Anisotropy in perceived nonrigidity

Shape-from-motion models generally assume that objects are rigid, which simplifies the computations but cannot handle movements and locomotion of organisms, all of which require nonrigid shape deformations. We have demonstrated that rotated rigid objects can appear strikingly nonrigid, depending on speed and shape. We showed that nonrigid percepts arise from the outputs of direction-selective motion cells and are countered by feature-tracking and shape-based priors. Now we present the surprising finding that perceived nonrigidity changes with the rigid object’s orientation, and model it with documented cortical anisotropies. When two solid 3D circular rings attached rigidly at an angle are rotated horizontally around a vertical axis at medium speed, observers see either rigid rotation or non-rigid wobbling. A 90° image rotation markedly enhances the non-rigid percept. We observed that the elliptical projections of the rings in the rotated image appear narrower and longer than in the original image, like the increased perceived height versus width when a square is rotated 45° to form a diamond. We successfully model the perceived changes in shape with optimal Bayesian decoding of V1 outputs, by incorporating anisotropies in the number and tuning-widths of orientation selective cells and the probability distribution of orientations in images of natural scenes. We show quantitatively that elongating the ellipses alone leads to more perceived nonrigidity even for horizontal rotation, but the vertical rotation further enhances nonrigidity. We incorporated the cortical anisotropies into motion flow computations. The estimated motion fields were decomposed into gradients of divergence, curl, and deformation and compared to the gradients for physical rotation and wobbling. The gradients for the vertical rotation were a closer match to physical wobbling, while the gradients for the horizontal rotation were in between physical wobbling and rotating. This asymmetry indicates that hardwired cortical anisotropies can explain changes in perceived non-rigidity with motion axis.