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Recovering Surfaces from the Restoring Force

  • George Kamberov
  • Gerda Kamberova
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2351)

Abstract

We present a new theoretical method and experimental results for direct recovery of the curvatures, the principal curvature directions, and the surface itself by explicit integration of the Gauss map. The method does not rely on polygonal approximations, smoothing of the data, or model fitting. It is based on the observation that one can recover the surface restoring force from the Gauss map, and (i) applies to orientable surfaces of arbitrary topology (not necessarily closed); (ii) uses only first order linear differential equations; (iii) avoids the use of unstable computations; (iv) provides tools for filtering noise from the sampled data. The method can be used for stable extraction of surfaces and surface shape invariants, in particular, in applications requiring accurate quantitative measurements.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • George Kamberov
    • 1
  • Gerda Kamberova
    • 2
  1. 1.Stevens Institute of TechnologyHobokenUSA
  2. 2.Hofstra UniversityHempsteadUSA

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