Direct Estimation of Shape from Texture

In [12], Witkin proposed a maximum likelihood (ML) estimator of surface orientation based on the observed directional bias of projected texture elements. However, a drawback of this procedure is that the estimate is only defined indirectly in terms of a set of non-linear equations. In this paper we propose an alternative method, which allows an estimate of the surface orientation to be computed directly in a single step from certain simple statistics of the image data. We also show that this direct estimate allows Witkin's ML estimate to be computed to within 0:05 ffi in only two or three iterative steps. The performance of the new estimator is demonstrated experimentally and compared to that of the ML estimator, using both synthetic data and real gray-level images. Index Terms: Shape from texture, surface orientation, foreshortening, isotropy, distributions on the circle, maximum likelihood, method of moments i 1 Introduction Although direct information about depth and three-dim..