Box splines
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
Multiresolution analysis for surfaces of arbitrary topological type
Multiresolution analysis for surfaces of arbitrary topological type
ACM Transactions on Graphics (TOG)
Compactly supported tight affine spline frames in L2Rd
Mathematics of Computation
Approximation properties of multivariate wavelets
Mathematics of Computation
Progressive geometry compression
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Spectral Analysis of the Transition Operator and Its Applications to Smoothness Analysis of Wavelets
SIAM Journal on Matrix Analysis and Applications
Quincunx fundamental refinable functions and Quincunx biorthogonal wavelets
Mathematics of Computation
Generalized B-Spline Subdivision-Surface Wavelets for Geometry Compression
IEEE Transactions on Visualization and Computer Graphics
√2 Subdivision for quadrilateral meshes
The Visual Computer: International Journal of Computer Graphics
Combining 4- and 3-direction subdivision
ACM Transactions on Graphics (TOG)
Biorthogonal loop-subdivision wavelets
Computing - Geometric modelling dagstuhl 2002
Efficient wavelet construction with Catmull–Clark subdivision
The Visual Computer: International Journal of Computer Graphics
Tight wavelet frames for subdivision
Journal of Computational and Applied Mathematics
Advances in Computational Mathematics
Nonseparable two- and three-dimensional wavelets
IEEE Transactions on Signal Processing
√3-Subdivision-Based Biorthogonal Wavelets
IEEE Transactions on Visualization and Computer Graphics
Computer Aided Geometric Design
Computer Aided Geometric Design
Nonseparable multidimensional perfect reconstruction filter banks and wavelet bases for Rn
IEEE Transactions on Information Theory - Part 2
Hi-index | 7.29 |
When bivariate filter banks and wavelets are used for surface multiresolution processing, it is required that the decomposition and reconstruction algorithms for regular vertices derived from them have high symmetry. This symmetry requirement makes it possible to design the corresponding multiresolution algorithms for extraordinary vertices. Recently lifting-scheme based biorthogonal bivariate wavelets with high symmetry have been constructed for surface multiresolution processing. If biorthogonal wavelets have certain smoothness, then the analysis or synthesis scaling function or both have big supports in general. In particular, when the synthesis low-pass filter is a commonly used scheme such as Loop's scheme or Catmull-Clark's scheme, the corresponding analysis low-pass filter has a big support and the corresponding analysis scaling function and wavelets have poor smoothness. Big supports of scaling functions, or in other words big templates of multiresolution algorithms, are undesirable for surface processing. On the other hand, a frame provides flexibility for the construction of ''basis'' systems. This paper concerns the construction of wavelet (or affine) bi-frames with high symmetry. In this paper we study the construction of wavelet bi-frames with 4-fold symmetry for quadrilateral surface multiresolution processing, with both the dyadic and 2 refinements considered. The constructed bi-frames have 4 framelets (or frame generators) for the dyadic refinement, and 2 framelets for the 2 refinement. Namely, with either the dyadic or 2 refinement, a frame system constructed in this paper has only one more generator than a wavelet system. The constructed bi-frames have better smoothness and smaller supports than biorthogonal wavelets. Furthermore, all the frame algorithms considered in this paper are given by templates so that one can easily implement them.