A gradient based neighborhood filter for disparity interpolation

In this work we propose a non-local gradient-based energy for interpolating incomplete disparity maps. It represents an extension of the bilateral filter adapted to reconstruct locally planar disparity maps. We assume that we have at our disposal a reference image from which similarity weights can be computed. When the spatial extend of the weights tends to zero, the proposed model can be shown to converge to an energy involving second order derivatives, explaining thus its ability to obtain higher order interpolations. The proposed energy can be minimized by solving its Euler-Lagrange equation via an iteration of second order Poisson equations. By including an edge map our model permits also to recover depth discontinuities.