A differential method for computing local shape-from-texture for planar and curved surfaces

Shape from texture is best analyzed in a two-stage framework: computing the texture gradient from the image, and interpreting the texture gradient to infer the distance and shape of the scene surface in 3-D. The texture distortion is modeled at a point in any particular direction on the image plane as an affine transformation. The parameters of the affine transform are related to the viewer. A technique is developed for estimating affine transforms between nearby image patches. It is based on solving a system of linear constraints derived from a differential analysis. Given the estimated affine transforms in a number of directions, it is possible to recover local shape and orientation of the surface. It is not necessary to explicitly identify texels or make restrictive assumptions about the nature of the image texture. Experimental results are presented on images of planar and curved surfaces under perspective projection