Continuity of discrete curve evolution

Recently Latecki and Lakamper [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 w e 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 evolut ion remain close. This result follows directly from the fact that the evolu tion of Q corresponds to the evolution of P if Q approximates P. This intui tively 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 ver tex of Q that is close to it is deleted in the corresponding evolution step of Q. (C) 2000 SPIE and IS&T. [S1017-9909(00)02002-X].