√3-Subdivision-Based Biorthogonal Wavelets
√3-Subdivision-Based Biorthogonal Wavelets
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DOI：
10.1109/tvcg.2007.1031
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发表时间：
2007-09
影响因子：
5.2
通讯作者：
Huawei Wang;K. Qin;Hanqiu Sun
中科院分区：
文献类型：
--
作者：
Huawei Wang;K. Qin;Hanqiu Sun
利用提升格式，提出了一种新的基于基3细分的双正交小波分析。由于radic3细分是最慢的拓扑细化在传统的三角形细分，基于radic3细分的多分辨率分析是更平衡的三角形网格比现有的小波分析，从而提供了更多的细节层次处理多边形模型。为了优化多分辨率分析，新的小波，无论是内部或边界上，正交的局部尺度函数的基础上的离散内积与细分掩模。由于小波分析与综合算法实际上是由一系列局部提升运算组成的，因此可以在线性时间内完成。实验表明，小波分析的效率和稳定性的封闭和开放的三角形网格与radic3细分连接。基3-细分的双正交小波可以用于许多应用，如渐进传输，形状近似，和多分辨率编辑和绘制的3D几何模型。
A new efficient biorthogonal wavelet analysis based on the radic3 subdivision is proposed in the paper by using the lifting scheme. Since the radic3 subdivision is of the slowest topological refinement among the traditional triangular subdivisions, the multiresolution analysis based on the radic3 subdivision is more balanced than the existing wavelet analyses on triangular meshes and accordingly offers more levels of detail for processing polygonal models. In order to optimize the multiresolution analysis, the new wavelets, no matter whether they are interior or on boundaries, are orthogonalized with the local scaling functions based on a discrete inner product with subdivision masks. Because the wavelet analysis and synthesis algorithms are actually composed of a series of local lifting operations, they can be performed in linear time. The experiments demonstrate the efficiency and stability of the wavelet analysis for both closed and open triangular meshes with radic3 subdivision connectivity. The radic3-subdivision-based biorthogonal wavelets can be used in many applications such as progressive transmission, shape approximation, and multiresolution editing and rendering of 3D geometric models.