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A Shape Reconstruction Method for Any Light Direction Based on Weighted Difference Scheme

Yu Hongbo, Zhao Rongchun, Liao Yi, Tian Guangjian (Department of Computer Science and Engineering, Northwestern Polytechnical University, Xi′an 710072, China)  
A new finite difference method is proposed to solve the image irradiance equation of shape from shading. Firstly, the non-linear term in the reflectance map is approximated by a Taylor-expansion. Then the resulting linear partial difference equation is solved numerically by a semi-implicit average difference scheme under initial and boundary conditions. Surface height is obtained iteratively by successive over-relaxation method, and the method for selecting optimal relaxation factor is also given in the paper. Experiments with synthetic images demonstrate that the new algorithm is suitable for any light direction and the reconstruction results compare favorably to the traditional ones.
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