Normals and Curvature Estimation for Digital Surfaces Based on Convolutions

  • Sébastien Fourey
  • Rémy Malgouyres
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4992)


In this paper, we present a method that we call on-surface convolution which extends the classical notion of a 2D digital filter to the case of digital surfaces (following the cuberille model). We also define an averaging mask with local support which, when applied with the iterated convolution operator, behaves like an averaging with large support. The interesting property of the latter averaging is the way the resulting weights are distributed: they tend to decrease following a “continuous” geodesic distance within the surface. We eventually use the iterated averaging followed by convolutions with differentiation masks to estimate partial derivatives and then normal vectors over a surface. We provide an heuristics based on [14] for an optimal mask size and show results.


Normal Vector Geodesic Distance Curvature Estimation Adjacency Relation Digital Plane 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Sébastien Fourey
    • 1
  • Rémy Malgouyres
    • 2
  1. 1.GREYC, UMR6072 – ENSICAEN, 6 bd maréchal Juin 14050 Caen cedexFrance
  2. 2.LAIC, EA2146 – Université Clermont 1, BP 86, Aubiére cedexFrance

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