Spherical wavelets: efficiently representing functions on the sphere
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Multiresolution analysis for surfaces of arbitrary topological type
ACM Transactions on Graphics (TOG)
Progressive geometry compression
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Bicubic subdivision-surface wavelets for large-scale isosurface representation and visualization
Proceedings of the conference on Visualization '00
Wavelet-Based Progressive Compression Scheme for Triangle Meshes: Wavemesh
IEEE Transactions on Visualization and Computer Graphics
Wavelet-Based Multiresolution Analysis of Irregular Surface Meshes
IEEE Transactions on Visualization and Computer Graphics
Generalized B-Spline Subdivision-Surface Wavelets for Geometry Compression
IEEE Transactions on Visualization and Computer Graphics
Unlifted Loop Subdivision Wavelets
PG '04 Proceedings of the Computer Graphics and Applications, 12th Pacific Conference
Biorthogonal loop-subdivision wavelets
Computing - Geometric modelling dagstuhl 2002
Efficient wavelet construction with Catmull–Clark subdivision
The Visual Computer: International Journal of Computer Graphics
From extension of Loop's approximation scheme to interpolatory subdivisions
Computer Aided Geometric Design
Deducing interpolating subdivision schemes from approximating subdivision schemes
ACM SIGGRAPH Asia 2008 papers
Biorthogonal wavelets based on gradual subdivision of quadrilateral meshes
Computer Aided Geometric Design
Computing Efficient Matrix-valued Wavelets for Meshes
PACIFIC_GRAPHICS '10 Proceedings of the 2010 18th Pacific Conference on Computer Graphics and Applications
√3-Subdivision-Based Biorthogonal Wavelets
IEEE Transactions on Visualization and Computer Graphics
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As an effective tool for the multiresolution rendering and editing for the complex models and scenes, the wavelet transforms attract more and more attention in recent years. While, the usual wavelet transforms developed for the mesh simplification still have some problems in the efficiency or shape preservation. They either consume much time and memory in the wavelet analysis, or generate low-detailed versions of models with the unwilling sharp convex edges. In this paper, we propose a novel and efficient wavelet transform based on the matrix-valued 1-ring interpolatory subdivision. Our matrix-valued wavelet transform is constructed on the function vectors, which makes it suitable for processing the vector-valued signals. Different from the usual multivariate wavelets, each component of the vector-valued signals processed by the matrix-valued wavelet are correlated. The resulted meshes are influenced by each component of the vector, which provides a way to adjust the shape of meshes. To overcome the defect that 1-ring subdivision surfaces is too sensitive to the initial shape control parameters, we develop a general approach to determine the shape control parameters for the subdivision and the wavelet transform, so making the multiresolution surfaces stable and smooth. We adopt the local lifting scheme to make the wavelet transform more efficient and low memory cost. The experiments have shown that our wavelet transform is efficient and stable, with the good shape-preserving ability. These features make it especially suitable for the resource-limited mobile computing.