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Journal of Electronic Imaging

Continuity of discrete curve evolution
Author(s): Longin Jan Latecki; R. R. Ghadially; Rolf Lakaemper; Ulrich Eckhardt
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Paper Abstract

Recently Latecki and Lakämper [Computer Vision and Image Understanding 73(3) (1999)] reported a process called discrete curve evolution. This process has various application possibilities, in particular, for noise removal and shape simplification of boundary curves in digital images. In this paper we prove that the process of the discrete curve evolution is continuous: if polygon Q is close to polygon P, then the polygons obtained by their evolution remain close. This result follows directly from the fact that the evolution of Q corresponds to the evolution of P if Q approximates P. This intuitively implies that first all vertices of Q are deleted that are not close to any vertex of P, and then, whenever a vertex of P is deleted, then a vertex of Q that is close to it is deleted in the corresponding evolution step of Q.

Paper Details

Date Published: 1 July 2000
PDF: 10 pages
J. Electron. Imag. 9(3) doi: 10.1117/1.482748
Published in: Journal of Electronic Imaging Volume 9, Issue 3
Show Author Affiliations
Longin Jan Latecki, Hamburg Univ. (United States)
R. R. Ghadially, Univ. Hamburg (Germany)
Rolf Lakaemper, Univ. Hamburg (Germany)
Ulrich Eckhardt, Univ. Hamburg (Germany)

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