Ten lectures on wavelets
An introduction to wavelets
Spherical wavelets: efficiently representing functions on the sphere
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Multiresolution analysis of arbitrary meshes
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Multiresolution analysis for surfaces of arbitrary topological type
Multiresolution analysis for surfaces of arbitrary topological type
Interactive multiresolution surface viewing
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Free-form deformations with lattices of arbitrary topology
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Multiresolution analysis for surfaces of arbitrary topological type
ACM Transactions on Graphics (TOG)
VIS '97 Proceedings of the 8th conference on Visualization '97
Analysis of Algorithms Generalizing B-Spline Subdivision
SIAM Journal on Numerical Analysis
Subdivision surfaces in character animation
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
MAPS: multiresolution adaptive parameterization of surfaces
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Exact evaluation of Catmull-Clark subdivision surfaces at arbitrary parameter values
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Wavelets for computer graphics: theory and applications
Wavelets for computer graphics: theory and applications
ACM Transactions on Information Systems (TOIS)
A multiresolution framework for variational subdivision
ACM Transactions on Graphics (TOG)
Multiresolution signal processing for meshes
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Optimal triangular Haar bases for spherical data
VIS '99 Proceedings of the conference on Visualization '99: celebrating ten years
Multiresolution hierarchies on unstructured triangle meshes
Computational Geometry: Theory and Applications - Special issue on multi-resolution modelling and 3D geometry compression
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
The digital Michelangelo project: 3D scanning of large statues
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Progressive geometry compression
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Filter bank algorithms for piecewise linear prewavelets on arbitrary triangulations
Journal of Computational and Applied Mathematics - Special issue/Dedicated to Prof. Larry L. Schumaker on the occasion of his 60th birthday
Bicubic subdivision-surface wavelets for large-scale isosurface representation and visualization
Proceedings of the conference on Visualization '00
Hybrid meshes: multiresolution using regular and irregular refinement
Proceedings of the eighteenth annual symposium on Computational geometry
Stationary Subdivision
Proceedings of the conference on Visualization '01
Multiresolution Analysis on Irregular Surface Meshes
IEEE Transactions on Visualization and Computer Graphics
Multiresolution modeling for scientific visualization
Multiresolution modeling for scientific visualization
On subdivision schemes generalizing uniform B-spline surfaces of arbitrary degree
Computer Aided Geometric Design
A unified framework for primal/dual quadrilateral subdivision schemes
Computer Aided Geometric Design
Wavelet representation of contour sets
Proceedings of the conference on Visualization '01
Single-knot wavelets for non-uniform B-splines
Computer Aided Geometric Design
Biorthogonal wavelets based on gradual subdivision of quadrilateral meshes
Computer Aided Geometric Design
Single-knot wavelets for non-uniform B-splines
Computer Aided Geometric Design
Bi-frames with 4-fold axial symmetry for quadrilateral surface multiresolution processing
Journal of Computational and Applied Mathematics
1-ring interpolatory wavelet using function vectors for mobile computing
Proceedings of the 10th International Conference on Virtual Reality Continuum and Its Applications in Industry
A discrete approach to multiresolution curves and surfaces
Transactions on Computational Science VI
Continuous and discrete Mexican hat wavelet transforms on manifolds
Graphical Models
Mesh connection with RBF local interpolation and wavelet transform
Proceedings of the Third Symposium on Information and Communication Technology
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Abstract--We present a new construction of lifted biorthogonal wavelets on surfaces of arbitrary two-manifold topology for compression and multiresolution representation. Our method combines three approaches: subdivision surfaces of arbitrary topology, B-spline wavelets, and the lifting scheme for biorthogonal wavelet construction. The simple building blocks of our wavelet transform are local lifting operations performed on polygonal meshes with subdivision hierarchy. Starting with a coarse, irregular polyhedral base mesh, our transform creates a subdivision hierarchy of meshes converging to a smooth limit surface. At every subdivision level, geometric detail can be expanded from wavelet coefficients and added to the surface. We present wavelet constructions for bilinear, bicubic, and biquintic B-Spline subdivision. While the bilinear and bicubic constructions perform well in numerical experiments, the biquintic construction turns out to be unstable. For lossless compression, our transform can be computed in integer arithmetic, mapping integer coordinates of control points to integer wavelet coefficients. Our approach provides a highly efficient and progressive representation for complex geometries of arbitrary topology.