Ibn al-Haytham's ground theory of distance perception.

The 11th-century Arab scholar, Ibn al-Haytham, in his Optics, offers a detailed, rigorous, empirically oriented explanation of distance perception that may be the first essentially modern, scientific theory of distance perception. Based on carefully described experiments, he argues that for distance to be perceived accurately: (1) the distance must lie along a continuous surface such as the ground; (2) the continuous surface must be visible; (3) the magnitudes of distances along the surface must be perceived and calibrated through bodily interaction (walking and reaching) with them; and finally (4) the distance must be moderate. Al-Haytham's work reached Europe early in the 13th century, and his was the dominant theory of distance perception there for about 400 years. It was superseded early in the 17th century by a theory, based on cues such as convergence and accommodation, of distance seen through empty, mathematized space. Around 1950, an explanation of distance perception strikingly like that of al-Haytham was independently developed by J. J. Gibson, who called his theory the "ground theory" of space perception.

J. J. Gibson's "Ground Theory of Space Perception".

J. J. Gibson's ground theory of space perception is contrasted with Descartes' theory, which reduces all of space perception to the perception of distance and angular direction, relative to an abstract viewpoint. Instead, Gibson posits an embodied perceiver, grounded by gravity, in a stable layout of realistically textured, extended surfaces and more delimited objects supported by these surfaces. Gibson's concept of optical contact ties together this spatial layout, locating each surface relative to the others and specifying the position of each object by its location relative to its surface of support. His concept of surface texture-augmented by perspective structures such as the horizon-specifies the scale of objects and extents within this layout. And his concept of geographical slant provides surfaces with environment-centered orientations that remain stable as the perceiver moves around. Contact-specified locations on extended environmental surfaces may be the unattended primitives of the visual world, rather than egocentric or allocentric distances. The perception of such distances may best be understood using Gibson's concept of affordances. Distances may be perceived only as needed, bound through affordances to the particular actions that require them.

Spatial compression produced by a stationary low-vision telescope.

PURPOSE: Geometrical analysis of the monocular information for visual space perception predicts that the magnification produced by a low-vision telescope will compress the depth dimension of space. To test this prediction we measured the compression in depth of perceived shape while looking through a stationary telescope. To control for the other aspects of telescopic viewing, apart from magnification, we also measured perception while looking through a plain tube having the same field of view. METHODS: A 2.75x Keplarian telescope was mounted 40 cm above a tabletop patterned with receding stripes. The 11.6 degrees field of view was centered on a series of rectangular stimulus cards lying flat on the table at a distance of 100 cm. Participants monocularly viewed each card through the telescope, or through a tube having the same field of view, and verbally judged the card's perceived length (in depth) relative to its width (in the frontal plane). RESULTS: Perceptual compression of shape was calculated by dividing the perceived proportion (length/width) by the actual proportion. The telescope and the tube both produced significant perceptual compression, but perception was significantly more compressed through the telescope (0.43) than through the tube (0.52). CONCLUSIONS: The magnification produced by a stationary low-vision telescope can result in a compression of perceived depth. In addition, other aspects of telescopic viewing, such as monocular vision, restricted head movements, and a restricted field of view, can together contribute substantially to such compression. Further research is needed to assess the clinical implications of these results.

Spatial compression and adaptation with the low vision telescope.

PURPOSE: Geometrical analysis of monocular visual information specifying distance shows that a low vision telescope compresses optically specified distances by a factor about equal to its magnification. Using a group of eight visually healthy adults, we investigated the initial perceptual effect of putting on a 2x Galilean telescope and the adaptation produced by wearing the telescope. METHODS: Viewing was monocular, and the environment was only visible through the telescope. Because the telescope reduced the field of view to 13 degrees , we also tested a different group of eight visually normal adults who wore a simple monocular tube that restricted the field of view to 13 degrees . We measured perceived distance in a corridor using a visually directed open-loop walking task with distances ranging from 4 to 8 m. For both groups, monocular distance perception was measured before putting on the viewing device (baseline), immediately after putting on the viewing device (preadaptation), after wearing the viewing device during a 30-minute period of visual-motor activities (postadaptation), and immediately after taking off the viewing device (aftereffect). RESULTS: Comparing preadaptation with baseline measurements, the viewing devices produced a 15.4% initial compression of perceived distance on average. Comparing aftereffect with baseline measurements, the adaptation period produced a negative aftereffect that was 56.5% of the initial compression, thus showing substantial adaptation. The initial compression and the adaptation were highly significant effects, but neither effect was significantly different for the telescope group and the tube group. CONCLUSION: We conclude that free head movements in a structured environment can largely overcome the optically specified compression of distance produced by the 2x magnification of a low vision telescope, but there remains a significant initial compression of perceived distance that is produced by the restricted field of view. This compression can be substantially reduced by a short period of interaction with the environment.

Distance perception across spatial discontinuities.

We investigated the use of nested contact relations in perceiving the relative distance of locations on discontinuous surfaces. Observers viewed computer-generated displays under monocular static conditions and adjusted a marker to match the perceived distance of a cube. The marker and cube were raised above the ground by two different platforms separated by a gap. The relative heights and distances of the platforms were varied. We found the following: (1) When spatially discontinuous surfaces are coplanar, locations of objects resting on these surfaces appear to be compared directly, bypassing relations with the underlying ground plane. (2) Spatial displacement between the platforms produces a bias, in the direction of the displacement, in the perceived relative locations of objects resting on the platforms. This suggests that local spatial relations between objects and their platforms are only partially integrated with more global spatial relations between the discontinuous surfaces of the platforms.

Distance perception mediated through nested contact relations among surfaces.

In complex natural scenes, objects at different spatial locations can usually be related to each other through nested contact relations among adjoining surfaces. Our research asks how well human observers, under monocular static viewing conditions, are able to utilize this information in distance perception. We present computer-generated naturalistic scenes of a cube resting on a platform, which is in turn resting on the ground. Observers adjust the location of a marker on the ground to equal the perceived distance of the cube. We find that (1) perceived distance of the cube varies appropriately as the perceived location of contact between the platform and the ground varies; (2) variability increases systematically as the relating surfaces move apart; and (3) certain local edge alignments allow precise propagation of distance information. These results demonstrate considerable efficiency in the mediation of distance perception through nested contact relations among surfaces.