Hou / Qin Diffusion-Driven Wavelet Design for Shape Analysis

1. Auflage 2014
ISBN: 978-1-4822-2030-8
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 232 Seiten

From Design Methods and Generation Schemes to State-of-the-Art Applications
Wavelets are powerful tools for functional analysis and geometry processing, enabling researchers to determine the structure of data and analyze 3D shapes. Suitable for researchers in computer graphics, computer vision, visualization, medical imaging, and geometric modeling as well as graduate and senior undergraduate students in computer science, Diffusion-Driven Wavelet Design for Shape Analysis presents recent research results in wavelet designs on 3D shapes and their applications in shape analysis. It explains how to apply the design methods to various types of 3D data, such as polygonal meshes, point clouds, manifolds, and volumetric images.

Extensions of Wavelet Generation on Volumetric and Manifold Data
The first part of the book introduces design methods of wavelets on manifold data, incorporating interdisciplinary knowledge from differential geometry, functional analysis, Fourier transform, spectral graph theory, and stochastic processes. The authors show how wavelets are purely determined by the shape geometry and how wavelet transforms are computed as inner products of wavelet kernels and input functions.

Wavelets for Solving Computer Graphics Problems
The second part presents applications in shape analysis/representation. The book looks at wavelets as spectral tools for geometry processing with filters in a joint space-frequency domain and examines wavelets as detail extractors for shape feature definition and detection. Going beyond these fundamental applications, the book also covers middle- and high-level applications, including shape matching, shape registration, and shape retrieval.

Easy-to-Understand Implementations and Algorithms
Unlike many other wavelet books, this one does not involve complicated mathematics. Instead, the book uses simplified formulations and illustrative examples to explain deep theories. Code and other materials are available on a supplementary website.

Zielgruppe

Researchers and professionals in computer graphics, visualization, and computer vision.

Autoren/Hrsg.

Hou, Tingbo

Qin, Hong

Fachgebiete

• Mathematik | Informatik EDV | Informatik Professionelle Anwendung

Inhaltsverzeichnis

Introduction
Wavelets on 3D Shapes
Book Contents

THEORIES
Wavelet Theory
Classical Wavelet
Subdivision Wavelet
Diffusion Wavelet
Spectral Graph Wavelet

Heat Diffusion Theory
Heat Equation
Heat Kernel
Applications in Shape Analysis

Admissible Diffusion Wavelets
Diffusion Operator
Wavelet Construction
Wavelet Transform
Relations
Space-Frequency Processing Framework

Mexican Hat Wavelet
Manifold Harmonics
Bivariate Kernels and Convolutions
Mexican Hat Wavelet
Properties
Wavelet Transform

Anisotropic Wavelet
Normal-Controlled Coordinates
Anisotropic Heat Kernel
Anisotropic Diffusion
Anisotropic Wavelet

Wavelet Generation
Volume Wavelets
Manifold Wavelet Generalization

APPLICATIONS
Implementation
Discrete Laplace-Beltrami Operator
Generalized Eigenvalue Problem
Matrix Power

Shape Representation
Related Work
Heat Kernel Signature
Wave Kernel Signature
Wavelet Signature

Geometry Processing
Fourier Transform
Admissible Diffusion Wavelets
Mexican Hat Wavelet

Feature Definition and Detection
Saliency Visualization
Feature Definition
Feature Detection

Shape Matching, Registration, and Retrieval
Shape Matching
Shape Registration
Shape Retrieval

Bibliography

Index