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-172

“Shape from Shading with A Linear Triangular Element Surface Model”

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

February 1991

We propose to combine a triangular element surface model with the linearized reflectance map to formulate the shape from shading problem in this research. The key idea is to approximate a smooth surface by the union of triangular surface patches called triangular elements, and express the approximating surface as a linear combination of a set of nodal basis functions. Since the surface normal of a triangular element is uniquely determined by the heights of its three vertices (or nodes), the image brightness can be directly related to the nodal heights via a linearized reflectance map. The surface height can therefore be determined by minimizing a quadratic cost functional corresponding to the squares of the brightness error and solved effectively with the multigrid computational technique. The proposed method does not require any integrability constraint or artificial assumptions on boundary conditions. Simulation results for several synthetic and real images are demonstrated to show the performance and efficiency of our new method.

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