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

Abstract

We examined the ability of human observers to discriminate between different 3-D quadratic surfaces defined by motion, and with head position fed back to the stimulus to provide an up-todate dynamical perspective view. We tested whether 3-D shape or 3-D curvature would affect discrimination performance. It appeared that discrimination of 3-D quadratic shape clearly depended on shape but not on the amount of curvature. Even when the amount of curvature was randomized, subjects' performance was not altered. On the other hand, the discrimination of 3-D curvature clearly depended linearly on curvature with Weber fractions of 20% on the average and, to a small degree, on 3-D shape. The experiment shows that observers can easily separate 3-D shape and 3-D curvature, and that Koenderink's shape index and curvedness provide a convenient way to specify shape. These results warn us against using just any arbitrary 3-D shape in 3-D shape perception tasks and indicate, for example, that emphasizing 3-D shape in computer displays by exaggerating curvature does not have any effect.Since Wallach and O'Connell (1953) demonstrated that three-dimensional (3-D) shape could be extracted from orthographic projections of rotating objects, there have been numerous studies of this phenomenon, which is commonly known as the kinetic depth effect. 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).The most common way to study the phenomenon of 3-D shape from motion is to use random dot cinematograms of moving 3-D objects. The objects under study are mostly cylinders, planes, or spheres. There is no reason to assume that the results of these studies hold for all kinds of 3-D shapes, but most studies have not included a wide range of shapes or curvature values. 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. for example, might have certain heuristic topological characteristics that would make them special objects, not suitable for a generalization to other 3-D objects. It has to be examined yet what exactly these "heuristic" properties are. It is well possible that a certain systematic 3-D shape dependency in structure from motion is responsible for this effect. A quantitative examination of 3-D shape perception obviously requires a mathematical defInition on-D shape. On the other hand, if we want to study 3-D shape perception in psychophysical experiments, this definition must be in some way ecologically valid so that ...

The perception of shape and curvedness from binocular stereopsis and structure from motion

“…A local surface property that is not coordinate system dependent can be obtained by measuring the curvature, or the rate at which orientation changes in a particular direction along a smoothly curved surface (i.e., secondorder surface structure). For any point on a quadric (i.e., second-order) surface, there will always be one direction The evidence from recent studies on binocular stereopsis (de Vries, Kappers, & Koenderink, 1993) and motion (van Damme, Oosterhoff, & van de Grind, 1994) is consistent with the idea that human observers can accurately judge shape index independently of variations in curvedness. Such results suggest that when studying the integration of 3-D shape from multiple visual cues, one should consider both scale-dependent and scaleindependent information.…”

The perception of surface curvature from optical motion

“…There have been a number of empirical studies reported in the literature that have examined observers' sensitivity to the 3-D curvature of moving surfaces (see Cornilleau-Peres & Droulez, 1989;Lappin et al, 1995;Norman & Lappin, 1992;van Damme et al, 1994). The present experiments were designed to extend this research by employing a response task with two degrees of freedom, so that we could separate the distinct components of shape characteristic and curvedness, and by including displays with first-order motion masks in an effort to restrict the relevant information to second-order spatial changes in velocity.…”

“…With appropriate information about interocular distance and the state of convergence, it would be theoretically possible to accurately compute 3-D structure from binocular disparity, but the available evidence does not suggest that human observers are capable of that (e.g., see Norman, Todd, Perotti, & Tittle, 1996;Tittle, Todd, Perotti, & Norman, 1995). Several studies have shown that either motion or stereo provides sufficient information to accurately discriminate the shape characteristics of quadric surfaces (de Vries, Kappers, & Koenderink, 1994;Phillips & Todd, 1996;van Damme, Oosterhoff, & van de Grind, 1994), but this does not appear to be true for the scale-dependent property of curvedness, as indicated by the low R2 values shown in Table 1. This also suggests, moreover, that the errors occurring in these two modalities are not linearly related to one another.…”

The Selectivity of Neurons in the Macaque Fundus of the Superior Temporal Area for Three-Dimensional Structure from Motion

“…The stimuli in these experiments were similar to those used in numerous human psychophysical experiments (van Damme et al, 1994;Phillips and Todd, 1996;Perotti et al, 1998). Their design was motivated by basic principles of differential geometry with which it is possible to decompose smooth surfaces into qualitatively distinct patches based on the relative patterns of curvature in different directions (Koenderink, 1990).…”

“…It is also possible to define more complex surface patches whose depth maps have nonzero higher-order spatial derivatives. Because of the evidence that human observers can successfully identify these different types of patch structures (van Damme et al, 1994;Phillips and Todd, 1996;Perotti et al, 1998), they were chosen to characterize the neural encoding of 3D surface shape in the present experiments.…”