Overview

This text provides a thorough development of ridges and their application to image and data analysis. It is self-contained by including a chapter on the necessary mathematical background, chapters on the formal ridge definitions in any geometric setting, and a chapter on the numerical implementation. An applications chapter covers three separate topics: medical image analysis, molecular modeling, and analysis of fluid flow.

Full Product Details

Author:   D. Eberly
Publisher:   Springer
Imprint:   Springer
Edition:   1996 ed.
Volume:   7
Dimensions:   Width: 21.00cm , Height: 1.40cm , Length: 29.70cm
Weight:   1.110kg
ISBN:  

9780792342687

ISBN 10:   0792342682
Pages:   215
Publication Date:   30 September 1996
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

1 Introduction.- 1.1 A History of Ridges.- 1.2 Reading Strategies.- 2 Mathematical Preliminaries.- 2.1 Linear Algebra.- 2.2 Differential Calculus.- 2.3 Tensors.- 3 Ridges in Euclidean Geometry.- 3.1 Generalized Local Extrema.- 3.2 Height Ridge Definition.- 3.3 1-Dimensional Ridges in ?2.- 3.4 1-Dimensional Ridges in ?3.- 3.5 1-Dimensional Ridges in ?n.- 3.6 2-Dimensional Ridges in ?3.- 3.7 2-Dimensional Ridges in ?4.- 3.8 d-Dimensional Ridges in ?n.- 4 Ridges in Riemannian Geometry.- 4.1 Generalized Local Extrema.- 4.2 Height Ridge Definition.- 4.3 1-Dimensional Ridges in ?2.- 4.4 1-Dimensional Ridges in ?3.- 4.5 1-Dimensional Ridges in ?n.- 4.6 2-Dimensional Ridges in ?3.- 4.7 2-Dimensional Ridges in ?4.- 4.8 d-Dimensional Ridges in ?n.- 5 Ridges of Functions Defined on Manifolds.- 5.1 Height Ridge Definition.- 5.2 Maximal Curvature Ridge Definitions.- 6 Applications to Image and Data Analysis.- 6.1 Medical Image Analysis.- 6.2 Molecular Modeling.- 6.3 Fluid Flow.- 7 Implementation Issues.- 7.1 Bridging the Gap Between Theory and Practice.- 7.2 B-spline Interpolation.- 7.3 Eigensystem Solvers.- 7.4 Ridge Construction.

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