Shape from texture: Estimation, isotropy and moments

A theory is proposed for the interpretation of 3D textures with oriented elements. It builds on two previous theories: a statistical one due to Witkin, and Kanatani's “Buffon” transform. We show that the statistical estimation of orientation of a textured plane is one of a general family of optimal backprojection problems which also includes “maximal compactness”. General uniqueness and convergence results are obtained for an efficient algorithm employing “second moment feedback”. This framework greatly enhances the usefulness of surface orientation estimation for texture in two ways. First, an error distribution is derived for the estimator, and this is crucial for integration of shape information. Second, hypotheses about intrinsic texture statistics can be verified by a Ï2 test which, if failed, warns that the orientation estimator is not to be believed. Finally, it is argued that these results suggest a general moment-tensor approach to analysis of 3D texture.