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Mutational and Morphological Analysis

Tools for Shape Evolution and Morphogenesis

  • Jean-Pierre Aubin

Part of the Systems & Control: Foundations & Applications book series (SCFA)

Table of contents

  1. Front Matter
    Pages i-xxxvii
  2. Mutational Analysis in Metric Spaces

    1. Front Matter
      Pages 1-1
    2. Jean-Pierre Aubin
      Pages 3-62
    3. Jean-Pierre Aubin
      Pages 63-97
  3. Morphological and Set-Valued Analysis

    1. Front Matter
      Pages 99-99
    2. Jean-Pierre Aubin
      Pages 101-165
    3. Jean-Pierre Aubin
      Pages 166-204
    4. Jean-Pierre Aubin
      Pages 205-264
  4. Geometrical and Algebraic Morphology

    1. Front Matter
      Pages 265-265
    2. Jean-Pierre Aubin
      Pages 267-318
    3. Jean-Pierre Aubin
      Pages 319-354
  5. Appendix

    1. Front Matter
      Pages 355-355
    2. Jean-Pierre Aubin
      Pages 357-383
  6. Back Matter
    Pages 384-429

About this book

Introduction

The analysis, processing, evolution, optimization and/or regulation, and control of shapes and images appear naturally in engineering (shape optimization, image processing, visual control), numerical analysis (interval analysis), physics (front propagation), biological morphogenesis, population dynamics (migrations), and dynamic economic theory.  

These problems are currently studied with tools forged out of differential geometry and functional analysis, thus requiring shapes and images to be smooth.  However, shapes and images are basically sets, most often not smooth.  J.-P. Aubin thus constructs another vision, where shapes and images are just any compact set.  Hence their evolution -- which requires a kind of differential calculus -- must be studied in the metric space of compact subsets.  Despite the loss of linearity, one can transfer most of the basic results of differential calculus and differential equations in vector spaces to mutational calculus and mutational equations in any mutational space, including naturally the space of nonempty compact subsets.  

"Mutational and Morphological Analysis" offers a structure that embraces and integrates the various approaches, including shape optimization and mathematical morphology.  

Scientists and graduate students will find here other powerful mathematical tools for studying problems dealing with shapes and images arising in so many fields.

Keywords

Analysis Derivative Finite Manifold Mathematics Maximum Topology calculus differential equation function functional analysis geometry logic theorem

Authors and affiliations

  • Jean-Pierre Aubin
    • 1
  1. 1.Centre de Recherche Viabilité, Jeux, ContrôleUniversité Paris-DauphineParisFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-1576-9
  • Copyright Information Birkhäuser Boston 1999
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-7200-7
  • Online ISBN 978-1-4612-1576-9
  • Series Print ISSN 2324-9749
  • Buy this book on publisher's site
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