Abstract
The rigidity assumption, ubiquitous in the study of Structure-From-Motion (SFM), states that if a rigid interpretation is available, the visual system will take that interpretation. We investigate a perceptual phenomenon where this assumption is strongly violated: a rigidly rotating plane with concave and convex parts is perceived as folding non-rigidly. Our stimuli consisted of a square plane with protrusions in the upper-left and bottom-right quadrants; each part could be convex or concave. The entire surface was defined by a random-dot texture, transparent, and orthographically projected. The surface began each motion sequence frontoparallel, then rotated rigidly about its central vertical axis. We observed that when one part was convex and the other concave, the surface was perceived as having two convex parts with the plane “folding” non-rigidly along its central axis like a book. We explored the parameters of this non-rigid interpretation. We manipulated the convexity of the parts; parts were either half ellipsoids or bivariate Gaussians (ellipsoids more convex). The angular range of rotation of the object (ranging from +/-30 to +/-75 degrees) manipulated the amount of non-rigidity (larger ranges lead to greater magnitudes of “folding”). Subjects reported whether the plane was “rigid” or “folding”. When one part was convex and the other concave, subjects perceived the plane as “folding” non-rigidly (with both parts convex) on a majority (>60%) of trials. The proportion of non-rigid responses were higher for half-ellipsoid than for Gaussian parts, and higher for smaller ranges of rotation. The results illustrate a competition between priors for rigidity and convexity. A rigid interpretation is available and yet it is often ignored in favor of a non-rigid interpretation. This points to the need for investigating various prior constraints used in the interpretation of SFM beyond just rigidity – and especially how these priors interact with each other.