SØG - mellem flere end 8 millioner bøger:
Viser: Functional and Shape Data Analysis
Functional and Shape Data Analysis Vital Source e-bog
Anuj Srivastava og Eric P. Klassen
(2016)
Functional and Shape Data Analysis Vital Source e-bog
Anuj Srivastava og Eric P. Klassen
(2016)
Functional and Shape Data Analysis Vital Source e-bog
Anuj Srivastava og Eric P. Klassen
(2016)
Functional and Shape Data Analysis
Anuj Srivastava og Eric P. Klassen
(2016)
Sprog: Engelsk
om ca. 10 hverdage
Detaljer om varen
- Vital Source searchable e-book (Reflowable pages)
- Udgiver: Springer Nature (Oktober 2016)
- Forfattere: Anuj Srivastava og Eric P. Klassen
- ISBN: 9781493940202
Bookshelf online: 5 år fra købsdato.
Bookshelf appen: ubegrænset dage fra købsdato.
Udgiveren oplyser at følgende begrænsninger er gældende for dette produkt:
Print: 2 sider kan printes ad gangen
Copy: højest 2 sider i alt kan kopieres (copy/paste)
Detaljer om varen
- Vital Source 90 day rentals (dynamic pages)
- Udgiver: Springer Nature (Oktober 2016)
- Forfattere: Anuj Srivastava og Eric P. Klassen
- ISBN: 9781493940202R90
Bookshelf online: 90 dage fra købsdato.
Bookshelf appen: 90 dage fra købsdato.
Udgiveren oplyser at følgende begrænsninger er gældende for dette produkt:
Print: 2 sider kan printes ad gangen
Copy: højest 2 sider i alt kan kopieres (copy/paste)
Detaljer om varen
- Vital Source 180 day rentals (dynamic pages)
- Udgiver: Springer Nature (Oktober 2016)
- Forfattere: Anuj Srivastava og Eric P. Klassen
- ISBN: 9781493940202R180
Bookshelf online: 180 dage fra købsdato.
Bookshelf appen: 180 dage fra købsdato.
Udgiveren oplyser at følgende begrænsninger er gældende for dette produkt:
Print: 2 sider kan printes ad gangen
Copy: højest 2 sider i alt kan kopieres (copy/paste)
Detaljer om varen
- 1. Udgave
- Hardback: 486 sider
- Udgiver: Springer New York (Oktober 2016)
- Forfattere: Anuj Srivastava og Eric P. Klassen
- ISBN: 9781493940189
Recently, a data-driven and application-oriented focus on shape analysis has been trending. This text offers a self-contained treatment of this new generation of methods in shape analysis of curves. Its main focus is shape analysis of functions and curves--in one, two, and higher dimensions--both closed and open. It develops elegant Riemannian frameworks that provide both quantification of shape differences and registration of curves at the same time. Additionally, these methods are used for statistically summarizing given curve data, performing dimension reduction, and modeling observed variability. It is recommended that the reader have a background in calculus, linear algebra, numerical analysis, and computation.
1.1 Motivation
1.1.1 Need for Function and Shape Data Analysis Tools
1.1.2 Why Continuous Shapes?
1.2 Important Application Areas
1.3 Specific Technical Goals
1.4 Issues & Challenges
1.5 Organization of This Textbook 2 Previous Techniques in Shape Analysis
2.1 Principal Component Analysis (PCA)
2.2 Point-Based Methods
2.2.1 ICP: Point Cloud Analysis
2.2.2 Active Shape Models
2.2.3 Kendall''s Landmark-Based Shape Analysis
2.2.4 Issue of Landmark Selection
2.3 Domain-Based Shape Representations
2.3.1 Level-Set Methods
2.3.2 Deformation-Based Shape Analysis
2.4 Exercises
2.5 Bibliographic Notes 3 Background: Relevant Tools from Geometry
3.1 Equivalence Relations
3.2 Riemannian Structure and Geodesics
3.3 Geodesics in Spaces of Curves on Manifolds
3.4 Parallel Transport of Vectors
3.5 Lie Group Actions on Manifolds
3.5.1 Actions of Single Groups
3.5.2 Actions of Product Groups
3.6 Quotient Spaces of Riemannian Manifolds
3.7 Quotient Spaces as Orthogonal Sections
3.8 General Quotient Spaces
3.9 Distances in Quotient Spaces: A Summary
3.10 Center of An Orbit
3.11 Exercises
3.11.1 Theoretical Exercises
3.11.2 Computational Exercises
3.12 Bibliographic Notes 4 Functional Data and Elastic Registration
4.1 Goals and Challenges
4.2 Estimating Function Variables from Discrete Data
4.3 Geometries of Some Function Spaces
4.3.1 Geometry of Hilbert Spaces
4.3.2 Unit Hilbert Sphere
4.3.3 Group of Warping Functions
4.4 Function Registration Problem
4.5 Use of L2-Norm And Its Limitations
4.6 Square-Root Slope Function (SRSF) Representation
4.7 Definition of Phase & Amplitude Components
4.7.1 Amplitude of a Function
4.7.2 Relative Phase Between Functions
4.7.3 A Convenient Approximation
4.8 SRSF-Based Registration
4.8.1 Registration Problem
4.8.2 SRSF Alignment Using Dynamic Programming
4.8.3 Examples of Functional Alignments
4.9 Connection to the Fisher-Rao Metric
4.10 Phase and Amplitude Distances
4.10.1 Amplitude Space and A Metric Structure
4.10.2 Phase Space and A Metric Structure
4.11 Different Warping Actions and PDFs
4.11.1 Listing of Different Actions
4.11.2 Probability Density Functions
4.12 Exercises
4.12.1 Theoretical Exercises
4.12.2 Computational Exercises
4.13 Bibliographic Notes 5 Shapes of Planar Curves
5.1 Goals & Challenges
5.2 Parametric Representations of Curves
5.3 General Framework
5.3.1 Mathematical Representations of Curves
5.3.2 Shape-Preserving Transformations
5.4 Pre-Shape Spaces
5.4.1 Riemannian Structure
5.4.2 Geodesics in Pre-Shape Spaces
5.5 Shape Spaces
5.5.1 Removing Parameterization
5.6 Motivation for SRVF Representation
5.6.1 What is an Elastic Metric?
5.6.2 Significance of the Square-Root Representation
5.7 Geodesic Paths in Shape Spaces
5.7.1 Optimal Re-Parameterization for Curve Matching
5.7.2 Geodesic Illustrations
5.8 Gradient-Based Optimization Over Re-Parameterization Group
5.9 Summary
5.10 Exercises
5.10.1 Theoretical Exercises
5.10.2 Computational Exercises
5.11 Bibliographic Notes 6 Shapes of Planar Closed Curves
6.1 Goals and Challenges
6.2 Representations of Closed Curves
6.2.1 Pre-Shape Spaces
6.2.2 Riemannian Structures
6.2.3 Removing Parameterization
6.3 Projection on a Manifold
6.4 Geodesic Computation
6.5 Geodesic Computation: Shooting Method
6.5.1 Example
1: Geodesics on S2
6.5.2 Example
2: Geodesics in Non-Elastic Pre-Shape Space
6.6 Geodesic Computation: Path Straightening Method
6.6.1 Theoretical Background
6.6.2 Numerical Implementation
6.6.3 Example
1: Geodesics on S2
6.6.4 Example
2: Geodesics in Elastic Pre-Shape Space
6.7 Geodesics in Shape Spaces
6.7.1 Geodesics in Non-Elastic Shape Space
6.7.2 Geodesics in Elastic Shape Space
6.8 Examples of Elastic Geodesics
6.8.1 Elastic Matching: Gradient Versus Dynamic Programming Algorithm
6.8.2 Fast Approximate Elastic Matching of Closed Curves
6.9 Elastic versus Non-Elastic Deformations
6.10 Parallel Transport of Shape Deformations
6.10.1 Prediction of Silhouettes from Novel Views
6.10.2 Classification of 3D Objects Using Predicted Silhouettes
6.11 Symmetry Analysis of Planar Shapes
6.12 Exercises
6.12.1 Theoretical Exercises
6.12.2 Computational Exercises
6.13 Bibliographic Notes 7 Statistical Modeling on Nonlinear Manifolds
7.1 Goals & Challenges
7.2 Basic Setup
7.3 Probability Densities on Manifolds
7.4 Summary Statistics on Manifolds
7.4.1 Intrinsic Statistics
7.4.2 Extrinsic Statistics
7.5 Examples on Some Useful Manifolds
7.5.1 Statistical Analysis on S1
7.5.2 Statistical Analysis on S2
7.5.3 Space of Probability Density Functions
7.5.4 Space of Warping Functions
7.6 Statistical Analysis on a Quotient Space M=G
7.6.1 Quotient Space as Orthogonal Section
7.6.2 General Case: Without Using Sections
7.7 Exercises
7.7.1 Theoretical Exercises
7.7.2 Computational Exercises
7.8 Bibliographic Notes 8 Statistical Modeling of Functional Data
8.1 Goals and Challenges
8.2 Template-Based Alignment & L2 Metric
8.3 Elastic Phase-Amplitude Separation
8.3.1 Karcher Mean of Amplitudes
8.3.2 Template: Center of the Mean Orbit
8.3.3 Phase-Amplitude Separation Algorithm
8.4 Alternate Interpretation as Estimation of Model Parameters
8.5 Phase-Amplitude Separation After Transformation
8.6 Penalized Function Alignment
8.7 Function Components, Alignment and Modeling
8.8 Sequential Approach 8.8.1 FPCA of Amplitude Functions: A-FPCA
8.8.2 FPCA of Phase Functions: P-FPCA
8.8.3 Joint Modeling of Principle Coefficients
8.9 Joint Approach: Elastic FPCA
8.9.1 Model-Based Elastic FPCA in Function Space F
8.9.2 Elastic FPCA Using SRSF Representation
8.10 Exercises
8.10.1 Theoretical Exercises
8.10.2 &n