Foreword

Preface

Notation

1   Introduction

1.1   Multiresolution methods
1.2   Historical perspective
1.3   Overview of the book

Part 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 editing 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

Part II: Curves

6   Subdivision curves

6.1   Uniform subdivision
6.2   Non-uniform 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   Semi-orthogonal wavelets
7.4   Biorthogonal wavelets
7.5   Summary

8   Multiresolution curves

8.1   Related curve representations
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

Part 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

Part 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
12.4   Variational modeling using wavelets
12.5   Adaptive variational modeling

13   Global illlumination

13.1   Radiosity
13.2   Finite elements and radiosity
13.3   Wavelet radiosity
13.4   Enhancements to wavelet radiosity

14   Further reading

14.1   Theory of multiresolution analysis
14.2   Image applications
14.3   Curve and surface applications
14.4   Physical simulation

Part V: Appendices

A   Linear algebra review

A.1   Vector spaces
A.2   Bases and dimension
A.3   Inner products and orthogonality
A.4   Norms and normalization
A.5   Eigenvectors and eigenvalues

B   B-spline wavelet matrices

B.1   Haar wavelets
B.2   Endpoint-interpolating linear B-spline wavelets
B.3   Endpoint-interpolating quadratic B-spline wavelets
B.4   Endpoint-interpolating cubic B-spline wavelets

C   Matlab code for B-spline wavelets

Bibliography

Index

Color plates