Shape from stereo and shading by gradient constrained interpolation

Textureless regions, though error prone in stereo, may contain shading information that may be exploited. Shape from shading (SFS) results relate to world coordinates by arbitrary scaling factors which are difficult to estimate. We propose a method for estimating dense disparities from sparse correspondences using SFS cues. We show that SFS can impose constraints on the gradient of disparity in textureless regions with constant albedo. Gradient Constrained Interpolation (GCI), which solves the estimation problem in one dimension, is presented. We efficiently generate paths between correspondences that cover the image and then use GCI to fill the pixels in between. Results are presented on real and synthetic images, and provide quantitative evaluations to show that the method outperforms baseline methods.