Highly symmetric bi-frames for triangle surface multiresolution processing. (English) Zbl 1238.42018
Symmetry property of wavelets or wavelet frames is of particular importance in applications such as triangle surface multiresolution processing. This paper introduces the concept of \(6\)-fold axial symmetry in Definition 1 for bivariate dyadic dual wavelet frames with four high-pass primal filters and four high-pass dual filters. Based on box splines and the butterfly interpolatory subdivision scheme and by solving systems of nonlinear algebraic equations, this paper presents in Sections 4–7 several interesting examples of bivariate dual wavelet frames having short supports and \(6\)-fold axial symmetry. For the constructed Loop’s scheme-based dual wavelet frames, multiresulotion algorithms are provided for extraordinary vertices and boundary vertices of triangular meshes. Its application to triangle surface multiresolution processing is given in Section 8.
Reviewer: Bin Han (Edmonton)
MSC:
| 42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |
| 42C15 | General harmonic expansions, frames |
Keywords:
6-fold symmetric frame filter bank; symmetric wavelet bi-frames; lifting scheme; frame multiresolution algorithm templates; loop’s scheme-based bi-frames; the butterfly scheme-based bi-frames; triangle surface multiresolution processingReferences:
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