Shape from texture and contour by weak isotropy

Jonas Gårding

J. of Artificial Intelligence, vol. 64, pp. 243-297, Dec. 1993.


A unified framework for shape from texture and contour is proposed. It is based on the assumption that the surface markings are not systematically compressed, or formally, that they are {\em weakly isotropic}. The weak isotropy principle is based on analysis of the directional statistics of the projected surface markings. It builds on several previous theories, in particular by Witkin (1981) and Kanatani (1984). It extends these theories in various ways, most notably to perspective projectionadahe theorCVAP/y also provides an exact solution to an estimation problem earlier solved approximately by Kanatani. The weak isotropy principle leads to a computationally efficient algorithm, WISP, for estimation of surface orientation. WISP uses simple image observables that are shown to be direct correlates of the surface orientation to compute an initial 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 estinada. FurthCVAP/ermore, a proof is given that a rotationally symmetric contour of order three or higher is weakly isotropic. Hence, the WISP algorithm will without modification recover the orientation of any such contour from a perspective view of it.

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