Recovery of 3-D structure from motion is neither euclidean nor affine.

Abstract

The relationship between simulated and judged depth separations for pairs of probe dots on planar surface patches was examined in a series of 6 experiments. The simulated slant of the patches was varied without varying the simulated depth separation of the probe dots by varying the depth gradient orthogonal to the direction determined by the probe dots on the image plane. Judged depth separation varied with mean slant for constant simulated depth separations. When observers judged depth separations along a closed path, the integral of the signed depths did not sum to zero, as would be required in Euclidean geometry. These results are inconsistent with the view that the mapping between simulated and perceived 3-D structure is alfme and indicate that, in general, the perceived structure cannot be represented in either a Euclidean space or an affine space. Moreover, these results are consistent with a first-order temporal analysis of the optic flow. A pattern of moving two-dimensional (2-D) features on a flat screen can give rise to a compelling impression of three-dimensionality. This phenomenon has been called the kinetic depth effect (Wallach & O'Connell, 1953) or structure from motion (Uliman, 1979). Numerous attempts have been made to understand the underlying perceptual process and to answer the question of how the three-dimensional (3-D) properties of the perceived object are related to characteristics of the moving pattern. Much of the research on this topic has been influenced by the computational approach to vision (Marr, 1982) and has sought algorithms that could recover the real structure of the distal objects from moving patterns. Indeed, the main issue has been to find the minimal conditions and constraints that are sufficient for an ideal observer to recover the 3-D Euclidean structure of an object from 2-D moving images and to investigate the psychological validity of the theoretical findings (see Braunstein, Hoffman, Shapiro, Andersen, & Bennett, 1987, for a discussion). Recently, the view that the structure derived by the perceptual system has the same Euclidean properties as the Fulvio Domini, Cognitive Technology Laboratory (a collaboration between the

Distortions of depth-order relations and parallelism in structure from motion

“…In the shape-from-shading literature, a similar result has been reported by Todd and Reichel (1989). In the SFM literature, Domini and Braunstein (1998) obtained a similar result in a study of perceived depth. Domini and Braunstein placed two pairs ofprobes-(P o, PI) and (P 2 , P 3)-on different regions of a curved surface and predicted that judged depth separation would vary with the mean slant of the regions on which the probes were placed for constant simulated depth separations and constant simulated angular velocities.…”

“…On the basis of Equation 3, therefore, we can formulate three hypotheses that will be directly tested in the present paper? (see also Domini & Braunstein, 1998).…”

Matching perceived depth from disparity and from velocity: Modeling and psychophysics

“…We provided evidence that this is achieved by a probabilistic process which assigns the most likely 3D interpretation to (ambiguous) local first-order properties of the optic flow. As a consequence, the perceptual interpretation of velocity information is, in general, neither veridical nor internally consistent Caudek & Proffitt, 1993;Caudek & Rubin, 2001;Di Luca, Domini, & Caudek, 2004Domini & Braunstein, 1998;Domini & Caudek, 1999, 2003a, 2003bDomini, Caudek, & Proffitt, 1997;Domini, Caudek, & Richman, 1998;Domini, Caudek, & Skirko, 2003;Domini, Caudek, & Tassinari, 2006;Domini, Caudek, Turner, & Favretto, 1998;Domini, Vuong, & Caudek, 2002;Tassinari, Domini, & Caudek, 2008).…”

A new theory of structure-from-motion perception

“…Surface slant from def: A more radical view is that of Domini et al (Domini & Braunstein, 1998; Domini & Caudek, 2003; Domini, Caudek, & Richman, 1998). They propose that the perceived slant of a surface is a function of the 1st-order optic-flow property def and predict that the structure of a shape recovered from SFM will be internally inconsistent.…”