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Shape-from-shading, viscosity solutions and edges. (English) Zbl 0804.68160
Summary: The article deals with the so-called Shape-from-Shading problem which arises when recovering a shape from a single image. The general case of a distribution of light sources illuminating a Lambertian surface is considered. This involves original definitions of three types of edges, mainly the apparent contours, the grazing light edges and the shadow edges. The elevation of the shape is expressed in terms of viscosity solution of a first-order Hamilton-Jacobi equation with various boundary conditions on these edges. Various existence and uniqueness results are presented.

MSC:
68U10 Computing methodologies for image processing
65D18 Numerical aspects of computer graphics, image analysis, and computational geometry
65Z05 Applications to the sciences
68T10 Pattern recognition, speech recognition
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