Diffusion-Driven Wavelet Design for Shape Analysis  book cover
1st Edition

Diffusion-Driven Wavelet Design for Shape Analysis

ISBN 9780367378240
Published October 23, 2019 by A K Peters/CRC Press
232 Pages

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Book 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 example

Table of Contents

Introduction. THEORIES: Wavelet Theory. Heat Diffusion Theory. Admissible Diffusion Wavelets. Mexican Hat Wavelet. Anisotropic Wavelet. Wavelet Generation. APPLICATIONS: Implementation. Shape Representation. Geometry Processing. Feature Definition and Detection. Shape Matching, Registration, and Retrieval. Bibliography. Index.

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Hou, Tingbo; Qin, Hong