Ridges in Image and Data Analysis

  • David Eberly

Part of the Computational Imaging and Vision book series (CIVI, volume 7)

Table of contents

  1. Front Matter
    Pages i-xi
  2. David Eberly
    Pages 1-7
  3. David Eberly
    Pages 9-38
  4. David Eberly
    Pages 39-63
  5. David Eberly
    Pages 65-73
  6. David Eberly
    Pages 75-95
  7. David Eberly
    Pages 97-154
  8. David Eberly
    Pages 155-201
  9. Back Matter
    Pages 203-215

About this book

Introduction

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.

Keywords

Riemannian geometry computer vision data analysis image analysis image processing manifold modeling

Authors and affiliations

  • David Eberly
    • 1
  1. 1.SAS Institute, Inc.CaryUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-015-8765-5
  • Copyright Information Springer Science+Business Media B.V. 1996
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-4761-8
  • Online ISBN 978-94-015-8765-5
  • Series Print ISSN 1381-6446
  • About this book