  In a computational topology of digital images, simplexes are replaced by
Delta sets in approximating image object shapes. For simplicity, simplexes and
Delta sets are restricted to the Euclidean plane. A planar simplex is either a
vertex, a line segment or a filled triangle. In this study of image shapes, a
planar Delta set is a sequence of ordered simplicial complexes. The basic
approach is to approximate an image shape by decomposing an image region
containing the shape into combinations of Delta sets called Delta complexes.
This approach to image shapes is motivated by the ease with which shapes
covered by Delta complexes can be measured and compared. A number of basic
results directly related to shape analysis are also given in the context of
Delta complex proximities.
