Ebook: Gaussian Scale-Space Theory

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.

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This book covers Gaussian scale-space theory from its applications to its mathematical foundation. The reader not so familiar with scale-space will find it instructive to first consider some potential applications described in Part I. The next two parts both address fundamental aspects of scale-space. Whereas scale is treated as an essentially arbitrary constant in Part II, Part III emphasises 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.
Audience: This volume is addressed to researchers in the field of image analysis seeking mathematical foundation of algorithms.

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This book covers Gaussian scale-space theory from its applications to its mathematical foundation. The reader not so familiar with scale-space will find it instructive to first consider some potential applications described in Part I. The next two parts both address fundamental aspects of scale-space. Whereas scale is treated as an essentially arbitrary constant in Part II, Part III emphasises 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.
Audience: This volume is addressed to researchers in the field of image analysis seeking mathematical foundation of algorithms.
Content:
Front Matter....Pages i-xx
Front Matter....Pages 1-1
Applications of Scale-Space Theory....Pages 3-19
Enhancement of Fingerprint Images using Shape-Adapted Scale-Space Operators....Pages 21-30
Optic Flow and Stereo....Pages 31-42
Front Matter....Pages 43-43
On the History of Gaussian Scale-Space Axiomatics....Pages 45-59
Scale-Space and Measurement Duality....Pages 61-74
On the Axiomatic Foundations of Linear Scale-Space....Pages 75-97
Scale-Space Generators and Functionals....Pages 99-114
Invariance Theory....Pages 115-128
Stochastic Analysis of Image Acquisition and Scale-Space Smoothing....Pages 129-136
Front Matter....Pages 137-137
Local Analysis of Image Scale Space....Pages 139-146
Local Morse Theory for Gaussian Blurred Functions....Pages 147-163
Critical Point Events in Affine Scale-Space....Pages 165-180
Topological Numbers and Singularities....Pages 181-189
Multi-Scale Watershed Segmentation....Pages 191-200
Front Matter....Pages 201-201
The Morphological Equivalent of Gaussian Scale-Space....Pages 203-220
Nonlinear Diffusion Scale-Spaces....Pages 221-234
Back Matter....Pages 235-265

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This book covers Gaussian scale-space theory from its applications to its mathematical foundation. The reader not so familiar with scale-space will find it instructive to first consider some potential applications described in Part I. The next two parts both address fundamental aspects of scale-space. Whereas scale is treated as an essentially arbitrary constant in Part II, Part III emphasises 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.
Audience: This volume is addressed to researchers in the field of image analysis seeking mathematical foundation of algorithms.
Content:
Front Matter....Pages i-xx
Front Matter....Pages 1-1
Applications of Scale-Space Theory....Pages 3-19
Enhancement of Fingerprint Images using Shape-Adapted Scale-Space Operators....Pages 21-30
Optic Flow and Stereo....Pages 31-42
Front Matter....Pages 43-43
On the History of Gaussian Scale-Space Axiomatics....Pages 45-59
Scale-Space and Measurement Duality....Pages 61-74
On the Axiomatic Foundations of Linear Scale-Space....Pages 75-97
Scale-Space Generators and Functionals....Pages 99-114
Invariance Theory....Pages 115-128
Stochastic Analysis of Image Acquisition and Scale-Space Smoothing....Pages 129-136
Front Matter....Pages 137-137
Local Analysis of Image Scale Space....Pages 139-146
Local Morse Theory for Gaussian Blurred Functions....Pages 147-163
Critical Point Events in Affine Scale-Space....Pages 165-180
Topological Numbers and Singularities....Pages 181-189
Multi-Scale Watershed Segmentation....Pages 191-200
Front Matter....Pages 201-201
The Morphological Equivalent of Gaussian Scale-Space....Pages 203-220
Nonlinear Diffusion Scale-Spaces....Pages 221-234
Back Matter....Pages 235-265
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