Topological feature extraction in binary images

Many problems in image processing and computer vision require the computation of topological characteristics of objects in images including the number of connected components and the number of holes. In this note, we introduce and discuss a new method based on combinatorial homology theory to compute these characteristics in a given image. This powerful concept can be used in any dimension and permits to retrieve the whole topological information at once without skeletonizing. We give a description of this theory and the associated computation algorithms. We also give examples emphasizing the application of homology and demonstrating its efficiency as a computation tool.