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Geometry-Driven Diffusion in Computer Vision

  • Book
  • © 1994

Overview

Editors:
  1. Bart M. Haar Romeny

    1. 3D Computer Vision Research Group, Utrecht University, Utrecht, The Netherlands

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Part of the book series: Computational Imaging and Vision (CIVI, volume 1)

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Table of contents (15 chapters)

  1. Front Matter

    Pages i-xxii
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  2. Linear Scale-Space I: Basic Theory

    • Tony Lindeberg, Bart M. ter Haar Romeny
    Pages 1-38

  3. Linear Scale-Space II: Early Visual Operations

    • Tony Lindeberg, Bart M. ter Haar Romeny
    Pages 39-72

  4. Anisotropic Diffusion

    • Pietro Perona, Takahiro Shiota, Jitendra Malik
    Pages 73-92

  5. Vector-Valued Diffusion

    • Ross Whitaker, Guido Gerig
    Pages 93-134

  6. Bayesian Rationale for the Variational Formulation

    • David Mumford
    Pages 135-146

  7. Variational Problems with a Free Discontinuity Set

    • Antonio Leaci, Sergio Solimini
    Pages 147-154

  8. Minimization of Energy Functional with Curve-Represented Edges

    • Niklas Nordström
    Pages 155-168

  9. Approximation, Computation, and Distortion in the Variational Formulation

    • Thomas Richardson, Sanjoy Mitter
    Pages 169-190

  10. Coupled Geometry-Driven Diffusion Equations for Low-Level Vision

    • Marc Proesmans, Eric Pauwels, Luc van Gool
    Pages 191-228

  11. Morphological Approach to Multiscale Analysis: From Principles to Equations

    • Luis Alvarez, Jean-Michel Morel
    Pages 229-254

  12. Differential Invariant Signatures and Flows in Computer Vision: A Symmetry Group Approach

    • Peter Olver, Guillermo Sapiro, Allen Tannenbaum
    Pages 255-306

  13. On Optimal Control Methods in Computer Vision and Image Processing

    • Benjamin Kimia, Allen Tannenbaum, Steven Zucker
    Pages 307-338

  14. Nonlinear Scale-Space

    • Luc M. J. Florack, Alfons H. Salden, Bart M. ter Haar Romeny, Jan J. Koenderink, Max A. Viergever
    Pages 339-370

  15. A Differential Geometric Approach to Anisotropic Diffusion

    • David Eberly
    Pages 371-392

  16. Numerical Analysis of Geometry-Driven Diffusion Equations

    • Wiro J. Niessen, Bart M. ter Haar Romeny, Max A. Viergever
    Pages 393-410

  17. Back Matter

    Pages 411-441
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Keywords

About this book

Scale is a concept the antiquity of which can hardly be traced. Certainly the familiar phenomena that accompany sc ale changes in optical patterns are mentioned in the earliest written records. The most obvious topological changes such as the creation or annihilation of details have been a topic to philosophers, artists and later scientists. This appears to of fascination be the case for all cultures from which extensive written records exist. For th instance, chinese 17 c artist manuals remark that "distant faces have no eyes" . The merging of details is also obvious to many authors, e. g. , Lucretius mentions the fact that distant islands look like a single one. The one topo­ logical event that is (to the best of my knowledge) mentioned only late (by th John Ruskin in his "Elements of drawing" of the mid 19 c) is the splitting of a blob on blurring. The change of images on a gradual increase of resolu­ tion has been a recurring theme in the arts (e. g. , the poetic description of the distant armada in Calderon's The Constant Prince) and this "mystery" (as Ruskin calls it) is constantly exploited by painters.

Editors and Affiliations

  • 3D Computer Vision Research Group, Utrecht University, Utrecht, The Netherlands

    Bart M. Haar Romeny

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