Ebook: Geometry-Driven Diffusion in Computer Vision

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.

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This seminal book is a primer on geometry-driven, nonlinear diffusion as a promising new paradigm for vision, with an emphasis on the tutorial. It gives a thorough overview of current linear and nonlinear scale-space theory, presenting many viewpoints such as the variational approach, curve evolution and nonlinear diffusion equations.
The book is meant for computer vision scientists and students, with a computer science, mathematics or physics background. Appendices explain the terminology. Many illustrated applications are given, e.g. in medical imaging, vector valued (or coupled) diffusion, general image enhancement (e.g. edge preserving noise suppression) and modeling of the human front-end visual system. Some examples are given to implement the methods in modern computer-algebra systems.

From the Preface by Jan J. Koenderink:
` I have read through the manuscript of this book in fascination. Most of the approaches that have been explored to tweak scale-space into practical tools are represented here. It is easy to appreciate how both the purist and the engineer find problems of great interest in this area. The book is certainly unique in its scope and has appeared at a time where this field is booming and newcomers can still potentially leave their imprint on the core corpus of scale related methods that still slowly emerge. As such the book is a very timely one. It is quite evident that it would be out of the question to compile anything like a textbook at this stage: this book is a snapshot of the field that manages to capture its current state very well and in a most lively fashion. I can heartily recommend its reading to anyone interested in the issues of image structure, scale and resolution. '

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This seminal book is a primer on geometry-driven, nonlinear diffusion as a promising new paradigm for vision, with an emphasis on the tutorial. It gives a thorough overview of current linear and nonlinear scale-space theory, presenting many viewpoints such as the variational approach, curve evolution and nonlinear diffusion equations.
The book is meant for computer vision scientists and students, with a computer science, mathematics or physics background. Appendices explain the terminology. Many illustrated applications are given, e.g. in medical imaging, vector valued (or coupled) diffusion, general image enhancement (e.g. edge preserving noise suppression) and modeling of the human front-end visual system. Some examples are given to implement the methods in modern computer-algebra systems.

From the Preface by Jan J. Koenderink:
` I have read through the manuscript of this book in fascination. Most of the approaches that have been explored to tweak scale-space into practical tools are represented here. It is easy to appreciate how both the purist and the engineer find problems of great interest in this area. The book is certainly unique in its scope and has appeared at a time where this field is booming and newcomers can still potentially leave their imprint on the core corpus of scale related methods that still slowly emerge. As such the book is a very timely one. It is quite evident that it would be out of the question to compile anything like a textbook at this stage: this book is a snapshot of the field that manages to capture its current state very well and in a most lively fashion. I can heartily recommend its reading to anyone interested in the issues of image structure, scale and resolution. '
Content:
Front Matter....Pages i-xxii
Linear Scale-Space I: Basic Theory....Pages 1-38
Linear Scale-Space II: Early Visual Operations....Pages 39-72
Anisotropic Diffusion....Pages 73-92
Vector-Valued Diffusion....Pages 93-134
Bayesian Rationale for the Variational Formulation....Pages 135-146
Variational Problems with a Free Discontinuity Set....Pages 147-154
Minimization of Energy Functional with Curve-Represented Edges....Pages 155-168
Approximation, Computation, and Distortion in the Variational Formulation....Pages 169-190
Coupled Geometry-Driven Diffusion Equations for Low-Level Vision....Pages 191-228
Morphological Approach to Multiscale Analysis: From Principles to Equations....Pages 229-254
Differential Invariant Signatures and Flows in Computer Vision: A Symmetry Group Approach....Pages 255-306
On Optimal Control Methods in Computer Vision and Image Processing....Pages 307-338
Nonlinear Scale-Space....Pages 339-370
A Differential Geometric Approach to Anisotropic Diffusion....Pages 371-392
Numerical Analysis of Geometry-Driven Diffusion Equations....Pages 393-410
Back Matter....Pages 411-441

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This seminal book is a primer on geometry-driven, nonlinear diffusion as a promising new paradigm for vision, with an emphasis on the tutorial. It gives a thorough overview of current linear and nonlinear scale-space theory, presenting many viewpoints such as the variational approach, curve evolution and nonlinear diffusion equations.
The book is meant for computer vision scientists and students, with a computer science, mathematics or physics background. Appendices explain the terminology. Many illustrated applications are given, e.g. in medical imaging, vector valued (or coupled) diffusion, general image enhancement (e.g. edge preserving noise suppression) and modeling of the human front-end visual system. Some examples are given to implement the methods in modern computer-algebra systems.

From the Preface by Jan J. Koenderink:
` I have read through the manuscript of this book in fascination. Most of the approaches that have been explored to tweak scale-space into practical tools are represented here. It is easy to appreciate how both the purist and the engineer find problems of great interest in this area. The book is certainly unique in its scope and has appeared at a time where this field is booming and newcomers can still potentially leave their imprint on the core corpus of scale related methods that still slowly emerge. As such the book is a very timely one. It is quite evident that it would be out of the question to compile anything like a textbook at this stage: this book is a snapshot of the field that manages to capture its current state very well and in a most lively fashion. I can heartily recommend its reading to anyone interested in the issues of image structure, scale and resolution. '
Content:
Front Matter....Pages i-xxii
Linear Scale-Space I: Basic Theory....Pages 1-38
Linear Scale-Space II: Early Visual Operations....Pages 39-72
Anisotropic Diffusion....Pages 73-92
Vector-Valued Diffusion....Pages 93-134
Bayesian Rationale for the Variational Formulation....Pages 135-146
Variational Problems with a Free Discontinuity Set....Pages 147-154
Minimization of Energy Functional with Curve-Represented Edges....Pages 155-168
Approximation, Computation, and Distortion in the Variational Formulation....Pages 169-190
Coupled Geometry-Driven Diffusion Equations for Low-Level Vision....Pages 191-228
Morphological Approach to Multiscale Analysis: From Principles to Equations....Pages 229-254
Differential Invariant Signatures and Flows in Computer Vision: A Symmetry Group Approach....Pages 255-306
On Optimal Control Methods in Computer Vision and Image Processing....Pages 307-338
Nonlinear Scale-Space....Pages 339-370
A Differential Geometric Approach to Anisotropic Diffusion....Pages 371-392
Numerical Analysis of Geometry-Driven Diffusion Equations....Pages 393-410
Back Matter....Pages 411-441
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