Diffusion-Driven Wavelet Design for Shape Analysis: 1st Edition (Hardback) book cover

Diffusion-Driven Wavelet Design for Shape Analysis

1st Edition

By Tingbo Hou, Hong Qin

A K Peters/CRC Press

208 pages | 70 B/W Illus.

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Hardback: 9781482220292
pub: 2014-10-22
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pub: 2014-10-22
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Description

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.

Table of Contents

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

Subject Categories

BISAC Subject Codes/Headings:
COM012000
COMPUTERS / Computer Graphics
TEC015000
TECHNOLOGY & ENGINEERING / Imaging Systems