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Continuity of discrete curve evolution

[+] Author Affiliations
L. J. Latecki, R.-R. Ghadially, R. Laka¨mper, U. Eckhardt

University of Hamburg, Department of Applied Mathematics, Bundesstr. 55, 20146?Hamburg, Germany

J. Electron. Imaging. 9(3), 317-326 (Jul 01, 2000). doi:10.1117/1.482748
History: Received Nov. 24, 1999; Revised Mar. 16, 2000; Accepted Mar. 20, 2000
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Abstract

Recently Latecki and Laka¨mper [Computer Vision and Image Understanding73(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. © 2000 SPIE and IS&T.

© 2000 SPIE and IS&T

Citation

L. J. Latecki ; R.-R. Ghadially ; R. Laka¨mper and U. Eckhardt
"Continuity of discrete curve evolution", J. Electron. Imaging. 9(3), 317-326 (Jul 01, 2000). ; http://dx.doi.org/10.1117/1.482748


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