Ambiguous Shape from Shading with Critical Points

  • Authors:
  • Jean-Denis Durou;Didier Piau

  • Affiliations:
  • Institut de Recherche en Informatique, Université Paul Sabatier (Toulouse III), 118, route de Narbonne, 31062 Toulouse Cedex, France. durou@irit.fr;Laboratoire de Probabilités, Université Claude Bernard (Lyon I), 43, boulevard du 11 Novembre 1918, 69622 Villeurbanne Cedex, France. piau@jonas.univ-lyon1.fr

  • Venue:
  • Journal of Mathematical Imaging and Vision
  • Year:
  • 2000

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Abstract

The eikonal equation can have an infinite number ofsolutions when the image has critical points. We exhibit a family,indexed by a continuous parameter, of non isomorphic surfaces withone critical point, which give the same simple image. Hence, shapefrom shading can be an ill-posed problem when no additional conditionon the shape is imposed, even when the image has critical points.Also, deformations without distortion are possible, i.e., there canexist a continuous deformation of the surface which does not modifyits image.