Ridges in Image and Data Analysis

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...

Full description

Bibliographic Details
Main Author: Eberly, D.
Format: eBook
Language:English
Published: Dordrecht Springer Netherlands 1996, 1996
Edition:1st ed. 1996
Series:Computational Imaging and Vision
Subjects:
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
LEADER 03706nmm a2200373 u 4500
001 EB000720987
003 EBX01000000000000001350579
005 00000000000000.0
007 cr|||||||||||||||||||||
008 140122 ||| eng
020 |a 9789401587655 
100 1 |a Eberly, D. 
245 0 0 |a Ridges in Image and Data Analysis  |h Elektronische Ressource  |c by D. Eberly 
250 |a 1st ed. 1996 
260 |a Dordrecht  |b Springer Netherlands  |c 1996, 1996 
300 |a XI, 215 p  |b online resource 
505 0 |a 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 
653 |a Geometry, Differential 
653 |a Physical chemistry 
653 |a Image processing / Digital techniques 
653 |a Classical Mechanics 
653 |a Computer vision 
653 |a Radiology 
653 |a Computer Imaging, Vision, Pattern Recognition and Graphics 
653 |a Physical Chemistry 
653 |a Differential Geometry 
653 |a Mechanics 
041 0 7 |a eng  |2 ISO 639-2 
989 |b SBA  |a Springer Book Archives -2004 
490 0 |a Computational Imaging and Vision 
028 5 0 |a 10.1007/978-94-015-8765-5 
856 4 0 |u https://doi.org/10.1007/978-94-015-8765-5?nosfx=y  |x Verlag  |3 Volltext 
082 0 |a 006 
520 |a 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