Numerical geometry of non rigid shapes 1st Edition by Alexander Bronstein, Michael Bronstein, Ron Kimmel ISBN 9780387733012 0387733019

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Product details:
ISBN 10: 0387733019
ISBN 13: 9780387733012
Author: Alexander Bronstein, Michael Bronstein, Ron Kimmel

Numerical geometry of non rigid shapes 1st Edition Table of contents:

Part I: Mathematical Foundations of Shape Representation

2. Geometric Shape Representations

   • Parametric and Implicit Representations of Shapes
   • Surface and Volume Representations
   • Discrete and Continuous Representations
   • Representing Shape with Points, Curves, and Surfaces

3. Differential Geometry for Shape Analysis

   • Curvature and Geodesics on Surfaces
   • The Role of Differential Geometry in Shape Processing
   • Computing Curvature and Normal Vectors
   • The Gauss-Bonnet Theorem and Its Applications

4. Riemannian Geometry of Shapes

   • Introduction to Riemannian Manifolds
   • Geodesic Distances and Metrics
   • Mapping Non-Rigid Shapes onto Riemannian Spaces
   • Shape Comparison Using Geodesic Distances

Part II: Numerical Techniques for Shape Analysis

5. Shape Matching and Alignment

   • The Problem of Shape Matching in Non-Rigid Settings
   • Global vs. Local Matching Techniques
   • Registration Algorithms for Non-Rigid Shapes
   • Computational Techniques for Shape Alignment

6. Spectral Methods for Shape Analysis

   • Spectral Decomposition and Eigenfunctions
   • Shape Eigenfunctions and Their Role in Shape Analysis
   • Spectral Geodesics and their Applications
   • Laplace-Beltrami Operators for Non-Rigid Shapes

7. Shape Correspondence and Shape Registration

   • Defining Correspondence between Non-Rigid Shapes
   • Methods for Computing Shape Correspondences
   • Techniques for Registering Shapes under Non-Rigid Deformations
   • Applications of Shape Correspondence in Medical Imaging

Part III: Non-Rigid Shape Deformation and Modeling

8. Shape Deformation Models

   • Parametric and Non-Parametric Deformation Models
   • Thin-Plate Spline Models and Their Applications
   • The Role of Non-Rigid Registration in Shape Modeling
   • Computing Deformation Fields and Optimal Alignments

9. Statistical Models of Shape Variation

   • Statistical Shape Analysis and Variability
   • Principal Component Analysis (PCA) in Shape Analysis
   • Active Shape Models (ASM) and Active Appearance Models (AAM)
   • Shape Priors and Deformation Models

10. Energy-Based Models for Shape Matching

    • Energy Functions in Shape Registration
    • Regularization Techniques in Non-Rigid Shape Matching
    • Optimization Methods for Energy Minimization
    • Energy Models for Shape Morphing and Interpolation

Part IV: Applications of Non-Rigid Shape Analysis

11. Shape Analysis in Computer Vision

    • Detecting and Analyzing Non-Rigid Objects in Images
    • Object Tracking and Motion Analysis
    • Shape-Based Object Recognition Techniques
    • Deformation Modeling in Video Sequences

12. Shape Analysis in Medical Imaging

    • Applications in Organ and Tissue Modeling
    • Non-Rigid Registration of Medical Scans
    • Shape Analysis for Surgical Planning and Simulation
    • Morphometric Analysis in Neuroscience and Anatomy

13. Non-Rigid Shape Modeling in Computer Graphics

    • Deformation and Animation of Non-Rigid Objects
    • Shape Registration for Animation and Simulation
    • Real-Time Deformation Models in Virtual Environments
    • Shape-Based Rendering Techniques for Non-Rigid Objects

Conclusion
14. Future Directions in Non-Rigid Shape Analysis
– Advances in Computational Techniques for Shape Matching
– The Role of Machine Learning in Shape Processing
– Future Challenges in Non-Rigid Shape Deformation
– Emerging Applications and Interdisciplinary Research Areas

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