Interpolation across surface discontinuities in structure from motion Asad Satdpour

Abstract

Interpolation across orientation discontinuities in simulated three-dimensional (3-D) surfaces was studied in three experiments with the use of structure-from-motion (SFM) displays. The displays depicted dots on two slanted planes with a region devoid of dots (a gap) between them. If extended through the gap at constant slope, the planes would meet at a dihedral edge. Subjects were required to place an SFM probe dot, located within the gap, on the perceived surface. Probe dot placements indicated that subjects perceived a smooth surface connecting the planes rather than a surface with a discontinuity. Probe dot placements varied with slope of the planes, density of the dots, and gap size, but not with orientation (horizontal or vertical) of the dihedral edge or of the axis of rotation. Smoothing was consistent with models of 2-D interpolation proposed by Ullman (1976) and Kellman and Shipley (1991) and with a model of 3-D interpolation proposed by Grimson (1981). Wallach and O'Connell (1953) demonstrated that if subjects are shown the two-dimensional (2-D) shadow cast by a clear glass sphere that has small opaque dots on its surface and rotates about a vertical axis, then subjects perceive a spherical surface. A similar perception is commonly reported for computer-generated displays in which dots move about on a computer screen in a manner consistent with their being projections of dots on a rotating sphere (see, e.g., Braunstein, 1966;Braunstein & Andersen, 1984). Apparently human vision is adept at inferring 3-D structure from the 2-D motions of projected features. This process of inferring 3-D structure from 2-D motions, referred to as structure from motion (SFM) after Ullman (1979), has been studied extensively since the advent of computer-generated displays. (For reviews, see Braunstein, 1978Braunstein, , 1983Braunstein, , 1988 In many displays of SFM in which dots alone are projected on the computer screen, observers report seeing more than just a 3-D structure for the dots. They report, in addition, that they perceive a continuous surface in 3-D passing through, or near, the dots. Such perceptions of "subjective surfaces" on the basis of sparse collections of dots are not limited to SFM displays. Subjective surfaces have also been reported,

3-D Interpolation in Object Perception: Evidence From an Objective Performance Paradigm.

“…These observations suggest that surface interpolation in three dimensions may proceed without contour interpolation. This 3-D surface spreading may be similar to effects observed in structure-from-motion displays (Saidpour, Braunstein, & Hoffman, 1994).…”

Object Interpolation in Three Dimensions.

“…The exact form of smooth, interpolated contours has proven difficult to determine, because many models make very similar predictions in many circumstances. Earlier work has looked at the shape of surface interpolation in structure-from-motion displays (Saidpour, Braunstein, & Hoffman, 1994). Saidpour et al found that the shapes of interpolated surfaces were smooth and dependent on the geometry of the motion-defined surface, consistent with 3-D extensions of the models proposed by Ullman (1976) and Kellman and Shipley (1991) or a 3-D model of shape interpolation based on minimization of the quadratic variation functional (Grimson, 1981).…”

A theory of dynamic occluded and illusory object perception.

“…Two contours are relatable if they can be connected by a smooth curve that bends monotonically through no more than about 90°. A number of empirical studies of the contour interpolation process have suggested that the geometric notion of relatability describes the conditions under which observers perceive fragmented regions of objects as unified into a single perceptual unit for both occluded and illusory objects (e.g., Field et al, 1993; Kellman, Garrigan, Shipley, et al, 2005; Kellman & Shipley, 1991; Kellman et al, 1998; Saidpour, Braunstein, & Hoffman, 1994).…”