Shape from texture and contour by weak isotropy

The authors present a unified framework for shape from texture and contour. The framework is based on a concept called weak isotropy and contains as a special case A.P. Witkin´s (1987) maximum-likelihood algorithm for shape from texture. The method is based on analysis of the directional statistics of the input data. It can be applied to both smooth curves and polygons, open or closed curves, symmetric figures, and scattered texture edges; thus, it appears to have wider applicability than previous methods. The weak isotropy heuristic captures many important properties (such as various types of symmetry) of both random and regular planar shape, and it also leads to a computationally efficient estimation algorithm based on observables in the image which are direct correlates of the surface orientation. These correlates make it possible to compute an approximate estimate of surface orientation in a single step. In certain simple cases this first estimate is exactly right, and in experiments with natural images it is typically within 5° of the final estimate