This paper revisits the numerical shape-from-shading method proposed in early 1980s. The original problem is non-convex due to the unit norm constraint for surface normal, and the existing approaches including the original Ikeuchi and Horn’s work uses approximate solution strategies for the original problem. This paper instead studies relaxation strategies for the original non-convex constraint and describes corresponding solution techniques that are built upon advanced convex optimization. We analyze the effect of the relaxations in terms of resulting accuracy and computational complexity.

中文翻译：

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阴影数字形状的再研究

本文回顾了1980年代初提出的数字“阴影着色”方法。由于表面法线的单位范数约束，原始问题是非凸的，包括原始Ikeuchi和Horn的工作在内的现有方法都对原始问题采用了近似求解策略。相反，本文研究了原始非凸约束的松弛策略，并描述了基于高级凸优化的相应求解技术。我们根据结果的准确性和计算复杂性来分析松弛的影响。