Ridges in Image and Data Analysis by D. EberlyRidges in Image and Data Analysis by D. Eberly

Ridges in Image and Data Analysis

byD. Eberly

Paperback | December 6, 2010

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The concept of ridges has appeared numerous times in the image processing liter­ ature. Sometimes the term is used in an intuitive sense. Other times a concrete definition is provided. In almost all cases the concept is used for very specific ap­ plications. When analyzing images or data sets, it is very natural for a scientist to measure critical behavior by considering maxima or minima of the data. These critical points are relatively easy to compute. Numerical packages always provide support for root finding or optimization, whether it be through bisection, Newton's method, conjugate gradient method, or other standard methods. It has not been natural for scientists to consider critical behavior in a higher-order sense. The con­ cept of ridge as a manifold of critical points is a natural extension of the concept of local maximum as an isolated critical point. However, almost no attention has been given to formalizing the concept. There is a need for a formal development. There is a need for understanding the computation issues that arise in the imple­ mentations. The purpose of this book is to address both needs by providing a formal mathematical foundation and a computational framework for ridges. The intended audience for this book includes anyone interested in exploring the use­ fulness of ridges in data analysis.
Title:Ridges in Image and Data AnalysisFormat:PaperbackDimensions:215 pages, 24.4 × 17 × 0.07 inPublished:December 6, 2010Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9048147611

ISBN - 13:9789048147618

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Table of Contents

Preface. 1. Introduction. 2. Mathematical Preliminaries. 3. Ridges in Euclidean Geometry. 4. Ridges in Riemannian Geometry. 5. Ridges of Functions Defined on Manifolds. 6. Applications to Image and Data Analysis. 7. Implementation Issues. Bibliography. Index.