SHAPE FROM TEXTURE AND CONTOUR BY WEAK ISOTROPY

A unified framework for shape from texture and contour is proposed. It is based on the assumption that the surface markings are not systemat ically compressed, or formally, that they are weakly isotropic. The we ak isotropy principle is based on analysis of the directional statisti cs of the projected surface markings. It builds on several previous th eories, in particular by Witkin [25] and Kanatani [15]. It extends the se theories in various ways, most notably to perspective projection. T he theory also provides an exact solution to an estimation problem ear lier solved approximately by Kanatani. The weak isotropy principle lea ds to a computationally efficient algorithm, WISP, for estimation of s urface orientation. WISP uses simple image observables that are shown to be direct correlates of the surface orientation to compute an initi al approximate estimate in a single step. In certain simple cases this first estimate is exact. and in experiments with natural images it is typically within 5-degrees of the final estimate. Furthermore, a proo f is given that a rotationally symmetric contour of order three or hig her is weakly isotropic. Hence, the WISP algorithm will without modifi cation recover the orientation of any such contour from a perspective view of it.