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WAVELETS FOR COMPUTER GRAPHICS
Wavelets for Computer Graphics
Theory and Applications
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By
Eric Stollnitz
Anthony DeRose
David Salesin

Included in series
The Morgan Kaufmann Series in Computer Graphics,

Description


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
    • 12.4 Variational modeling using wavelets
    • 12.5 Adaptive variational modeling
  • 13 Global Illumination
    • 13.1 Radiosity
    • 13.2 Finite elements and radiosity
    • 13.3 Wavelet radiosity


Bibliographic details
Hardbound, 245 pages, publication date: AUG-1996
ISBN-13: 978-1-55860-375-2
ISBN-10: 1-55860-375-1
Imprint: MORGAN KAUFFMAN

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EUR 69.95
USD 94.95
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Last update: 7 Sep 2009
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