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Well-posedness of linear shape-from-shading problem

  • Ryszard Kozera
  • Reinhard Klette
Shape
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1296)

Abstract

We continue to study here a global shape recovery of a smooth surface for which the reflectance map is linear. It was recently proved that under special conditions the corresponding finite difference based algorithms are stable and thus convergent to the ideal solution. The whole analysis was based on the assumption that the problem related to the linear image irradiance equation is well-posed. Indeed, we show in this paper that under certain conditions there exists a unique global C2 solution (depending continuously on the initial data) to the corresponding Cauchy problem defined over the entire image domain (with non-smooth boundary).

Keywords

Cauchy Problem Global Solution Global Existence Class Global Solution Simple Geometric Interpretation 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Ryszard Kozera
    • 1
  • Reinhard Klette
    • 2
  1. 1.Department of Computer ScienceThe University of Western AustraliaNedlandsAustralia
  2. 2.Tamaki Campus, Computer Science DepartmentThe Auckland UniversityAucklandNew Zealand

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