Variational methods for discontinuous structures : applications to image segmentation, continuum mechanics, homogenization : Villa Olmo, Como, 8-10 September 1994
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Bibliographic Information
Variational methods for discontinuous structures : applications to image segmentation, continuum mechanics, homogenization : Villa Olmo, Como, 8-10 September 1994
（Progress in nonlinear differential equations and their applications / editor, Haim Brezis, v. 25）
Birkhäuser Verlag, 1996
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
C-P||Como||1994.996044834
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Proceedings of an international conference
Includes bibliographical references
Description and Table of Contents
Description
In recent years many researchers in material science have focused their attention on the study of composite materials, equilibrium of crystals and crack distribution in continua subject to loads. At the same time several new issues in computer vision and image processing have been studied in depth. The understanding of many of these problems has made significant progress thanks to new methods developed in calculus of variations, geometric measure theory and partial differential equations. In particular, new technical tools have been introduced and successfully applied. For example, in order to describe the geometrical complexity of unknown patterns, a new class of problems in calculus of variations has been introduced together with a suitable functional setting: the free-discontinuity problems and the special BV and BH functions. The conference held at Villa Olmo on Lake Como in September 1994 spawned successful discussion of these topics among mathematicians, experts in computer science and material scientists.
Table of Contents
Movimenti di partizioni.- The crystalline algorithm for computing motion by curvature.- Uses of elliptic approximations in computer vision.- A Kanisza programme.- A second order model in image segmentation: Blake & Zisserman functional.- Optimal approximation by piecewise constant functions.- Indefinite superlinear elliptic problems.- On the regularity of the edge set of Mumford-Shah minimizers.- Capacity and Dirichlet problems in varying domains.- General growth conditions and regularity.- Geodesic lines in metric spaces.- Flow by mean curvature of surfaces of any codimension.- Functions of bounded variation over nonsmooth manifolds and generalized curvatures.- Remarks on a numerical study of convexity, quasi-convexity, and rank-one convexity.- Homogeneous fractal spaces.- Variational techniques for problems in material science.- Magnetoelastic interactions.- Contributors.- List of participants.
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