The USC Andrew and Erna Viterbi School of Engineering USC Signal and Image Processing Institute USC Ming Hsieh Department of Electrical Engineering University of Southern California

Technical Report USC-SIPI-235

“Shape from Shading with A Generalized Reflectance Map Model”

by Kyoung Mu Lee and C.-C. Jay Kuo

June 1993

Most conventional SFS (Shape from Shading) algorithms have been developed under three basic assumptions on surface properties and imaging geometry to simplify the problem, namely, a Lambertian surface, a distant point light source and orthographic projection. In this research, we derive a general physics-based reflectance map model which includes diffuse and specular reflection effects, a nearby point light source and perspective projection, and then develop a new direct shape recovery algorithm from shaded images. The basic idea of our solution method is to discretize the image irradiance equation with a finite triangular element surface model, to express the resulting nonlinear system of equations in terms of depth variables only, and to recover the object shape by linearizing the nonlinear equations and minimizing a quadratic cost functional. We perform numerical experiments with one or multiple photometric stereo images to demonstrate the performance of the derived physics-based reflectance map model and the proposed SFS algorithm.

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