Stollnitz E. Wavelets for Computer Graphics. A Primer 1994
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Stollnitz E. Wavelets for Computer Graphics. A Primer 1994
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Wavelets are a mathematical tool for hierarchically decomposing functions. Wavelets allow any function to be described in terms of a coarse overall shape, plus details that range from broad to narrow. Regardless of whether the function of interest is an image, a curve, or a surface, wavelets provide an elegant technique for representing the levels of detail present.
Introduction.
The Haar wavelet basis.
The one-dimensional Haar wavelet transform.
One-dimensional Haar wavelet basis functions.
Two-dimensional Haar wavelet transforms.
Two-dimensional Haar basis functions.
Application I: Image compression.
Compression.
L2 compression.
Wavelet image compression in the L2 norm.
Wavelet image compression in other L2 norms.
Multiresolution analysis.
A matrix formulation for refinement.
The filter bank.
Designing a multiresolution analysis.
Spline Wavelets.
B-spline scaling functions.
Inner product.
B-spline wavelets.
B-spline filter bank.
Application II: Multiresolution curves and surfaces.
Editing the sweep of the curve.
Editing the character of the curve.
Multiresolution surfaces.
Acknowledgements.
References.
Appendix.
Linear algebra review.
Vector spaces.
Bases and dimension.
Inner products and orthogonality.
Norms and normalization.
Duals.
Computing the duals.
Details on endpoint-interpolating B-spline wavelets.
Haar wavelets.
Endpoint-interpolating linear B-spline wavelets.
Endpoint-interpolating quadratic B-spline wavelets.
Endpoint-interpolating cubic B-spline wavelets