Distance/Depth

An Empirical Explanation: The Perception of Distance and Depth

The observations described here imply that perception of egocentric distance and stereo depth are manifestations of a broader visual strategy that allows the human visual system to contend with the inherent ambiguity of visual stimuli.

Much evidence suggests that both monocular and binocular depth are also determined empirically, placing on the same probabilistic footing two aspects of vision that, historically, have been regarded as having different physiological bases.

The phenomenology of distance perception clearly provides some puzzles that need to be explained. As illustrated in Figure 1, it has long been known that the apparent distance of objects bears a peculiar relationship to their physical distance from the observer. When subjects are asked to make judgments with little or no contextual information (e.g., the distance of a luminous but otherwise featureless object in a darkened room), the distances reported differ in several ways from the corresponding physical distances.

First, objects in these circumstances are typically perceived to be at a distance of 2-4m, a phenomenon referred to as the “specific distance tendency” (Figure 1A). Second, objects that are relatively near each other in the retinal image appear to be about the same distance from the observer, a phenomenon called the “equidistance tendency” (Figure 1B). Third, when presented at or near eye-level, the distance of objects relatively near the observer tends to be overestimated, whereas the distance of objects that are further away tends to be underestimated (Figure 1C). Finally, the apparent distance of objects on the ground varies with the angle of declination of the line of sight: objects on the ground that are at least several meters away appear closer than they really are, and with increasing distance are judged to be progressively more elevated than warranted by their physical position (Figure 1D).
Although a variety of explanations have been proposed in the various studies cited, there has been little or no agreement about the basis of these unusual perceptions of egocentric distance. More often than not, the several tendencies illustrated in Figure 1 have simply been accepted as empirical facts that are then used to rationalize other aspects of visual space.

Given the ability of the probabilistic relationship between retinal images and sources to explain a variety of other geometrical percepts, it makes sense to ask whether the probability distributions of the possible sources of visual stimuli also determine apparent distance. Using the same database of natural scene geometry described in the sections on other geometrical illusions, the anomalous perceptions of distance illustrated in Figure 1 can all be accounted for by the probability distributions of the physical distances of object surfaces from human observers (see Yang and Purves, 2003).

The ability to explain these anomalies in the perception of distance based on the statistics of the physical distances of object surfaces from the observer in natural scenes offers further evidence that rationalizing perceived geometry in a probabilistic framework is a powerful way of understanding visual space. In addition to successfully explaining the specific anomalies that have been difficult to rationalize in other ways (see Yang and Purves, 2003), these observations imply that the sense of egocentric distance is another manifestation of the probabilistic strategy that allows the human visual system to contend with the inherent ambiguity of visual stimuli.

Another aspect of depth perception that is particularly interesting is stereopsis. The aforementioned aspects of depth perception are approximately the same whether an observer views the distant object with one eye (monocular) or two eyes (binocular). Stereopsis, on the other hand, concerns seeing relatively near objects with binocular vision. The importance of this type of depth perception is particularly experienced when we engage in activities that require relatively fine manipulation, such as threading a needle. Such tasks are almost impossible without binocular vision.

Stereopsis, or stereo depth, is generally explained in terms of retinal disparity. Light rays reflected from the same object stimulate loci on the two retinas. In turn, the neural computation of the differences between these two loci (i.e. retinal disparity) gives rise to stereo depth. In support of this claim, neurophysiological studies have shown that some neurons in the visual cortex of cats and monkeys are selectively responsive to certain retinal disparities (e.g. Poggio, 1995). Nevertheless, understanding how the nervous system implements the comparison of a stereo pair has remained difficult without a general agreement on how this could be done. Additionally, a number of psychophysical studies have found problems in rationalizing binocular vision with retinal disparity. For instance, stereo depth was accorded even though an object was viewed with only one eye and the perception of depth did not reverse (i.e. further objects to be seen as nearer) when retinal disparity was reversed. Finally, another indication that stereoscopic percepts might not represent neural computations of retinal disparity as such is the inherent ambiguity of retinal disparity (see Figure 2).

Much work on stereopsis has used random dot stereograms (RDSs). These eliminate all monocular depth cues and cognitive information (e.g. prior knowledge of objects which could aid recognition) that could obscure neural activity specific to stereo depth. An interesting phenomenon that has been observed from these studies is that RDSs with the same geometry can elicit different sensations of depth. Viewing through an aperture, participants usually perceive a ‘hidden object’ to be located in front of the background or behind the background (see Figure 3). Here, we propose a straightforward explanation for these effects using the same empirical framework. When an object is seen through an aperture, distal elements near the object are seen by both eyes, whereas the elements near the frame is seen by only one eye of the other. The retinal image in each eye thus provides an empirically informative context for the other eye. Hence, by associating the patterns of stimulation on the left and right retinas with experience with objects in the past, the perceived depth would presumably correspond to the relative frequency of occurrence of possible image sources.

References

Purves D, Lotto B (2011) Why We See What We Do Redux: A Wholly Empirical Theory of Vision. Sunderland, MA: Sinauer Associates.

Purves Purves D, Monson BB, Sundararajan J, Wojtach WT (2014). How biological vision succeeds in the physical world. In: Proceedings of the National Academy of Sciences 111: 4750-4755

Howe CQ, Purves D (2005) Natural scene geometry predicts the perception of angles and line orientation. Proc Natl Acad Sci 102 (25): 1228-1233.

Purves D, Howe CQ (2005) Perceiving Geometry: Geometrical Illusions Explained by Natural Scene Statistics. Springer: New York, NY.

Yang Z, Purves D (2003) A statistical explanation of visual space. Nature Neurosci 6: 632 – 640.

Nundy S, Lotto RB, Coppola D, Shimpi A, Purves D (2000) Why are angles misperceived? Proc Natl Acad Sci USA 97:5592-5597.

Coppola DM, Purves H, McCoy A, Purves D (1998) The distribution of oriented visual contours. Proc Natl Acad Sci USA 95:4002-4006.