: A study of The phenomenon as influenced by horizontal disparity of the fusion contours. Archs Ophrhal.. X.1: 22. 613-635. Ogle K. N. (1950) Researches in &ocular Vision. Saunders. Philadelphia. Smith A. H. (1967) Perceived slant as a function of stimulus contour and vertical dimension. Percrpt. Mot. Skills 24. 167-173.
OF PERSPECTIVE
CUES ON THE PERCEPTION
AND DISPARITY OF SLANT
WILLLAM M. YOUKGS’ Dartmouth College. Department of Psychology. Hanover. NH 03755. U.S.A. (Rrceiced 4 ~Vocembrr 1974; in recisedform
14 March 1975)
Abstract-A rectangle rotated about its vertical axis provides many cues regarding its slant relative to the frontoparallel plane including linear perspective and binocular disparity. In thisexperiment, five OS estimated the slant of stereoscopictargets containing one, both, or neither of these cues. Data analysis indicated for figures with vertical contours separated by 3.80” horizontally that perspective was the most effective cue to slant. The results are discussed in relation to Freeman’s theory of slant perception. Further quantitative work concerning the functional relationship between contour separation and the effectiveness of the disparity code is suggested.
basis of Freeman’s work that line and surface targets would be equally effective in perceptually defining slant.
began as an attempt to make a target rectangle presented in a stereoscope appear slanted with respect to the frontoparallel plane using the horizontal disparity cue alone. Specifically, we wanted to make a rectangle appear rotated about its vertical axis. In pilot work, it turned out to be surprisingly difficult to create an impression of slant in the target rectangle using the horizontal disparity cue. We reasoned that either some other cue was compromising the disparity manipulation, or that the disparity manipulation itself was ineffective. For a rectangle slanted with respect to the frontoparallel plane, Freeman (1966; 1970) has argued that the effective retinal stimulus for slant is the difference in the visual angles subtended by the near and far edges of the rectangle. Adopting this angular difference as our working definition of linear perspective, we hypothesized that the relative ineffectiveness of the disparity manipulation in our pilot work may have been due to the absence of linear perspective in the target rectangle, an absence suggestive of a rectangle oriented in a frontoparallel plane. -l-he present investigation was designed to determine the separate and combined influences of linear perspective and binocular disparity cues on the perception of slant and to test Freeman’s assertion that the difference in angular subtense between the near and far edges of a rectangle, in the absence ofother cues, is the effective retinal stimulus for slant. In our study, we employed two main types of targets, surface targets and line targets. Surface targets were either rectangles or trapezoids, the latter designed to represent the appearance of rectangle slanted 45’ relative to an objective frontoparallel plane. Line targets resembled surface targets stripped of everything but their two parallel vertical contours. Line targets contained only those components of a rectangle that Freeman has asserted are used to evaluate slant. Therefore, we hypothesized on the This investigation
METHOD Targets
Four of the eight pairs of target half-images were surfaces, either rectangles or trapezoids. and the remaining four pairs consisted of half-images with two parallel vertical lines having lengths and center-to-center separations identical to the vertical edges of analogous surface targets. Vertical lines were constructed from a black matte contact tape (Chartpak cat. No. 3101 M) which was 08 mm wide. The background for all targets was vellum paper (Aquabee Bristol Pad 1171) which had a luminance of 85 ft-L under lighting conditiohs of the experiment. as contrasted with black matte lines and surfaces which had a luminance of 3 ft-L. Both the background and the targets had a uniform, textureless appearance under conditions of this experiment. The four surface targets in the experiment had either disp$y and perspective (DP), no disparity but perspective (DP), disparity but no perspective (DP), or no disparity and no perspective (m). Line targets were completely analogous. Illustrative examples of surface and line half-image pairs from the DP condition are shown in Fie. 1. The table in the lower portion of Fig. I provides the dkensions (in cm) of the target half-images used in .the experiment. Note that the same target dimensions apply to the four surface condit&ns as a& to the analogous iour line conditions (DP. DP. DF. DP). Vie&d through the stereoscope. the lengths of the left and right vertical contours in each ha[f-image of a stereo-
gram with perspective (P) were 2” (2.90cm) and 2.1’ (3.10cm), respectively, whereas the lengths were both 2’ for the vertical contours in no perspective conditions (p). The horizontal separations of the vertical contours for the left and right stereoscopic half-images in all stereograms with disparity (D) was 3.95” (5.80 cm) and 3.65’ (5.35 cm) visual angle, respectively. For targets without disparity @), the horizontal separation of the vertical contours for both left and right half-images was 3.80” (5.55 cm) visual angle. The horizontal separation of the vertical contours in all experimental stereograms appeared constant inasmuch as the mean separation of the vertical contours for all halfimage pairs was always 3.80. (i.e. D: (3.95 + $65)/2 = 3.80:b: (3.80 -t 3.80)/2 = 3.80). Thus. apparent foreshort-
’ Present address: The Worcester Foundation for Experimental Biology, 222 Maple Avenue, Shrewsbury, MA 01545, U.S.A. 79
TARGET Surfac.
DIMENSIONS Targer Target
t
f
AL
8,
I
holder
1 -c,
-
-c,
-
(b)
Headr
Fig. I. The dimensions of surface and line targets in the experiment. Values in the table apply to both surface and line target half-images. Sample stereograms in the top portion of the figure are from the DP condition of the experiment.
Fig. 2. Schematic diagram of the Wheatstone-style stereoscope used in the experiment as seen in perspective view (a) and from above (b). Dashed lines in Part (b) refer to o’s lines of sight from left and right eyes to the target plane.
ening along the horizontal axis. which normally accompanies slant when rigid bodies are rotated about the vertical axis in physical space, was eliminated as a cue to slant in the present experiment. Both perspective and disparity were calculated to accurately represent surface and line targets in physical space which were rotated 45’ with respect to an objective frontoparallel plane such that the right vertical contour was nearest to 0. Alternatively. we could have placed a meridional afocal magnification lens in front of one eye to introduce horizontal disparity in the targets of this experiment (see Ogle, 1950). However, we elected to use the present target construction technique because a meridional lens would have magnified ecer);thirtg along the horizontal meridian. Thus, in the case of line targets with disparity (DP, D’ii), a meridional lens would have increased effectively not only the horizontal separation of the two vertical lines but would have increased also the apparent width of the vertical lines seen by one eye. Increasing line width to one ey-e would have provided stimulus conditions appropriate for the rotation ofeachICte itself about a vertical axis, a potential cue to the roration of the plane of the pair of lines which we sought to eliminate.
less than 96% on the Fry-Shepard Scale. In addition. OS demonstrated normal near lateral and vertical phoria scores. All OS were naive to the experimental hypotheses.
A Wheatstone-style stereoscope with first surface mirrors was employed (see Fig. 2). The viewing distance from the bisector of the interpupillary axis to the center of the target field was S4cm. A padded forehead rest served to limit head movement and to maintain O’s interocular axis parallel to the front of the stereoscope. Square viewing apertures I.1 cm on a side located approx 4 cm forward of O’s cornea were adjustable to individual pupillary separation. Room lights were off and each target half-image was front illummated by two vertically oriented 15-W fluorescent lights (not shown in Fig. 2) sufIiciently lateral to O’s restricted field of view so as to be out of sight. Obsrrcers
Five undergraduates (two men. three women) enrolled in introductory psychology participated in the experiment. A preliminary vision test conducted with a Bausch and Lomb IMaster Ortho-Rater (cat. No. 71-21-40-65) indicated that all OS had visual acuities corresponding to a Snellen fraction of 20:22 or better and stereoscopic acuities of not
Trairling
During training OS were seated in a chair facing the training apparatus which consisted of a dark rectangle on a light background. The dark rectangle was hinged about its left vertical edge and could be swung toward the 0 and fixed at any desired angle relative to the background. The OS were trained to judge the angle formed by the plane of the dark rectangle relative to the light background which remained in an objective frontoparallel plane. Training was carried out in a semidarkened room with only the training apparatus illuminated. The rectangle, viewed from a distance of I m, had a height and width of 2” and 4” visual angle, respectively, when in the frontoparallel plane. The OS were given a minimum of IO training trials with feedback about their performance after every judgment. Each 0 was required to make five consecutive judgments correct to within 5’ of the actual angle set by E. During training, angles of the rectangle relative to the background were varied between 0” and 5.5”.Each training series consisted of a random series of angles with each 0 seeing a different random series. All OS trained to criterion in fewer than 20 trials. Experimental
task
Immediately following training, each 0 saw the set of eight stereoscopic target pairs five times in random order. Trial order was randomized across conditions and repetitions such that a given target could, and sometimes did, follow itself. The OS were asked to close their eyes between trials while targets were being changed and, just as in training, they were asked to judge the angle formed between the surface and the background but were given no feedback about their performance. In the case of the line targets, OS were told to imagine a plane passing through the two vertical lines and to report the angle formed with the background by that plane. The OS were allowed to report angles which indicated that the right edge or line appeared further away than the left edge or line even though target conditions were inappropriate for such reports.
Perspective and disparity cues RESLZTS
Mean judged slant for each of the eight experimental stereograms are shown in Fig. 3. For data collapsed over repetitions. an analysis of variance (disparity level x perspective condition x target type x observers) revealed a significant main effect of perspective (F = 78.4: d.f. = I. 4; P < O-002). No other significant main effect or interaction was found. The mean judged slant for targets with perspective (P) was 24.3”, whereas the mean judged slant for targets without perspective (P) was only 8.2”Aative to the frontoparallel plane. Analysis of the DP data alone indicates that OS reported a small but significant slant for surface and line targets in the absence of perspective and disparity (t = 364; d.f. = 9: P < O-005). As can be seen in Fig. 3, OS underestimated the 45” slant predicted by the perspective and disparity cues. DISCUSSION
Results of the present study are consistent with the assertion that a visual angle difference between the near and far edges of a rectangle (perspective) is an effective retinal stimulus for slant. The data reveal that. as a group, surface and line targets with perspective were judged to have significantly more slant than targets without perspective. Failure to find significant differences between the slants reported for surface and line targets suggests that perspective is just as effective a cue to slant for line targets as it is for rectangles. This experiment raises some questions. It is not clear. for example, why OS in this experiment underes50
45
40
DP
6P
Di
ET;
Condition
Fig. 3. Mean judged slants relative to the frontoparallel plane (fpp) for each of the eight experimental stereograms. Inset shows the summary table for the analysis of variance. The analysis revealed that surface and line targets with perspective (P) were judged to have significantly more slant than surface and line targets without perspective. The type of target (T = surface or lines) and the presence of disparity (D) had no significant effect on the amount of slant
reported.
81
timated the slant of surface and line targets even in the presence of perspective and disparity cues. Judgments of slant, on the average, were less than half the amount expected on the bases of the perspective and disparity cues. Smith (1967) reports similar underestimations by OS viewing trapezoids under monocular and binocular viewing conditions. In addition. Beck and Gibson (1955) report that, “the presumption of frontal position wins out in a striking way over the presumption of rectangular shape” when OS are required to judge both the shape and orientation of quadrilateral forms viewed under reduced cues. Whether the underestimation of slant represents the influence of a similar presumption by OS in the present experiment, or is attributable to the loss of such cues as foreshortening or texture gradients. remains to be determined. Whatever the causes of underestimation. it is clear from the training procedure that 0s in a full cue situation given feedback about their performance rapidly acquire an ability to judge slant with high accuracy. Reports of small but significant slants in the absence of experimentally defined appropriate perspective and disparity cues has precedence but is nonetheless curious. While determining slant thresholds for 14 sizes of textureless rectangles. Freeman (1966) found that the median subjective frontoparallel plane for OS in his experiment deviated from the objective frontoparallel plane by 3.55’. He proposed that the bias shown by his subjects may have been a simple response tendency related to the button pushing experimental task or that the bias may have reflected an adaptation to retinal perspective brought about by long-term, extraexperimental experience with slanted surface in the visual environment. Given the difference in the axis of rotation of our targets and the difference in our experimental task relative to Freeman’s, neither of these explanations of the bias seems applicable to the present case. Ogle (1938; 1939a; 1939b) has demonstrated that meridional differences in the size of ocular images can result in an apparent tilt of the visual field. If naturally occurring meridional differences in the size of ocular images (i.e. aniseikonia) are responsible for the tendency of OS in this experiment to report small slants in the absence of appropriate target cues, then why are similar experimentally imposed manipulations so ineffective in enhancing th_e impression of slant? Compare, for e.xample, the DP and DP conditions for surface targets. A full understanding of this response tendency awaits further study. Finally, the results of this experiment demonstrate a clear need to understand better the limits of the disparity coding mechanism in the human visual system. Much psychophysical and electrophysiological evidence has emerged over the years to suggest highly sophisticated and sensitive disparity coding mechanisms in mammalian visual systems including man (for representative psychophysical data, see Lawson and Gulick. 1967; Foley, 1968; Foley and Richards. 1971; an article by Bishop, 1973, summarizes much of the electrophsyiological evidence gathered over the last decade). Why the mechanism for disparity coding fails so miserably in the present case needs CIarification. Specifically, we need to understand more fully the functional relationship between
2
WfLL1A.M
the effectiveness of disparity coding and the horizontal separation of disparate contours. Acl;nowledgemenr--The author wishes to thank Professor W. L. &lick for his helpful comments offered during the preparation of this manuscript.
REFERESCE!3
Beck J. and Gibson J. J. (19%) The relation of apparent shape to apparent slant in the perception of objects. 1. up: Psychbi. 50. 1X-133. Bishoo P. 0. (1973) \ , Neuroohvsioloev ., *_ of binocular single vision and stereopsis. In Handbook of Srrisory Ph.&ology. Vol. VII’3A (Edited by Jung R.) chap. 4. Springer, Berlin. Foley J. M. (1968) Depth. size and distance in stereoscopic vision. Prrcepr. Ps!~chophys. 3. 265-274. Foley J. M. and Richards W. (1972) Effects of voluntary eye movement and convergence on the binocular appreciation of depth. Percept. Psychophn. 11. 423-437.
hit
:OUNGS
F mnnn. R. B. (1966) Absolute
threshold for visual slant: the effect of stimulus size and retinal perspective J. e?cp. Psvchol.
71. 170--176.
Freeman R. B. (1970) Theory of cues and the psychophysics of visual space perception. Psychon. Monogr. Suppl. 3(13). Whole No. 45. 171-181. Lawson R. B. and Gulick W. L. (1967) Stereopsis and ano_?qlous contour. Vision Res. 7. 271-297. Ogle K. N. (1938) Induced size effect--I: A new phenomenon in binocular space perception associated with relative sizes of the images of the two eyes. Archs Ophthal.. .V.Y 20. 604-623. Ogle K. N. (1939a) Induced size effect-II: An experimental study of the phenomenon with restricted fusion stimuli. Archs Ophrhal., N.E 21. 605-625. Ogle K. N. (l939b) Induced size effect-III: A study of The phenomenon as influenced by horizontal disparity of the fusion contours. Archs Ophrhal.. X.1: 22. 613-635. Ogle K. N. (1950) Researches in &ocular Vision. Saunders. Philadelphia. Smith A. H. (1967) Perceived slant as a function of stimulus contour and vertical dimension. Percrpt. Mot. Skills 24. 167-173.
