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Motivated by a variational model concerning the depth of the objects in a picture and the problem of hidden and illusory contours, this book investigates one of the central problems of computer vision: the  topological and algorithmic reconstruction of a smooth three dimensional scene starting from the visible part of an apparent contour. The authors focus their attention on the manipulation of apparent contours using a finite set of elementary moves, which correspond to diffeomorphic deformations of three dimensional scenes. A large part of the book is devoted to the  algorithmic part, with implementations, experiments, and computed examples. The book is intended also as a user's guide to the software code appcontour, written for the manipulation of apparent contours and their invariants. This book is addressed to theoretical and applied scientists working in the field of mathematical models of image segmentation.

Mathematics. --- Mathematical Applications in Computer Science. --- Image Processing and Computer Vision. --- Manifolds and Cell Complexes (incl. Diff.Topology). --- Calculus of Variations and Optimal Control; Optimization. --- Mathematical Software. --- Computer vision. --- Computer software. --- Mathematical optimization. --- Cell aggregation --- Mathématiques --- Vision par ordinateur --- Logiciels --- Optimisation mathématique --- Geometry -- Data processing. --- Three-dimensional imaging. --- Engineering & Applied Sciences --- Computer Science --- Geometry --- Data processing. --- Machine vision --- Vision, Computer --- 3-D imaging --- 3D imaging --- Three-dimensional imaging systems --- Three-dimensional imaging techniques --- Three-dimensional visualization --- Visualization, Three-dimensional --- Image processing. --- Computer science --- Computer mathematics. --- Calculus of variations. --- Manifolds (Mathematics). --- Complex manifolds. --- Imaging systems --- Artificial intelligence --- Image processing --- Pattern recognition systems --- Aggregation, Cell --- Cell patterning --- Cell interaction --- Microbial aggregation --- Software, Computer --- Computer systems --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Computer science—Mathematics. --- Optical data processing. --- Isoperimetrical problems --- Variations, Calculus of --- Analytic spaces --- Manifolds (Mathematics) --- Geometry, Differential --- Topology --- Optical computing --- Visual data processing --- Bionics --- Electronic data processing --- Integrated optics --- Photonics --- Computers --- Computer mathematics --- Mathematics --- Optical equipment