Geometry-Driven Diffusion in Computer Vision

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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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.

• Diffusion
• Optimal control
• anisotropic diffusion
• computer vision
• image processing
• modeling
• system
• partial differential equations

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

  Bart M. Haar Romeny

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