简介
Summary:
Publisher Summary 1
This introduction provides computer graphics professionals and researchers with the mathematical foundations for understanding and applying wavelets. Some applications include: image editing and compression, automatic level-of-detail control of curves and surfaces, surface reconstruction form contours, and physical simulation for global illumination and animation. The generalized theory in this text stresses intuition over rigor, and accommodates the kinds of objects that commonly arise in computer graphics, including images, open curves, and surfaces of arbitrary topology. Readers must have at least a vague sense of linear algebra; most of the necessary background algebra information is in the appendix. Annotation c. by Book News, Inc., Portland, Or.
Publisher Summary 2
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.
目录
Table Of Contents:
Foreword vii
Ingrid Daubechies
List of Figures xv
Preface xxi
Notation xxv
Introduction 1(8)
Multiresolution methods 2(1)
Historical perspective 3(2)
Overview of the book 5(4)
I IMAGES
Haar: The Simplest Wavelet Basis 9(12)
The one-dimensional Haar Wavelet transform 9(2)
One-dimensional Haar basis functions 11(5)
Orthogonality and normalization 16(2)
Wavelet compression 18(3)
Image Compression 21(12)
Two-dimensional Haar wavelet transforms 21(4)
Two-dimensional Haar basis functions 25(3)
Wavelet image compression 28(2)
Color images 30(1)
Summary 31(2)
Image Editing 33(10)
Multiresolution image data structures 34(2)
Image editing algorithm 36(3)
Boundary conditions 39(1)
Display and editing at fractional resolutions 40(1)
Image editing examples 41(2)
Image Querying 43(18)
Image querying by content 45(1)
Developing a metric for image querying 46(4)
Image querying algorithm 50(3)
Image querying examples 53(2)
Extensions 55(6)
II CURVES
Subdivision curves 61(18)
Uniform subdivision 62(4)
Nonuniform subdivision 66(2)
Evaluation masks 68(4)
Nested spaces and refinable scaling functions 72(7)
The Theory of Multiresolution Analysis 79(30)
Multiresolution analysis 80(5)
Orthogonal wavelets 85(4)
Semiorthogonal wavelets 89(8)
Biorthogonal wavelets 97(10)
Summary 107(2)
Multiresolution Curves 109(16)
Related curve representations 110(1)
Smoothing a curve 111(1)
Editing a curve 112(8)
Scan conversion and curve compression 120(5)
Multiresolution Tiling 125(16)
Previous solutions to the tiling problem 126(3)
The multiresolution tiling algorithm 129(6)
Time complexity 135(1)
Tiling examples 136(5)
III SURFACES
Surface Wavelets 141(20)
Overview of multiresolution analysis for surfaces 142(1)
Subdivision surfaces 143(8)
Selecting an inner product 151(1)
A biorthogonal surface wavelet construction 152(6)
Multiresolution representations of surfaces 158(3)
Surface Applications 161(10)
Conversion to multiresolution form 161(2)
Surface compression 163(1)
Continuous level-of-detail control 164(1)
Progressive transmission 165(1)
Multiresolution editing 165(1)
Future directions for surface wavelets 166(5)
IV PHYSICAL SIMULATION
Variational Modeling 171(10)
Setting up the objective function 172(1)
The finite-element method 173(1)
Using finite elements in variational modeling 173(4)
Variational modeling using wavelets 177(2)
Adaptive variational modeling 179(2)
Global Illumination 181(14)
Radiosity 181(2)
Finite elements and radiosity 183(3)
Wavelet radiosity 186(6)
Enhancements to wavelet radiosity 192(3)
Further Reading 195(28)
Theory of multiresolution analysis 195(2)
Image applications 197(1)
Curve and surface applications 198(1)
Physical simulation 199(4)
V APPENDICES
A Linear Algebra Review 203(6)
A.1 Vector spaces 203(1)
A.2 Bases and dimension 204(1)
A.3 Inner products and orthogonality 205(1)
A.4 Norms and normalization 206(1)
A.5 Eigenvectors and eigenvalues 207(2)
B B-Spline Wavelet Matrices 209(8)
B.1 Haar wavelets 210(1)
B.2 Endpoint-interpolating linear B-spline wavelets 211(1)
B.3 Endpoint-interpolating quadratic B-spline wavelets 212(2)
B.4 Endpoint-interpolating cubic B-spline wavelets 214(3)
C Matlab Code For B-Spline Wavelets 217(6)
Bibliography 223(12)
Index 235
Foreword vii
Ingrid Daubechies
List of Figures xv
Preface xxi
Notation xxv
Introduction 1(8)
Multiresolution methods 2(1)
Historical perspective 3(2)
Overview of the book 5(4)
I IMAGES
Haar: The Simplest Wavelet Basis 9(12)
The one-dimensional Haar Wavelet transform 9(2)
One-dimensional Haar basis functions 11(5)
Orthogonality and normalization 16(2)
Wavelet compression 18(3)
Image Compression 21(12)
Two-dimensional Haar wavelet transforms 21(4)
Two-dimensional Haar basis functions 25(3)
Wavelet image compression 28(2)
Color images 30(1)
Summary 31(2)
Image Editing 33(10)
Multiresolution image data structures 34(2)
Image editing algorithm 36(3)
Boundary conditions 39(1)
Display and editing at fractional resolutions 40(1)
Image editing examples 41(2)
Image Querying 43(18)
Image querying by content 45(1)
Developing a metric for image querying 46(4)
Image querying algorithm 50(3)
Image querying examples 53(2)
Extensions 55(6)
II CURVES
Subdivision curves 61(18)
Uniform subdivision 62(4)
Nonuniform subdivision 66(2)
Evaluation masks 68(4)
Nested spaces and refinable scaling functions 72(7)
The Theory of Multiresolution Analysis 79(30)
Multiresolution analysis 80(5)
Orthogonal wavelets 85(4)
Semiorthogonal wavelets 89(8)
Biorthogonal wavelets 97(10)
Summary 107(2)
Multiresolution Curves 109(16)
Related curve representations 110(1)
Smoothing a curve 111(1)
Editing a curve 112(8)
Scan conversion and curve compression 120(5)
Multiresolution Tiling 125(16)
Previous solutions to the tiling problem 126(3)
The multiresolution tiling algorithm 129(6)
Time complexity 135(1)
Tiling examples 136(5)
III SURFACES
Surface Wavelets 141(20)
Overview of multiresolution analysis for surfaces 142(1)
Subdivision surfaces 143(8)
Selecting an inner product 151(1)
A biorthogonal surface wavelet construction 152(6)
Multiresolution representations of surfaces 158(3)
Surface Applications 161(10)
Conversion to multiresolution form 161(2)
Surface compression 163(1)
Continuous level-of-detail control 164(1)
Progressive transmission 165(1)
Multiresolution editing 165(1)
Future directions for surface wavelets 166(5)
IV PHYSICAL SIMULATION
Variational Modeling 171(10)
Setting up the objective function 172(1)
The finite-element method 173(1)
Using finite elements in variational modeling 173(4)
Variational modeling using wavelets 177(2)
Adaptive variational modeling 179(2)
Global Illumination 181(14)
Radiosity 181(2)
Finite elements and radiosity 183(3)
Wavelet radiosity 186(6)
Enhancements to wavelet radiosity 192(3)
Further Reading 195(28)
Theory of multiresolution analysis 195(2)
Image applications 197(1)
Curve and surface applications 198(1)
Physical simulation 199(4)
V APPENDICES
A Linear Algebra Review 203(6)
A.1 Vector spaces 203(1)
A.2 Bases and dimension 204(1)
A.3 Inner products and orthogonality 205(1)
A.4 Norms and normalization 206(1)
A.5 Eigenvectors and eigenvalues 207(2)
B B-Spline Wavelet Matrices 209(8)
B.1 Haar wavelets 210(1)
B.2 Endpoint-interpolating linear B-spline wavelets 211(1)
B.3 Endpoint-interpolating quadratic B-spline wavelets 212(2)
B.4 Endpoint-interpolating cubic B-spline wavelets 214(3)
C Matlab Code For B-Spline Wavelets 217(6)
Bibliography 223(12)
Index 235
- 名称
- 类型
- 大小
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