Abstract
In this paper a definition of the boundary of a finite set of points in the plane is given. It is based on the concept of the density of such a set of points. An algorithm is given for finding an approximation to such a boundary. They are well-known definitions of connectedness, boundary, hole, and cluster for a finite set of points in the plane (see, e.g., A. Rosenfeld, Amer. Math. Monthly 86 1979, 621–630; Inform. and Contr. 39 1978, 19–34) and algorithms for constructing these objects (see, e.g., A Rosenfeld and A. C. Kak, Digital Picture Processing, Academic Press, New York 1976). These definitions have been given for subsets of a grid of points. This paper attempts to define these objects for an arbitrary finite set of points.
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