Affine plane curve evolution: a fully consistent scheme

  • Authors:
  • L. Moisan

  • Affiliations:
  • CMLA, Ecole Normale Superieure de Cachan

  • Venue:
  • IEEE Transactions on Image Processing
  • Year:
  • 1998

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Abstract

We present an accurate numerical scheme for the affine plane curve evolution and its morphological extension to grey-level images. This scheme is based on the iteration of a nonlocal, fully affine invariant and numerically stable operator, which can be exactly computed on polygons. The properties of this operator ensure that a few iterations are sufficient to achieve a very good accuracy, unlike classical finite difference schemes that generally require a lot of iterations. Convergence results are provided, as well as theoretical examples and experiments