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Ridges in Image and Data Analysis 1996 ed. [Kõva köide]

  • Formaat: Hardback, 215 pages, kõrgus x laius: 297x210 mm, kaal: 1110 g, XI, 215 p., 1 Hardback
  • Sari: Computational Imaging and Vision 7
  • Ilmumisaeg: 30-Sep-1996
  • Kirjastus: Springer
  • ISBN-10: 0792342682
  • ISBN-13: 9780792342687
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Ridges in Image and Data Analysis 1996 ed.Suurem pilt
  • Formaat: Hardback, 215 pages, kõrgus x laius: 297x210 mm, kaal: 1110 g, XI, 215 p., 1 Hardback
  • Sari: Computational Imaging and Vision 7
  • Ilmumisaeg: 30-Sep-1996
  • Kirjastus: Springer
  • ISBN-10: 0792342682
  • ISBN-13: 9780792342687
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780792342687.html
Märksõnad:
Primarily addressed to scientists in computer vision and imaging processing who have a solid background in mathematics and scientific computation, but also of possible interest to practitioners in any field that requires analyzing data, such as statistics, the physical sciences, or engineering. Develops the concept of ridges and their applications to image and data analysis. Includes a chapter on the formal ridge definitions in any geometric setting, and another on the numerical implementation. Describes applications in medical image analysis, molecular modeling, and the analysis of fluid flow. Annotation c. by Book News, Inc., Portland, Or.

This book provides a thorough development of ridges and their application to image and data analysis. The text 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. Audience: The book is intended primarily for computer vision and image processing scientists with a background in mathematics and scientific computation. However, ridges provide a general purpose tool for multidimensional data analysis, so the book will be of interest to practitioners in any field which requires the analyzing of data, such as statistics, the physical sciences, or engineering.
Preface ix
1 Introduction
1(8)
1.1 A History of Ridges
1(5)
1.2 Reading Strategies
6(3)
2 Mathematical Preliminaries
9(30)
2.1 Linear Algebra
9(8)
2.1.1 Eigenvalues and Eigenvectors
10(3)
2.1.2 Gram-Schmidt Orthonormalization
13(1)
2.1.3 Symmetric, Unitary, and Definite Matrices
14(2)
2.1.4 Maxima of Quadratic Forms
16(1)
2.2 Differential Calculus
17(5)
2.2.1 Derivative and Index Notation
17(1)
2.2.2 Summation Convention
18(1)
2.2.3 Directional Derivatives
19(1)
2.2.4 Local Extrema of Functions
20(2)
2.3 Tensors
22(17)
2.3.1 Cartesian Coordinates
22(1)
2.3.2 General Coordinates
23(2)
2.3.3 Tensor Calculus
25(4)
2.3.4 Curves
29(1)
2.3.5 Surfaces
30(5)
2.3.6 Manifolds
35(4)
3 Ridges in Euclidean Geometry
39(26)
3.1 Generalized Local Extrema
39(3)
3.2 Height Ridge Definition
42(3)
3.3 1-Dimensional Ridges in IR2
45(3)
3.3.1 Continuous Formulations
45(1)
3.3.2 Differential Geometric Relationships
46(1)
3.3.3 Ridge Tangents
47(1)
3.4 1-Dimensional Ridges in IR3
48(4)
3.4.1 Continuous Formulations
48(1)
3.4.2 Differential Geometric Relationships
49(1)
3.4.3 Ridge Tangents
49(3)
3.5 1-Dimensional Ridges in IRn
52(4)
3.5.1 Continuous Formulations
52(1)
3.5.2 Differential Geometric Relationships
52(1)
3.5.3 Ridge Tangents
53(3)
3.6 2-Dimensional Ridges in IR3
56(1)
3.6.1 Continuous Formulations
56(1)
3.6.2 Ridge Tangents
57(1)
3.7 2-Dimensional Ridges in IR4
57(3)
3.7.1 Continuous Formulations
57(1)
3.7.2 Ridge Tangents
58(2)
3.8 d-Dimensional Ridges in IRn
60(5)
3.8.1 Continuous Formulations
60(1)
3.8.2 Ridge Tangents
61(4)
4 Ridges in Riemannian Geometry
65(10)
4.1 Generalized Local Extrema
65(1)
4.2 Height Ridge Definition
66(1)
4.3 1-Dimensional Ridges in IR2
66(2)
4.4 1-Dimensional Ridges in IR3
68(1)
4.5 1-Dimensional Ridges in IRn
69(1)
4.6 2-Dimensional Ridges in IR3
70(1)
4.7 2-Dimensional Ridges in IR4
71(1)
4.8 d-Dimensional Ridges in IRn
72(3)
5 Ridges of Functions Defined on Manifolds
75(22)
5.1 Height Ridge Definition
75(11)
5.1.1 1-Dimensional Ridges in M2 C IR3
75(7)
5.1.2 d-Dimensional Ridges in Mn C IRp
82(4)
5.2 Maximal Curvature Ridge Definitions
86(11)
5.2.1 Curvature Extrema of Planar Curves
86(5)
5.2.2 Curvature Extrema of Surfaces
91(3)
5.2.3 Extensions and Generalizations
94(3)
6 Applications to Image and Data Analysis
97(58)
6.1 Medical Image Analysis
97(34)
6.1.1 Linear Scale Space
97(2)
6.1.2 Boundary Measurements
99(3)
6.1.3 Medial Measurements
102(9)
6.1.4 Cores
111(17)
6.1.5 Nonlinear Scale Space
128(3)
6.2 Molecular Modeling
131(13)
6.2.1 DNA Structure
131(2)
6.2.2 Protein Structure
133(3)
6.2.3 X-Ray Crystallography
136(2)
6.2.4 Electron Density Maps
138(3)
6.2.5 Ridges of Electron Density
141(3)
6.3 Fluid Flow
144(11)
6.3.1 Vector Field Analysis
144(4)
6.3.2 Newtonian Viscous Fluids
148(2)
6.3.3 Pressure Ridges
150(5)
7 Implementation Issues
155(48)
7.1 Bridging the Gap Between Theory and Practice
155(1)
7.2 B-spline Interpolation
156(26)
7.2.1 Definitions
156(2)
7.2.2 Basis Matrices
158(1)
7.2.3 Direct Implementation
159(3)
7.2.4 Generalized and Optimized Spline Calculation
162(14)
7.2.5 Polynomial Construction
176(1)
7.2.6 Avoiding Intermediate Calculations
177(1)
7.2.7 Computing Data On-Demand
178(3)
7.2.8 Putting It All Together
181(1)
7.3 Eigensystem Solvers
182(4)
7.3.1 Symbolic Tridiagonalization
183(2)
7.3.2 QR Iteration with Explicit Shifting
185(1)
7.3.3 Generalized Eigensystems
185(1)
7.4 Ridge Construction
186(17)
7.4.1 Multidimensional Bisection
187(3)
7.4.2 Minimization without Derivatives
190(4)
7.4.3 Manifold Extraction
194(6)
7.4.4 Arbitrarily Spaced Data
200(3)
Bibliography 203(8)
Index 211