Various fields of image analysis, computer vision, and artificial intelligence require a description of shape in grey-level images, but the automatic performance of these tasks can only succeed if a suitable description of shape is available. This book presents a comprehensive overview of the mathematical description of shape from the viewpoint of a broad range of disciplines. The emphasis is on the methodology and theunderlying mathematics. The concept of shape is explored in terms of such disciplines as digital topology and geometry, categorial shape theory, mathematical morphology, wavelets, differential geometry, graph and hierarchical representation methods, and evolutionary systems.