Despite the many successes of digital processing in domains as far apart as space science, robotics, forensics, and microscopy, many fundamental problems remain unsolved or imperfectly understood. Much of the work described in this volume has not been previously surveyed systematically, therefore, these accounts may form an indispensible addition to the image processing literature. This book sets out to survey systematically image related topics such as vector quantization, lattice transforms, invariant pattern representations, topology, algebra and estimation theory and echographic imaging.