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Objective and perceived motion

Objects translating and rotating

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An Empirical Explanation: Objective and Perceived Motion

A solution to the retinal stimulus ambiguity is to accumulate experience interacting with moving objects, such that motion percepts gradually come to accord with the statistics of the possible displacements underlying the stimulus.
In objective terms, motion is the continuous displacement of an object within a spatial frame of reference; as such, motion is fully described by physical measurements (direction and speed). In subjective terms, however, the corresponding sensation of motion is not so easily defined or understood. Because the real-world displacement of an object is conveyed to an observer by a changing projection on the retinal surface, the velocity field that uniquely defines motion in physical terms is ambiguous with respect to the possible causes of the changing retinal image: indeed, an infinite number of physical displacements can generate the same stimulus sequence (Demonstration). As in other aspects of vision, this ambiguity presents a fundamental problem, namely how in the face of such uncertainty the brain generates quite definite percepts that usually (but not always) allow the observer to deal successfully with the real-world cause of the retinal stimulus.
A solution to this problem is evidently to accumulate experience interacting with moving objects, such that motion percepts gradually come to accord with the statistics of the possible displacements underlying the stimulus. The physical correspondences of the points along the line in in any two sequential images cannot be determined directly because some points come into the view, others disappear, and still others could represent deformation as the line in view 'expands' or 'contracts'. Although it is generally believed that physical correspondence is the basic requirement for a stimulus to be correctly perceived as moving (both motion and stereoscopic vision have long been assumed to be 'correspondence problems'), it seems more likely that motion perception is derived empirically from the complete set of possible correspondences and differences between any sequential images. As shown in Figure 1, his set entails: 1) the identity of some, but not necessarily all, the elements in any two sequential images; 2) the possible appearance of some, but not necessarily all, the elements in the second image not present in the first; 3) the possible disappearance of some, but not necessarily all, the elements in the first image compared to the second; and 4) the possible deformation of the stimulus during the interval between the two images.
Figure 1
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Figure 1 / The complete set of correspondences and differences between sequential images of a line moving uniformly is determined by four factors. A) Identity: A line point or segment at time t1 that occupies any position on the visible line at time t2 defines identical elements in the two images (in this and the subsequent panels black indicates an identical line segment in the two images in the sequence). B) Appearance: The elements of the line indicated in blue at time t2 don't correspond to any of the elements visible at time t1, and have thus appeared in the interval between the generation of the two images. C) Disappearance: The elements of the line indicated in red at time t1 do not correspond to any visible elements at time t2, and have thus disappeared in the interval. D) Deformation: The projected line images can also differ as a result of movement of the source toward (or away) from the observer, by rotation, or by a physical deformation (here indicated by a uniform extension of the line segment during the interval; deformation is indicated in green). (After Yang et al., 2001)

Since the relative contribution of these correspondences and differences to the physical displacements underlying the stimulus cannot be determined by inspection of stimulus per se, the problem posed by this inevitable uncertainty can only be solved empirically by generating motion percepts based on past experience of what such stimuli have typically turned out to be.
To assess this conception of perceived motion, we computed the probability distribution of the possible physical displacements underlying simple image sequences. In this way we could predict the percepts that subjects would be expected to see on a wholly empirical basis, and compare them to actual performance. Given the fundamental ambiguities embedded in the correspondences and differences underlying sequential images any motion stimulus, this approach entails: 1) describing quantitatively how these correspondences and differences in the image plane are generated in case of a straight line moving in the fronto-parallel plane; 2) using this information to derive a set of probability distributions of the possible real-world displacements underlying the stimulus; 3) deriving a principle for combining these probability distributions based on the statistical structure of the underlying events in the stimulus; and 4) devising a procedure for predicting motion perception based on this joint probability (see Yang et al., 2001a).
The way subjects perceived the direction and speed of a line moving in any of a variety of apertures in the fronto-parallel plane can be accounted for quite well on this basis. For instance, the perceived direction of motion of a line oriented at 45° and translating horizontally from left to right, should change when constrained by a circular aperture, now being seen moving downward and to the right (a shift in direction of 45°) (see Demonstration). Moreover, the perceived speed of the line in this circumstance should be about 30% less than the perceived speed without the aperture in place. These predicted effects for this and a variety of other apertures correspond remarkably well with what subjects in fact see (Figures 2, 3, 4). This wholly empirical framework can apparently account for the full range of phenomena first described by Hans Wallach 65 years ago.
Figure 2
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Figure 2 / Comparison of the perceived motion of a line moving across a circular aperture and the perceptions predicted by the probability distribution the possible sources of the stimulus. A) A representative stimulus (in this example, a line oriented at 30° with respect to the horizontal axis, moving from left to right at a given speed). B) The probability distribution of possible physical motions underlying the stimulus in (A), computed as outlined in the text. C) Comparison of the directions and speeds of the motion perceived (dotted lines) and the directions and speeds implied by the probability distribution (solid lines) (vertical bars are the standard deviations of the performance of the different subjects examined). Directions are indicated in degrees relative to the moving line (90° being perpendicular to the line), and speeds as the distance traveled per unit time between two subsequent line positions in that direction. (Courtesy of Z. Yang, A. Shimpi and D. Purves; see Yang et al., 2001 for methodological details)

Figure 3
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Figure 3 / The perceived motion of a line moving across an inverted V aperture. A) A representative stimulus, showing a line orientated at 20° with respect to the horizontal axis. B) Probability distribution of the possible translations underlying the stimulus in (A). C) Comparison of the average directions (left) and speeds (right) of the motion perceived (dotted lines) and the directions and speeds predicted by the local mass mean of the relevant probability distributions (solid lines). (After Yang et al., 2001)

Figure 4
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Figure 1 / Comparison of the perceived motion of a line moving across a vertical aperture and the values of direction and speed predicted empirically in these circumstances. A) A representative stimulus oriented at 40° with respect to the horizontal axis. B) The probability distribution of the possible sources underlying the stimulus in (A). C) Comparison of the average directions (left) and speeds (right) of the motion perceived (dotted lines) by subjects and the directions and speeds predicted (solid lines) (the two plateaus in the perceived speed are a reflection of the limited range of physical speeds that could be used in generating the test stimuli, resulting in the same rate of translation for two different orientations). (Courtesy of Z. Yang, A. Shimpi and D. Purves)

References

Yang Z, Shimpi A, Purves D (2001) A wholly empirical explanation of perceived motion. Proc Natl Acad Sci USA 9:5252-5257.

Yang Z, Shimpi A, Purves D (2002) Perception of objects that are translating and rotating. Perception, in press.