## Abstract

Many algorithms for deriving surface shape from shading require an estimate of the direction of illumination. This paper presents a new estimator for illuminant direction, which also generates an estimate of the degree of surface relief, that is measured by the variance of surface orientation (the partial derivatives of surface depth). Surfaces are considered to be samples of a stochastic process representing depth as a function of position in the image plane. We derive an estimator for illuminant tilt that is based only on some general assumptions about the process. The assumptions are that the process is wide-sense stationary, strictly isotropic, and mean-square differentiable and that the second partial derivatives of surface depth are locally independent of the first partial derivatives. We develop an estimator of illuminant slant and degree of surface relief in two stages. In the first, we develop a general format for an estimator based on the same assumptions that are used for the tilt estimator. The second stage is the actual implementation of the estimator and requires the specification of a functional form for the local probability distribution of surface orientations. This approach contrasts with previous ones, which begin their development with an assumption of a particular distribution for surfaces. The approach has the advantage that it separates the problems of surface modeling and light-source estimation, permiting one to easily implement specific estimators for different surface models. We implement the illuminant slant estimator for surfaces that have a Gaussian distribution of surface orientations and show simulation results. Degraded performance in the presence of self-shadowing is discussed.

© 1990 Optical Society of America

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