1 July 2000 Continuity of discrete curve evolution
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J. of Electronic Imaging, 9(3), (2000). doi:10.1117/1.482748
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.
Longin Jan Latecki, R. R. Ghadially, Rolf Lakaemper, Ulrich Eckhardt, "Continuity of discrete curve evolution," Journal of Electronic Imaging 9(3), (1 July 2000). http://dx.doi.org/10.1117/1.482748

Image segmentation

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