Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The aim of the book is to study some aspects of geometric evolutions, such as mean curvature flow and anisotropic mean curvature flow of hypersurfaces. We analyze the origin of such flows and their geometric and variational nature. Some of the most important aspects of mean curvature flow are described, such as the comparison principle and its use in the definition of suitable weak solutions. The anisotropic evolutions, which can be considered as a generalization of mean curvature flow, are studied from the view point of Finsler geometry. Concerning singular perturbations, we discuss the convergence of the Allen–Cahn (or Ginsburg–Landau) type equations to (possibly anisotropic) mean curvature flow before the onset of singularities in the limit problem. We study such kinds of asymptotic problems also in the static case, showing convergence to prescribed curvature-type problems.

Mathematics --- Physical Sciences & Mathematics --- Geometry --- Mathematics. --- Geometry. --- Euclid's Elements --- Math --- Science --- Curvature. --- Flows (Differentiable dynamical systems) --- Differentiable dynamical systems --- Calculus --- Curves --- Surfaces

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

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