Boundary tracing

Boundary tracing, also known as contour tracing, of a binary digital region can be thought of as a segmentation technique that identifies the boundary pixels of the digital region. Boundary tracing is an important first step in the analysis of that region. In topology, a boundary can be defined precisely due to the precise nature of topological spaces. However, digital images do not obey the same rules as topological spaces, and thus the appropriate definition of boundary is less clear. For example, most publications about tracing the boundary of a subset S of a digital image I describe algorithms which find a set of pixels belonging to S and having in their direct neighborhood pixels belonging both to S and to its complement I - S. According to this definition, the boundary of a subset S is different from the boundary of its complement I – S, which is impossible in normal topology. To define the boundary correctly it is necessary to introduce a topological space corresponding to the given digital image. Such space can be a two-dimensional abstract cell complex. It contains cells of three dimensions: the two-dimensional cells corresponding to pixels of the digital image, the one-