Boundary extraction of discrete objects

One of the aims in the field of computer vision is to acquire information about the geometric and topological properties of objects in a three-dimensional world. First, we measure the objects and then we convert the measured data into geometric and topological properties of the objects. As an intermediate between the measured data and the geometric and topological properties, a representation of the objects for computers is desired. In this paper, we propose a representation of objects and their boundaries, which is based on combinatorial topology, and develop a method of extracting boundaries of objects from measured data. It is sufficient to extract boundaries, because they include information about the shape of the objects; the internal structure of the objects is not necessary far information about the shape. In addition, we prove that boundaries are uniquely obtained using our algorithm. (C) 1998 Academic Press.