Ambiguous Shape from Shading with Critical Points |
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Authors: | Jean-Denis Durou Didier Piau |
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Affiliation: | (1) Institut de Recherche en Informatique, Université Paul Sabatier (Toulouse III), 118, route de Narbonne, 31062 Toulouse Cedex, France;(2) Laboratoire de Probabilités, Université Claude Bernard (Lyon I), 43, boulevard du 11 Novembre 1918, 69622 Villeurbanne Cedex, France |
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Abstract: | The eikonal equation can have an infinite number of solutions when the image has critical points. We exhibit a family, indexed by a continuous parameter, of non isomorphic surfaces with one critical point, which give the same simple image. Hence, shape from shading can be an ill-posed problem when no additional condition on the shape is imposed, even when the image has critical points. Also, deformations without distortion are possible, i.e., there can exist a continuous deformation of the surface which does not modify its image. |
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Keywords: | shape from shading eikonal equation ill-posed problem shape reconstruction |
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