Singularity theory appears in numerous branches of mathematics, as well as in many other areas such as robotics, control theory, imaging, and various areas in physics. This book covers the developments in singularity theory and intends to introduce young researchers from developing countries to singularities in geometry and topology.

This monograph considers a basic problem in the computer analysis of natural images, which are images of scenes involving multiple objects that are obtained by a camera lens or a viewer's eye. The goal is to detect geometric features of objects in the image and to separate regions of the objects with distinct visual properties. When the scene is illuminated by a single principal light source, we further include the visual clues resulting from the interaction of the geometric features of objects, the shade/shadow regions on the objects, and the "apparent contours." We do so by a mathematical...