Competition between priors for convexity and rigidity in Structure-From-Motion

We investigated the competition between priors for convexity and rigidity in Structure-From-Motion. We found that a preference for convexity can override the ubiquitous rigidity assumption: a rigidly rotating plane with a convex hill and a concave valley is perceived as a surface with two hills, moving non-rigidly. Our SFM stimuli consisted of two vertically elongated parts (both half-ellipsoids or bivariate Gaussians; each a convex “hill” or concave “valley”), centered in the left and right halves of a square plane. Competition between priors occurs with “one hill–one valley” stimuli: when convexity wins, the surface is seen as moving non-rigidly, with two hills. When rotated about its central vertical axis (Experiments 1,2), the non-rigid percept is of “folding” along that axis; when rotated about its horizontal axis (Experiments 3,4) it is of “twisting.” We manipulated the strength of convexity through the shape of the parts: half-ellipsoids (more convex) vs. bivariate-Gaussians (less convex); and non-rigidity through the angular range of rotation (larger ranges lead to greater non-rigidity). Observers reported whether the surface was “rigid” or “non-rigid,” and the parts “hills” or “valleys”. Under orthographic projection (Experiments 1,3), observers perceived non-rigid motion on a large percentage of trials for both vertical (93%) and horizontal (53%) axis rotation. The proportion of “non-rigid” responses was higher for the ellipsoids than Gaussians, and for smaller ranges of rotation (consistent with the expected effects of convexity and rigidity respectively). While perspective (Experiments 2,4) lowered the overall percentage of non-rigid responses (31% and 10% for vertical and horizontal axis rotation respectively), they remained significantly above zero (the prediction of the rigidity assumption), while maintaining the trends observed under orthographic projection. The results demonstrate even when a rigid interpretation is available, and even when perspective supports that interpretation, a convexity bias can overcome both, leading to a non-rigid percept.