A Computational Model for Shape from Texture

Shape from texture is best analysed in a two-stage framework analogous to stereopsis and structure from motion: (a) computing the 'texture distortion' from the image; and (b) interpreting the 'texture distortion' to infer the orientation and shape of the scene surface in 3D. We model the texture distortion at a point in any particular direction on the image plane as an affine transformation and derive the relationship between the parameters of the affine transformation and the surface shape and orientation. We have developed a technique for estimating affine transforms between nearby image patches which is based on solving a system of linear constraints derived from a differential analysis. It is not necessary explicitly to identify texels or make restrictive assumptions about the nature of the image texture like isotropy. We have developed two different models for recovering surface orientation (slant and tilt) and shape (principal curvatures and directions) based on the estimated affine transforms in a number of directions. Experimental results are presented on images of planar and curved surfaces under perspective projection.