Combinatorial and discrete geometric problems in image analysis

Abstract

Image analysis is a scientific discipline which provides theoretical foundations and methods for solving problems appearing in a range of areas as diverse as biology, medicine, physics, astronomy, chemistry, robotics, industrial manufacturing, and security. The very nature of the subject of image analysis determines its close relations to various facets of artificial intelligence. Unlike traditional approaches, which are based on continuous models requiring float arithmetic computations and rounding, “combinatorial” (or “discrete”) approaches are based on studying combinatorial properties of discrete structures. They provide models and algorithms, which often appear to be more efficient and accurate than those based on continuous models. Some recent combinatorial approaches aim at constructing a self-contained digital topology and geometry, which might be of interest and importance not only for image analysis, but also as independent mathematical disciplines.