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.

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Authors and Affiliations

SAS Institute, Inc., Cary, USA

David Eberly

Bibliographic Information

Book Title: Ridges in Image and Data Analysis
Authors: David Eberly
Series Title: Computational Imaging and Vision
DOI: https://doi.org/10.1007/978-94-015-8765-5
Publisher: Springer Dordrecht
eBook Packages: Springer Book Archive
Copyright Information: Springer Science+Business Media Dordrecht 1996
Hardcover ISBN: 978-0-7923-4268-7Published: 30 September 1996
Softcover ISBN: 978-90-481-4761-8Published: 06 December 2010
eBook ISBN: 978-94-015-8765-5Published: 06 December 2012
Series ISSN: 1381-6446
Edition Number: 1
Number of Pages: XI, 215
Topics: Computer Imaging, Vision, Pattern Recognition and Graphics, Differential Geometry, Imaging / Radiology, Physical Chemistry, Classical Mechanics

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Table of contents (7 chapters)

Front Matter

Introduction

Mathematical Preliminaries

Ridges in Euclidean Geometry

Ridges in Riemannian Geometry

Ridges of Functions Defined on Manifolds

Applications to Image and Data Analysis

Implementation Issues

Back Matter

About this book