Ebook: Variational Methods for Discontinuous Structures: Applications to image segmentation, continuum mechanics, homogenization Villa Olmo, Como, 8–10 September 1994

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.

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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.

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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.
Content:
Front Matter....Pages I-VIII
Movimenti di Partizioni....Pages 1-5
The Crystalline Algorithm for Computing Motion by Curvature....Pages 7-18
Uses of Elliptic Approximations in Computer Vision....Pages 19-34
A Kanizsa Programme....Pages 35-55
A Second Order Model in Image Segmentation: Blake & Zisserman Functional....Pages 57-72
Optimal Approximation by Piecewise Constant Functions....Pages 73-85
Indefinite Superlinear Elliptic Problems....Pages 87-92
On the Regularity of the Edge Set of Mumford-Shah Minimizers....Pages 93-103
Capacity and Dirichlet Problems in varying Domains....Pages 105-110
General Growth Conditions and Regularity....Pages 111-118
Geodesic Lines in Metric Spaces....Pages 119-122
Flow by Mean Curvature of Surfaces of Any Codimension....Pages 123-134
Functions of Bounded Variation over Non-Smooth Manifolds and Generalized Curvatures....Pages 135-142
Remarks on a Numerical Study of Convexity, Quasiconvexity, and Rank One Convexity....Pages 143-154
Homogeneous Fractal Spaces....Pages 155-160
Variational Techniques for Problems in Materials Science....Pages 161-175
Magnetoelastic Interactions....Pages 177-189
Back Matter....Pages 191-196

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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.
Content:
Front Matter....Pages I-VIII
Movimenti di Partizioni....Pages 1-5
The Crystalline Algorithm for Computing Motion by Curvature....Pages 7-18
Uses of Elliptic Approximations in Computer Vision....Pages 19-34
A Kanizsa Programme....Pages 35-55
A Second Order Model in Image Segmentation: Blake & Zisserman Functional....Pages 57-72
Optimal Approximation by Piecewise Constant Functions....Pages 73-85
Indefinite Superlinear Elliptic Problems....Pages 87-92
On the Regularity of the Edge Set of Mumford-Shah Minimizers....Pages 93-103
Capacity and Dirichlet Problems in varying Domains....Pages 105-110
General Growth Conditions and Regularity....Pages 111-118
Geodesic Lines in Metric Spaces....Pages 119-122
Flow by Mean Curvature of Surfaces of Any Codimension....Pages 123-134
Functions of Bounded Variation over Non-Smooth Manifolds and Generalized Curvatures....Pages 135-142
Remarks on a Numerical Study of Convexity, Quasiconvexity, and Rank One Convexity....Pages 143-154
Homogeneous Fractal Spaces....Pages 155-160
Variational Techniques for Problems in Materials Science....Pages 161-175
Magnetoelastic Interactions....Pages 177-189
Back Matter....Pages 191-196
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