Gaussian Scale-Space Theory

1. Front Matter

   Pages i-xx

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2. Applications

   1. Front Matter

      Pages 1-1

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   2. Applications of Scale-Space Theory

      • Bart ter Haar Romeny

      Pages 3-19

   3. Enhancement of Fingerprint Images using Shape-Adapted Scale-Space Operators

      • Andrés Almansa, Tony Lindeberg

      Pages 21-30

   4. Optic Flow and Stereo

      • Wiro J. Niessen, Robert Maas

      Pages 31-42

3. The Foundation

   1. Front Matter

      Pages 43-43

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   2. On the History of Gaussian Scale-Space Axiomatics

      • Joachim Weickert, Seiji Ishikawa, Atsushi Imiya

      Pages 45-59

   3. Scale-Space and Measurement Duality

      • Luc Florack

      Pages 61-74

   4. On the Axiomatic Foundations of Linear Scale-Space

      • Tony Lindeberg

      Pages 75-97

   5. Scale-Space Generators and Functionals

      • Mads Nielsen

      Pages 99-114

   6. Invariance Theory

      • Alfons Salden

      Pages 115-128

   7. Stochastic Analysis of Image Acquisition and Scale-Space Smoothing

      • Kalle Åström, Anders Heyden

      Pages 129-136

4. The Structure

   1. Front Matter

      Pages 137-137

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   2. Local Analysis of Image Scale Space

      • Peter Johansen

      Pages 139-146

   3. Local Morse Theory for Gaussian Blurred Functions

      • James Damon

      Pages 147-163

   4. Critical Point Events in Affine Scale-Space

      • Lewis Griffin

      Pages 165-180

   5. Topological Numbers and Singularities

      • Stiliyan Kalitzin

      Pages 181-189

   6. Multi-Scale Watershed Segmentation

      • Ole Fogh Olsen

      Pages 191-200

5. Non-linear Extensions

   1. Front Matter

      Pages 201-201

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   2. The Morphological Equivalent of Gaussian Scale-Space

      • Rein van den Boomgaard, Leo Dorst

      Pages 203-220

Gaussian scale-space is one of the best understood multi-resolution techniques available to the computer vision and image analysis community. It is the purpose of this book to guide the reader through some of its main aspects. During an intensive weekend in May 1996 a workshop on Gaussian scale-space theory was held in Copenhagen, which was attended by many of the leading experts in the field. The bulk of this book originates from this workshop. Presently there exist only two books on the subject. In contrast to Lindeberg's monograph (Lindeberg, 1994e) this book collects contributions from several scale­ space researchers, whereas it complements the book edited by ter Haar Romeny (Haar Romeny, 1994) on non-linear techniques by focusing on linear diffusion. This book is divided into four parts. The reader not so familiar with scale-space will find it instructive to first consider some potential applications described in Part 1. Parts II and III both address fundamental aspects of scale-space. Whereas scale is treated as an essentially arbitrary constant in the former, the latter em­ phasizes the deep structure, i.e. the structure that is revealed by varying scale. Finally, Part IV is devoted to non-linear extensions, notably non-linear diffusion techniques and morphological scale-spaces, and their relation to the linear case. The Danish National Science Research Council is gratefully acknowledged for providing financial support for the workshop under grant no. 9502164.

• Diffusion
• Stereo
• algorithms
• calculus
• image analysis
• remote sensing/photogrammetry

• DIKU, Department of Computer Science, University of Copenhagen, Copenhagen, Denmark

  Jon Sporring, Peter Johansen

• 3D-Laboratory, School of Dentistry, University of Copenhagen, Copenhagen, Denmark

  Mads Nielsen

• Department of Computer Science, Faculty of Mathematics and Computer Science, University of Utrecht, Utrecht, The Netherlands

  Luc Florack

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