The pursuit of Leonardo's constraint

Independence of Size and Distance in Binocular Vision

For too long, the size distance invariance hypothesis (SDIH) has been the prevalent explanation for size perception. Despite inconclusive evidence, the SDIH has endured, primarily due to lack of suitable information sources for size perception. Because it was derived using the geometry of monocular viewing, another issue is whether the SDIH can encompass binocular vision. A possible alternative to SDIH now exists. The binocular source of size information proposed by Kim (2017) provides metric information about an object's size. Comprised of four angular measures and the interpupillary distance (IPD), with the explicit exclusion of egocentric distance information, Kim's binocular variable demands independence of perceived size and perceived distance, whereas the SDIH assumes interdependence of the two percepts. The validity of Kim's proposed information source was tested in three experiments in which participants viewed a virtual object stereoscopically then judged its size and distance. In Experiments 1 and 2, participants' size judgments were more accurate and less biased than their distance judgments, a finding further reinforced by the results of partial correlation analyses, demonstrating that perceived (stereoscopic) size and distance are independent, rather than interdependent as the SDIH assumes. Experiment 3 manipulated participants' IPDs, one component of Kim's proposed variable. Size and distance judgments were overestimated under a diminished IPD, but underestimated under an enlarged IPD, a result consistent with predictions based on participants' utilization of the proposed information source. Results provide unequivocal evidence against the SDIH as an account of size perception and corroborate the utility of Kim's proposed variable as a viable alternative for the binocular visual system.

Seeing Double and Depth with Wheatstone's Stereograms

Charles Wheatstone, in his classic paper on the invention of the stereoscope, concluded “… objects whose pictures do not fall on corresponding points of the two retinæ may still appear single” (1838 Philosophical Transactions of the Royal Society of London128 384). Soon after, Ernst Brücke, Alexandre Prévost, David Brewster, Joseph Towne, and Joseph LeConte all published disagreements with this conclusion. LeConte's objections were most frequent and most prolonged. To understand the basis of the disagreements, we conducted three experiments using Wheatstone's original stereograms and found that most stereograms produced depth perception with diplopia, which partially explains the consistency among his critics' conclusions. Most of the criticism at variance with Wheatstone's conclusion was based on research conducted outside Germany. We argue that LeConte's lack of knowledge of the German literature on vision research prevented him from considering investigating Wheatstone's experiment with a stereogram having a smaller disparity.

Contrast Configuration Influences Grouping in Apparent Motion

We investigated whether the same principles that influence grouping in static displays also influence grouping in apparent motion. Using the Ternus display, we found that the proportion of group motion reports was influenced by changes in contrast configuration. Subjects made judgments of completion of these same configurations in a static display. Generally, contrast configurations that induced a high proportion of group motion responses were judged as more ‘complete’ in static displays. Using a stereo display, we then tested whether stereo information and T-junction information were critical for this increase in group motion. Perceived grouping was consistently higher for same contrast polarity configurations than for opposite contrast polarity configurations, regardless of the presence of stereo information or explicit T-junctions. Thus, while grouping in static and moving displays showed a similar dependence on contrast configuration, motion grouping showed little dependence on stereo or T-junction information.

Angle Illusion in a Straight Road

We report a new angle illusion observed when viewing a real scene involving a straight road. The scene portrays two white lines which outline a traffic lane on a road and converge to a vanishing point. In experiment 1, observers estimated the angle created by these converging lines in this scene or in its image projected onto a screen. Results showed strong underestimation of the angle, ie over 50% for observations of both the real scene and its projected image. Experiment 2 assessed how depth cues in projected images influence the angle illusion. Results showed that this angle illusion disappeared when scene information surrounding convergent lines was removed. In addition, the illusion was attenuated with projection of an inverted scene image. These findings are interpreted in terms of a misadoption of depth information in the processing of angle perception in a flat image; in turn, this induces a massive angle illusion.

The role of monocularly visible regions in depth and surface perception

The mainstream of binocular vision research has long been focused on understanding how binocular disparity is used for depth perception. In recent years, researchers have begun to explore how monocular regions in binocularly viewed scenes contribute to our perception of the three-dimensional world. Here we review the field as it currently stands, with a focus on understanding the extent to which the role of monocular regions in depth perception can be understood using extant theories of binocular vision.

Perspectives on science and art

Artists try to understand how we see, sometimes explicitly exploring rules of perspective or color, visual illusions, or iconography, and conversely, scientists who study vision sometimes address the perceptual questions and discoveries raised by the works of art, as we do here.

The lost direction in binocular vision: the neglected signs posted by Wells, Towne, and LeConte

Studies of vision have informed theories first in philosophy and then in psychology. Over the centuries, an increasing number of phenomena have been enlisted to refute or reinforce particular theories. Nowhere has this been more evident than in binocular vision. How we see a single world with two eyes is one of the oldest and most consistently studied topics in vision research. It has been discussed at least since the time of Aristotle and it has been examined experimentally since the second century, when Ptolemy defined lines of visual correspondence for the two eyes. Prior to Wheatstone's invention of the stereoscope in the 1830s, binocular vision had been studied in terms of visual directions. The stereoscope established distance (or depth) as well as direction as dimensions of binocular vision. Subsequently, depth rather than direction has been the principal concern of students of vision, and texts in English devoted to analyses of direction rather than depth have been neglected. We examine the experiments on binocular visual direction conducted by Wells before Wheatstone, and by Towne and LeConte after him, and discuss the reasons for their neglect.

Kanizsa's shrinkage illusion produced by a misapplied 3-D corrective mechanism

In order to include the monocular areas from the left and the right eye in the cyclopean view, the visual system displaces the occluded elements which would result in a horizontal elongation of the shape but does not occur thanks to a correction mechanism which preserves the shape. We hypothesised that this mechanism causes Kanizsa's amodal shrinkage illusion (the apparent elongation of a partially occluded square) when it is incorrectly applied by the visual system to a two-dimensional stimulus. Four experiments tested this hypothesis: (i) one-eyed observers were less susceptible to the illusion than people with normal binocular vision because, for them, the correction for shape is unnecessary; (ii) the illusion was stronger with binocular than with monocular vision since binocularity induces the visual system to correct for the shape distortion; (iii) the illusion diminished when the stimulus was rotated 90 degrees given that displacement and compression are not required for vertical occlusion; (iv) the magnitude of the illusion was a function of the width of the occluder because, as previous research has shown, the edges of a partially occluded square are less displaced the farther they are from the edges of the occluder. The data from the four experiments support our hypothesis even though no condition was able to eliminate the illusion; other possible causes are discussed.

Localization of monocular stimuli in different depth planes

We examined the phenomenon in which two physically aligned monocular stimuli appear to be non-collinear when each of them is located in binocular regions that are at different depth planes. Using monocular bars embedded in binocular random-dot areas that are at different depths, we manipulated properties of the binocular areas and examined their effect on the perceived direction and depth of the monocular stimuli. Results showed that (1) the relative visual direction and perceived depth of the monocular bars depended on the binocular disparity and the dot density of the binocular areas, and (2) the visual direction, but not the depth, depended on the width of the binocular regions. These results are consistent with the hypothesis that monocular stimuli are treated by the visual system as binocular stimuli that have acquired the properties of their binocular surrounds. Moreover, partial correlation analysis suggests that the visual system utilizes both the disparity information of the binocular areas and the perceived depth of the monocular bars in determining the relative visual direction of the bars.

Evidence for the correcting-mechanism explanation of the Kanizsa amodal shrinkage

An object phenomenally shrinks in its horizontal dimension when shown on a 2-D plane as if the central portion of the object were partially occluded by another vertical one in 3-D space (the Kanizsa amodal shrinkage). We examined the predictions of the correcting-mechanism hypothesis proposed by Ohtsuka and Ono (2002, Proceedings of SPIE 4864 167-174), which states that an inappropriate operation of the mechanism that corrects a phenomenal increase in monocularly visible areas accompanied by a stereoscopic occluder gives rise to the illusion. In this study we measured the perceived width (or height in experiment 3) of a square seen behind a rectangle, while controlling other factors which potentially influence the illusion, such as the division of space or depth stratification. The results of five experiments showed that (a) the perceived width was not influenced when the occluder had a relatively large binocular disparity, but was underestimated when the occluder did not have disparity, and (b) the shrinkage diminished when the foreground rectangle was transparent, was horizontally oriented, or contained no pictorial occlusion cues. These results support the hypothesis that the correcting mechanism, triggered by pictorial occlusion cues, contributes to the Kanizsa shrinkage.

Naive optics: Predicting and perceiving reflections in mirrors

Undergraduate students predicted what would be made visible by a planar mirror. A paper-and-pencil task confirmed previous findings that when approaching a mirror from the side, participants expected to see their reflection in the mirror earlier than they actually would. This early response was found for all mirrors when the observer moved horizontally--even when the mirror was placed on the floor or the ceiling--but not when the observer moved vertically (in a lift). The data support the hypothesis that many people imagine the world in the mirror as rotated around the vertical axis. When participants had to judge manipulated mirror reflections according to their naturalness, a high degree of tolerance was found. In contrast to the prediction task, a rotation around the vertical axis was judged to be less natural than other distortions. The authors conclude that perceptual knowledge and predictive knowledge lead to different patterns of errors. ((c) 2003 APA, all rights reserved)

The cyclopean eye in vision: the new and old data continue to hit you right between the eyes

We argue against recent claims by Erkelens and van Ee (Vision Res., in press) and by Erkelens (Vision Res. 40 (2000) 2411) that "the concept of the cyclopean eye is em leader always irrelevant as far as vision is concerned" (p. 1157) [corrected] and that "perceived direction during monocular viewing is based on the signals of the viewing eye only" (p. 2411), respectively. In Experiment 1, we presented a pair of small lights on a visual axis and measured the absolute visual direction of the near light with reference to different parts of the face. The near light appeared in front of the bridge of the nose or very near it, contrary to what was expected from Erkelens and van Ee's claim that monocular stimuli are seen in their correct locations. In Experiment 2, we replicated Erkelens' experiments with measurements of phoria and analyses of eye movements. The results confirmed his finding that the cyclopean illusion occurred rarely in the monocular condition, but our phoria and eye movement data provided the basis for a very different interpretation. Our data show that the oculomotor signal in his particular monocular condition was considerably weaker than in his binocular condition; therefore, the rarity of the monocular cyclopean illusion is not surprising. Moreover, since both claims above are based on an over-generalization of the results of Erkelens' study, neither claim is persuasive.

Monocular alignment in different depth planes

We examined (a) whether vertical lines at different physical horizontal positions in the same eye can appear to be aligned, and (b), if so, whether the difference between the horizontal positions of the aligned vertical lines can vary with the perceived depth between them. In two experiments, each of two vertical monocular lines was presented (in its respective rectangular area) in one field of a random-dot stereopair with binocular disparity. In Experiment 1, 15 observers were asked to align a line in an upper area with a line in a lower area. The results indicated that when the lines appeared aligned, their horizontal physical positions could differ and the direction of the difference coincided with the type of disparity of the rectangular areas; this is not consistent with the law of the visual direction of monocular stimuli. In Experiment 2, 11 observers were asked to report relative depth between the two lines and to align them. The results indicated that the difference of the horizontal position did not covary with their perceived relative depth, suggesting that the visual direction and perceived depth of the monocular line are mediated via different mechanisms.