Continuity of the discrete curve evolution

Longin J. Latecki, R. R. Ghadially, Rolf Lakaemper, Ulrich Eckhardt, Longin J. Latecki, Robert A. Melter, David M. Mount, Angela Y. Wu
1999 Vision Geometry VIII  
Recently Latecki and Lak amper (Computer Vision and Image Understanding 73:3, March 1999) reported a novel process for a discrete curve evolution. This process has various application possibilities, in particular, for noise removal and shape simpli cation of boundary curves in digital images. In this paper we prove t h a t 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
more » ... This result follows directly from the fact that the evolution of Q corresponds to the evolution of P if Q approximates P. This intuitively means that rst all vertices of Q are deleted that are not close to any v ertex 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. Keywords: discrete curve e v olution, polygon evolution, shape simpli cation, curve a p p r o ximation Figure 1. Retrieval of similar objects based on a similarity measure of object contours. Emails: flatecki, ghadially, l a k aemper,
doi:10.1117/12.364095 fatcat:dgcq7cso7ra5njryz25u46dsr4