Direct estimation of shape from texture

Witkin (1981) has 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 nonlinear equations. An alternative method is proposed, 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° 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