基于渐进插值的Catmull-Clark双正交细分小波及其应用

Biorthogonal Wavelet Construction with Progressive Interpolation Based on Catmull-Clark Subdivision and Applications

针对lifting双正交Catmull-Clark细分小波在数据压缩、噪声滤波和低分辨率模型稳定性等方面的不足,提出基于渐进插值的Catmull-Clark双正交细分小波算法.对于任意拓扑的四边形网格,Catmull-Clark细分的极限曲面渐进插值于原有网格控制点,并且相邻2次细分之间网格改变程度很小,导致大量小波系数值趋于0,非常适于用零树编码提高3D网格的压缩性能;同时,该小波变换具有局部正交性和对位计算等特点,可显著减少内存占用量和计算复杂度.实验结果表明,与同类算法相比较,该算法在压缩效率、噪声滤波和低分辨率模型曲面的稳定性等方面均有明显提高,其中压缩编码Bits/vertex值减小14%,重构模型PSNR值增大5%,编解码耗时分别减少6%和9%.

Biorthogonal Catmull-Clark subdivision wavelet transforms constructed via lifting scheme have beenproposed to speed up processing of geometric models.However,their compression qualities and noise-filteringeffects are insufficient,particularly the model stability at low-resolution level is deficient.Therefore,a waveletconstruction with progressive-interpolation-based biorthogonal Catmull-Clark subdivision is presented to generatea new control mesh whose limit surface progressively interpolates all vertices in the original quadrilateralmesh with arbitrary topology.It can achieve an exponential convergence rate and slight differences of subdivisionsurfaces between successive levels,which are suitable to data compression,noise-filtering,and so on.Combinedwith the local and in-place lifting operations,the proposed wavelet transform can dramatically decrease the memoryconsumption and computation complexity.Experimental results show that compared with the previous biorthogonalCatmull-Clark wavelet constructions,the proposed wavelet transform achieves high compression ratio,steady noise-filtering and better progressive transmission quality,decreasing the bits/vertex of3D meshes about14%,improving the PSNR of reconstruction model about5%,and reducing the time costs of coding and decodingby6%and9%,respectively.