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Ambiguous Shape from Shading with Critical Points

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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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Authors and Affiliations

  1. Institut de Recherche en Informatique, Université Paul Sabatier (Toulouse III), 118, route de Narbonne, 31062, Toulouse Cedex, France

    Jean-Denis Durou

  2. Laboratoire de Probabilités, Université Claude Bernard (Lyon I), 43, boulevard du 11 Novembre 1918, 69622, Villeurbanne Cedex, France

    Didier Piau

Authors
  1. Jean-Denis Durou
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  2. Didier Piau
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Durou, JD., Piau, D. Ambiguous Shape from Shading with Critical Points. Journal of Mathematical Imaging and Vision 12, 99–108 (2000). https://doi.org/10.1023/A:1008361021281

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  • DOI: https://doi.org/10.1023/A:1008361021281

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