Geometry-Driven Diffusion in Computer Vision: (1 Computational Imaging and Vision)

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. '

Table of Contents:
1 Linear Scale-Space I: Basic Theory.- 2 Linear Scale-Space II: Early Visual Operations.- 3 Anisotropic Diffusion.- 4 Vector-Valued Diffusion.- 5 Bayesian Rationale for the Variational Formulation.- 6 Variational Problems with a Free Discontinuity Set.- 7 Minimization of Energy Functional with Curve-Represented Edges.- 8 Approximation, Computation, and Distortion in the Variational Formulation.- 9 Coupled Geometry-Driven Diffusion Equations for Low-Level Vision.- 10 Morphological Approach to Multiscale Analysis: From Principles to Equations.- 11 Differential Invariant Signatures and Flows in Computer Vision: A Symmetry Group Approach.- 12 On Optimal Control Methods in Computer Vision and Image Processing.- 13 Nonlinear Scale-Space.- 14 A Differential Geometric Approach to Anisotropic Diffusion.- 15 Numerical Analysis of Geometry-Driven Diffusion Equations.