Shape from shading
International Journal of Computer Vision
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Shadows provide perceptually important information about the shape of an illuminated three-dimensional (3D) surface. In this article, we present the topological properties of the shading problem in the Morse-theoretic framework, and we establish some key theoretical properties of the height function in the light direction of an illuminated 3D surface. We also describe a link between the shading problem and the height function in the light direction, and we derive the necessary and sufficient conditions for the shading function to be a Morse function.