The detection of surface curvatures defined by optical motion

Abstract

The detectability of surface curvatures defined by optical motion was evaluated in three experiments. Observers accurately detected very small amounts of curvature in a direction perpendicular to the direction of rotation, but they were less sensitive to curvatures along the direction of rotation. Variations in either the number of points (between 91 and 9) or the number of views (from 15 to 2) had little or no effect on discrimination accuracy. The results of this study demonstrate impressive visual sensitivity to surface curvature. Several characteristics of this sensitivity to curvature are inconsistent with many computational models for deriving three-dimensional structure from motion.The results of nearly a century of research have shown that optical motion is a powerful source of information about an object's three-dimensional (3-D) shape. To this day, however, it remains unclear exactly which 2-D image properties are detected and exactly which 3-D structural relations are perceived when observers view structurefrom-motion displays. As recently as 1989, Sperling, Landy, Dosher, and Perkins asked: "Does the observer perceive the correct shape in a display? The correct depths? The correct depth order? The correct curvature?' , (p. 826). Contemporary research, they argued, has failed to resolve such issues.Most current computational models operate on a number of discrete points contained within a set of distinct "views." These models typically assume that appropriate correspondences have been established between the same physical object points across the discrete views. Given this assumption, such models recover depth and/or orientation values for each identifiable feature. When the set of all such pointwise depths has been recovered, a primary computational problem has been solved, but other substantial problems remain. What remains is to parse this collection of depths into separate objects and to interpolate This research was supported in part by National Research Service Award EY-07007-10 to the first author and Nlli Grant EY-05926 to the second author. Many of the analyses accompanying the empirical results contained in this manuscript were aided by Grant 89-00 16 from the Air Force Office of Scientific Research, Grant BNS-8908426 from the National Science Foundation, and grants from the Office of Naval Research, and the Air Force Office of Scientific Research to James Todd. We are grateful to James Todd for his helpful comments on an earlier version of this manuscript. Correspondence should be addressed to J. F. Norman, Department of Psychology, Brandeis University, Waltham, MA 02254-9110. smooth surfaces between connected feature points. Object surfaces and properties such as curvature are thought to be secondarily derived from the more elementary features and their depths.One problematic phenomenon for such models is the finding of directional anisotropies. Rogers and Graham (1983) and Rogers and Cagenello (1989) have documented anisotropies for both stereopsis and motion parallax. Rogers and Grah...

The perception of length on curved and flat surfaces

“…Norman & Lappin, 1992; 1. F. Norman & Todd, 1995;Rogers & Graham, 1983) may also occur when curved surfaces are viewed in the physical environment.…”

“…The same pattern of results was found for surfaces defined by structure-from-motion (see, e.g., 1. F. Norman & Lappin, 1992) when the axis of rotation was vertical. An analogous result was found in the present experiments for 3 of the 5 observers: In-depth lengths along the curvature of the cylinder were perceived to be longer when the cylinder was horizontal and were perceived to be shorter when the cylinder was rotated to a vertical orientation.…”

Discrimination of 3-D shape and 3-D curvature from motion in active vision

“…No thorough comparison is m'hde between active and passive vision, nor do we provide an extensive analysis of all conceivable forms of active vision. Our primary goal was to examine avoids possible orientation anisotropies such as those reported by Droulez and Cornilleau-Peres (1990) and Norman and Lappin (1992).…”

“…Such psychophysical studies include, for example, those on object rigidity (Todd, 1984), perceived depth or curvature (Dosher, Landy, & Sperling, 1989;Norman & Lappin, 1992;Saidpour, Braunstein, & Hoffman, 1992), minimal conditions for the perception of 3-D shape from motion in multidot displays (Sperling, Landy, Dosher, & Perkins, 1989;Todd & Norman, 1991;Treue, Husain, & Andersen, 1991), projection methods (Todd, 1984), and token dependency (Landy, Dosher, Sperling, & Perkins, 1991).…”

“…On the other hand, the importance of a multiobject study has been pointed out by several authors. Norman and Lappin (1992) reported differences in discriminability between cylinders and spheres, spheres and planes, and cylinders and planes. Sperling et al (1989) used a fInite set of 53 different 3-D shapes in a shape identifIcation task, but did not report quantitative differences in performance for different 3-D shapes.…”