The visual perception of rigid motion from constant flow fields

Abstract

Four experiments investigated observers' judgments of rigidity for different types of optical motion. The depicted structural deformations were of two types: (1) those with nonparallel image trajectories that are detectable from the first-order spatiotemporal relations between pairs of views; and (2) those with parallel image trajectories that can only be detected from higher order relations among three or more views. Patterns were composed of smooth flow fields in Experiments 1 and 3, and of wire frame figures in Experiments 2 and 4. For both types of display,the nonrigidity detectable from the first-order spatiotemporal structure of the motion sequence was much more salient than the deformation detectable only from the higher order spatiotemporal structure. These results indicate that observers' judgments of rigidity are based primarily on a two-view analysis, but that some useful information can be obtained under appropriate circumstances from higher order spatiotemporal relations among three or more views.When a visible object rotates in depth, its projected pattern of optical flow on the retina provides perceptually compelling information about its three-dimensional (3-D) structure. During the past decade, there has been a rapid growth in our theoretical understanding ofhow optical motion could potentially be analyzed. Much of this research was initiated by the early work ofUllman (1977, 1979), who provided the first computational analysis about the minimum amounts of motion information needed to obtain a unique interpretation ofeuclidean metric structure. Ingeneral, this analysis requires a minimum of three views of four noncoplanar points, though there are a few special cases in which these limits can be reduced (see, e.g., , 1986Hoffman & Flinchbaugh, 1982).There has also been a considerable amount of psychophysical research during this period to determine how closely the performance of these models compares with that of actual human observers, but these empirical investigations have produced a rather surprising pattern of results. Whereas the computational analysis of euclidean metric structure in most instances requires a minimum of three distinct orthographically projected views, there is a growing amount of evidence to suggest that human observers can obtain compelling kinetic depth effects from two-view apparent motion sequences, and that there is only minimal improvement in performance on most objective response tasks as additional views are added (see, e.g.,

Temporal integration in structure from motion.

“…This point can be illustrated by considering the case of a constant optic flow (see Perotti, Todd, & Norman, 1996). In the case of Figure 2b, for example, the models described earlier predict a constant surface slant, because the gradient x at any moment is constant.…”

Large continuous perspective transformations are necessary and sufficient for accurate perception of metric shape

“…The sliding sleeve transformation would yield a constant flow display-that is, a structure-from-motion display in which the optic flow at any given point in the image would be constant. Perotti, Todd, and Norman (1996) used constant flow displays to investigate whether human observers use information available over more than two frames-that is, greater than first-order flow. They found that observers did not and, thus, that observers could not distinguish nonrigid constant flow from rigid rotation.…”

Monocular discrimination of rigidly and nonrigidly moving objects

“…Several authors have attempted to deduce the minimum number of views and number of elements that are required by the visual system to detect nonrigidity from parallel projections (Braunstein, Hoffman, & Pollick, 1990;Braunstein et al, 1987;Norman & Todd, 1993;Perotti, Todd, & Norman, 1996;Todd, 1982;Todd & Bressan, 1990). These experiments show that various types of nonrigidity are detectable with the theoretical minimum number ofelements and views.…”

“…He determined the impact that various changes in these characteristics have on the human ability to judge whether the objects move rigidly or not. In experiments done by Norman and Todd (1993) and Perotti et al (1996), human perception of rigidity appears to have been determined primarily by first-order temporal relations available in two frames, although in some cases higher order temporal relations seem to have been used. In our experiments, we explore this issue further.…”