A psychologically plausible algorithm for binocular shape reconstruction

Binocular shape reconstruction is an inverse problem of inferring a 3-D similarity structure of an object from two perspective views. As most inverse problems, shape reconstruction is ill-posed and ill-conditioned, which implies that its solution is unstable, i.e., the reconstructed shape is extremely sensitive to noise present in the images. In order to accurately reconstruct a shape from noisy images, a priori knowledge (constraints) must be used. Two types of constraints are considered here: (a) system constraints; and (b) constraints of the geometrical properties of the objects. We first modified the 8 point algorithm by adding a binocular fixation constraint (system constraint). The reconstruction performance of this algorithm is substantially better than that of the 8 point algorithm. We also compared the performance of these two algorithms to the performance of humans. The results show that the accuracy of the new algorithm is similar to that of humans, but the stability of the solutions is still very poor. To obtain more stable solutions, geometrical constraints must be used to restrict a family of possible solutions. Recent psychophysical experiments showed that monocular cues related to 3-D topology, and constraints such as planarity of surface contours and symmetry of the object are crucial in shape perception. Based on these results, we developed a new algorithm for binocular shape reconstruction. In this algorithm, a 3-D shape is first obtained by means of monocular reconstruction, and then binocular disparity is used to correct the shape. The reconstruction performance of this new algorithm is substantially more stable and accurate than that of the first algorithm, and it is similar to that of humans. The psychological plausibility of this method has been tested and confirmed in a psychophysical experiment