Highly symmetric bi-frames for triangle surface multiresolution processing

作者：Jiang Qingtang^*; Pounds Dale K

来源：Applied and Computational Harmonic Analysis, 2011, 31(3): 370-391.

DOI：10.1016/j.acha.2011.01.007

• Lifting scheme
• 6-fold symmetric frame filter banks
• Symmetric wavelet bi-frames
• Frame multiresolution algorithm templates
• Loop's scheme-based bi-frames
• The butterfly scheme-based bi-frames
• Surface multiresolution decomposition/reconstruction

In this paper we investigate the construction of dyadic affine (wavelet) bi-frames for triangular-mesh surface multiresolution processing. We introduce 6-fold symmetric bi-frames with 4 framelets (frame generators). 6-fold symmetric bi-frames yield frame decomposition and reconstruction algorithms (for regular vertices) with high symmetry, which is required for the design of the corresponding frame multiresolution algorithms for extraordinary vertices on the triangular mesh. Compared with biorthogonal wavelets, the constructed bi-frames have better smoothness and smaller supports. In addition, we also provide frame multiresolution algorithms for extraordinary vertices. All the frame algorithms considered in this paper are given by templates (stencils) so that they are implementable. Furthermore, we present some preliminary experimental results on surface processing with frame algorithms constructed in this paper.

• 出版日期2011-11