A nonlinear diffusion model for discontinuous disparity and half-occlusions in stereo

Most stereo algorithms do not take into account discontinuities in disparity and the fact that there are half-occlusions consisting of areas seen by one eye but not the other. Very few are formulated using the framework of energy functionals. A formulation that lies within such a framework and addresses the discontinuities and half-occlusions is presented. The formulation follows directly from the assumption that, when matching the left and right images, the order of points must be preserved. A model consisting of two coupled energy functions, corresponding to the two eyes, is presented. They are coupled in the sense that the discontinuity locus determined by one eye also determines the occluded area in the image seen by the other eye. A nonlinear system of diffusion equations is derived by simultaneously applying gradient descent to these functionals. The diffusion equations are implemented by a finite-difference scheme.<>