Deriving shape information from occluding contours in shape-from-shading problems

Alexander M. Bonch-Osmolovsky

doi:10.1117/12.57062

1 February 1992 Deriving shape information from occluding contours in shape-from-shading problems

Alexander M. Bonch-Osmolovsky

Proceedings Volume 1607, Intelligent Robots and Computer Vision X: Algorithms and Techniques; (1992) https://doi.org/10.1117/12.57062
Event: Robotics '91, 1991, Boston, MA, United States

Abstract

There is considerable ambiguity in literature as to how much information can be derived from the occluding contour in shape-from-shading reconstruction. It is often argued that because the derivatives p equals (partial)z/(partial)x and/or q equals (partial)z/(partial)y are infinite on occluding contours, such contours cannot supply the initial slope values needed for integrating the image irradiance equation by the characteristic strip method. By this method surface shape along the strip is uniquely determined by image data and the initial slopes at just one starting point. By contrast, the variational approach to shape-from-shading claims to make full use of information contained in the shape of the occluding contour in the form of boundary values set for the appropriate Euler second order PDEs, which are solved as though the solution had a global dependence on its boundary values. To analyze this controversy, we transform the characteristic strip equations in surface gradients into equivalent equations in surface normals. A nice system of equations was obtained, with no singularities on the limb of the object, which, we hoped, could be integrated starting right from the occluding contour. It turned out, however, that for most reflectance functions (one exception is the familiar eikonal equation) the occluding contour is the envelope of the family of characteristics and is itself a solution to the characteristic strip equations, which at the occluding boundary turn out to have multiple solutions. This is the true reason precluding numerical integration of these equations from the occluding contour.

Citation Download Citation

Alexander M. Bonch-Osmolovsky "Deriving shape information from occluding contours in shape-from-shading problems", Proc. SPIE 1607, Intelligent Robots and Computer Vision X: Algorithms and Techniques, (1 February 1992); https://doi.org/10.1117/12.57062

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