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has been cited by the following article:

• TITLE: Optimal Interpolatory Wavelets Transform for Multiresolution Triangular Meshes

  AUTHORS: Chong Zhao, Hanqiu Sun

  KEYWORDS: Lifting Scheme, Subdivision Wavelets, Matrix-Valued Subdivision

  JOURNAL NAME: Applied Mathematics, Vol.2 No.3, March 24, 2011

  ABSTRACT: In recent years, several matrix-valued subdivisions have been proposed for triangular meshes. The ma-trix-valued subdivisions can simulate and extend the traditional scalar-valued subdivision, such as loop and subdivision. In this paper, we study how to construct the matrix-valued subdivision wavelets, and propose the novel biorthogonal wavelet based on matrix-valued subdivisions on multiresolution triangular meshes. The new wavelets transform not only inherits the advantages of subdivision, but also offers more resolutions of complex models. Based on the matrix-valued wavelets proposed, we further optimize the wavelets transform for interactive modeling and visualization applications, and develop the efficient interpolatory loop subdivision wavelets transform. The transform simplifies the computation, and reduces the memory usage of matrix-valued wavelets transform. Our experiments showed that the novel wavelets transform is sufficiently stable, and performs well for noise reduction and fitting quality especially for multiresolution semi-regular triangular meshes.