This distinctly accessible introduction to wavelets provides computer graphics professionals and researchers with the mathematical
foundations for understanding and applying this powerful tool.
Wavelets are rapidly becoming a core technique in computer graphics,
with applications for
* Image editing and compression
* Automatic level-of-detail control for editing and rendering curves and surfaces
* Surface reconstruction from contours
* Physical simulation for global illumination and animation
Stressing intuition and clarity,
this book offers a solid understanding of the theory of wavelets and their proven applications in computer graphics.
Although
previous introductions to wavelets have presented an elegant mathematical framework, that framework is too restrictive to apply to many
problems in graphics. In contrast, this book focuses on a generalized theory that naturally accommodates the kinds of objects that commonly
arise in computer graphics, including images, open curves, and surfaces of arbitrary topology.
This book also contains a foreword
by Ingrid Daubechies and an appendix covering the necessary background material in linear algebra.
Contents
Wavelets for Computer Graphics: Theory and Applications by Eric J. Stollnitz, Tony D. DeRose, David H. Salesin
1
Introduction
1.1 Multiresolution methods
1.2 Historical perspective
1.3 Overview of the book
I
Images
2 HAAR: The Simplest Wavelet Basis
2.1 The one-dimensional Haar wavelet transform
2.2 One-dimensional Haar basis functions
2.3 Orthogonality and normalization
2.4 Wavelet compression
3 Image Compression
3.1 Two-dimensional Haar wavelet transforms
3.2 Two-dimensional Haar basis
functions
3.3 Wavelet image compression
3.4 Color images
3.5 Summary
4 Image Editing
4.1 Multiresolution image data structures
4.2 Image diting algorithm
4.3 Boundary conditions
4.4 Display
and editing at fractional resolutions
4.5 Image editing examples
5 Image Querying
5.1
Image querying by content
5.2 Developing a metric for image querying
5.3 Image querying algorithm
5.4 Image
querying examples
5.5 Extensions
II Curves
6 Subdivision Curves
6.1 Uniform subdivision
6.2 Nonuniform subdivision
6.3 Evaluation masks
6.4 Nested spaces and refinable
scaling functions
7 The Theory of Multiresolution Analysis
7.1 Multiresolution analysis
7.2 Orthogonal wavelets
7.3 Semiorthogonal wavelets
7.4 Biorthogonal wavelets
7.5 Summary
8 Multiresolution Curves
8.1 Related curve representation
8.2 Smoothing a curve
8.3 Editing
a curve
8.4 Scan conversion and curve compression
9 Multiresolution Tiling
9.1 Previous
solutions to the tiling problem
9.2 The multiresolution tiling algorithm
9.3 Time complexity
9.4 Tiling examples
III
Surfaces
10 Surface Wavelets
10.1 Overview of multiresolution analysis for surfaces
10.2
Subdivision surfaces
10.3 Selecting an inner product
10.4 A biorthogonal surface wavelet construction
10.5
Multiresolution representations of surfaces
11 Surface Applications
11.1 Conversion to multiresolution
form
11.2 Surface compression
11.3 Continuous level-of-detail control
11.4 Progressive transmission
11.5
Multiresolution editing
11.6 Future directions for surface wavelets
IV Physical Simulation
12 Variational Modeling
12.1 Setting up the objective function
12.2 The finite-element method
12.3 Using finite elements in variational modeling
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