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Abstract: this article we review techniques for building and analyzing wavelets on irregular point sets in one and two dimensions. We discuss current results both on the practical and theoretical side. In particular we focus on subdivision schemes and commutation rules. Several examples are included. (Update)
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BibTeX entry: (Update)
Daubechies, I & Sweldens, W. 1999 Wavelets on irregular pointsets. Phil. Trans. R. Soc. Lond. http://citeseer.ist.psu.edu/article/daubechies99wavelets.html More
@misc{ daubechies99wavelets,
author = "I. Daubechies and W. Sweldens",
title = "Wavelets on irregular pointsets",
text = "Daubechies, I & Sweldens, W. 1999 Wavelets on irregular pointsets. Phil.
Trans. R. Soc. Lond.",
year = "1999",
url = "citeseer.ist.psu.edu/article/daubechies99wavelets.html" }
Citations (may not include all citations):770 Orthonormal bases of compactly supported wavelets (context) - Daubechies - 1988
437 Laplacian pyramid as a compact image code - Burt, Adelson - 1983
254 Multiresolution approximations and wavelet orthonormal bases.. (context) - Mallat - 1989
201 spline surfaces on arbitrary topological meshes (context) - Catmull, Clark et al. - 1978
190 Smooth subdivision surfaces based on triangles (context) - Loop - 1987
157 The lifting scheme: A construction of second generation wave.. - Sweldens - 1997
145 A butterfly subdivision scheme for surface interpolation wit.. (context) - Dyn, Levin et al. - 1990 ACM DBLP
135 Symmetric iterative interpolation processes (context) - Deslauriers, Dubuc - 1989
112 Survey of polygonal surface simplification algorithms - Heckbert, Garland - 1997
102 Interpolation through an iterative scheme (context) - Dubuc - 1986
94 Multiresolution signal processing for meshes - Guskov, Sweldens et al. - 1999 ACM DBLP
86 point interpolatory subdivision scheme for curve design (context) - Dyn, Levin et al. - 1987
77 Stability of multiscale transformations - Dahmen - 1996
76 Building your own wavelets at home - Sweldens, Schroder - 1996
70 Interpolating wavelet transforms - Donoho - 1992
65 Sobolev characterization of solutions of dilation equations (context) - Eirola - 1992 ACM
61 A unified approach to subdivision algorithms near extraordin.. (context) - Reif - 1995 ACM DBLP
55 Simple regularity criteria for subdivision schemes - Rioul - 1992 ACM
50 Existence and global regularity of solutions (context) - Daubechies, Lagarias et al. - 1991
49 An algorithm for high speed curve generation (context) - Chaikin - 1974
48 Interpolatory subdivision on open quadrilateral nets with ar.. - Kobbelt - 1996 DBLP
47 Interpolation dyadique (context) - Deslauriers, Dubuc - 1987
34 Analysis of uniform binary subdivision schemes for curve des.. (context) - Dyn, Gregory et al. - 1991
33 Analysis and Application of Subdivision Surfaces - Schweitzer - 1996 ACM
33 Discrete fairing - Kobbelt - 1997
27 Subdivision methods for geometric design - Warren ACM
24 Using parameters to increase smoothness of curves and surfac.. (context) - Dyn, Levin et al. - 1990 ACM DBLP
22 Analysis of the behaviour of recursive division surfaces nea.. (context) - Doo, Sabin - 1978
22 Wavelet analysis of refinement equations (context) - Villemoes - 1994
14 Regularity of irregular subdivision - Daubechies, Guskov et al. - 1999
12 Computing surfaces invariant under subdivision (context) - Cavaretta, Micchelli - 1987 DBLP
12 Computing surfaces invariant under subdivision (context) - Micchelli, Prautzsch - 1987 DBLP
9 Multivariate subdivision schemes and divided di#erences - Guskov - 1998
9 California Institute of Technology (context) - Zorin, of et al. - 1996
8 Binary subdivision schemes for functions over irregular knot.. - Warren - 1995
6 Number 27 in Applied Mathematical Sciences (context) - De Boor, guide et al. - 1978
6 Sur une courbe plane (context) - de Rham - 1956
6 Constructing variationally optimal curves through subdivion (context) - Kobbelt, Schroder - 1997
4 Commutation for irregular subdivision - Daubechies, Guskov et al. - 1998
1 The desing of curves and surfaces by subdivision algorithms (context) - Cavaretta, Micchelli - 1989
1 Andre Citroen Automobiles SA (context) - de Casteljau, calcul - 1959
1 Course Notes: Subdivision for Modeling and Animation (context) - Schroder, Zorin - 1998
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