The perception of surface curvature from optical motion

Abstract

Observers viewed the optical flow field of a rotating quadric surface patch and were required to match its perceived structure by adjusting the shape of a stereoscopically presented surface. In Experiment 1, the flow fields included rigid object rotations and constant flow fields with patterns of image acceleration that had no possible rigid interpretation. In performing their matches, observers had independent control of two parameters that determined the surface shape. One of these, called the shape characteristic, is defined as the ratio of the two principle curvatures and is independent of object size. The other, called curvedness, is defined as the sum of the squared principle curvatures and depends on the size of the object. Adjustments of shape characteristic were almost perfectly accurate for both motion conditions. Adjustments of curvedness, on the other hand, were systematically overestimated and were not highly correlated with the simulated curvedness of the depicted surface patch. In Experiment 2, the same flow fields were masked with a global pattern of curl, divergence, or shear, which disrupted the first-order spatial derivatives of the image velocity field, while leaving the secondorder spatial derivatives invariant. The addition of these masks had only negligibleeffects on observers' performance. These findings suggest that observers' judgments of three-dimensional surface shape from motion are primarily determined by the second-order spatial derivatives of the instantaneous field of image displacements.Human observers make use of many different sources of information to perceive the three-dimensional (3-D) structure of their environment. One of the most important of these sources is the changing pattern of retinal stimulation created by the movements of the observer and environmental objects. Wallach and Q'Connell (1953) showed that motion information could by itself create an impression of 3-D structure. In their demonstration, an apparently two-dimensional (2-D) form created by the projected shadows of a wireframe figure suddenly appeared to have a compelling 3-D structure when the wireframe was rotated in depth.Early theoretical analyses of this phenomenon defined the minimal information that would permit an observer to determine the 3-D structure ofa configuration ofpoints. To simplify the analysis, these models typically assume that the input is a set of image points moving across discrete frames. For general configurations under orthographic projection, a minimum of three distinct views of

Trajectory forms as a source of information about events

“…A quantity that has been studied in the structure-frommotion literature is curvature (Koenderink, 1990;Perotti et al, 1998;Tittle & Perotti, 1997). There, it has been used to describe the structure of perceived surfaces.…”

“…Accelerations-that is, second-order temporal properties-are not used (Liter, Braunstein, & Hoffman, 1993;Todd & Bressan, 1990;Todd & Norman, 1991). Nevertheless, higher order properties of motion are involved: spatial variations in velocity (i.e., dv/dx, d 2 v/dx 2 ) and properties derived from these (Perotti, Todd, Lappin, & Phillips, 1998; see also Dijkstra, Snoeren, &Gielen, 1994, andvan Doorn, 1992).…”

Merging the senses into a robust percept

“…Jacobs and others (e.g. [28]) tried to minimize this problem by weakening the texture cue when assessing the 'motion-alone' reliability. However, it is difficult to determine how far this is possible.…”

Poor shape perception is the reason reaches-to-grasp are visually guided online

“…The shape can be characterized by the aspect ratio of object depth to width or by curvedness (Koenderink, 1990, pp. 319-324;Perotti, Todd, Lappin, & Phillips, 1998). Specification of the metric object size in the frontoparallel plane together with the aspect ratio (or the curvedness) would determine the metric object depth.…”