Mesh Smoothing Method Based on Local Wave Analysis  

作　　者：QIN Xujia ZHENG Hongbo CHENG Shiwei LIU Shishuang XU Xiaogang 

机构地区：[1]School of Computer Science and Technology,Zhejiang University of Technology,Hangzhou 310023,China [2]Department of Equipment system and Automatization,Dalian Naval Academy,Dalian 116018,China [3]State Key Laboratory of CAD&CG,Zhejiang University,Hangzhou 310058,China

出　　处：《Chinese Journal of Mechanical Engineering》2012年第3期598-607,共10页中国机械工程学报（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant No. 61075118,Grant No. 61005056,Grant No. 60975016);National Key Technology Support Program of China (Grant No. 2007BAH11B02);Zhejiang Provincial Natural Science Foundation of China (Grant No. Y1100880);Open Project Program of State Key Laboratory of CAD&CG of China (Grant No. A0906)

摘　　要：As the mesh models usually contain noise data,it is necessary to eliminate the noises and smooth the mesh.But existed methods always lose geometric features during the smoothing process.Hence,the noise is considered as a kind of random signal with high frequency,and then the mesh model smoothing is operated with signal processing theory.Local wave analysis is used to deal with geometric signal,and then a novel mesh smoothing method based on the local wave is proposed.The proposed method includes following steps：Firstly,analyze the principle of local wave decomposition for 1D signal,and expand it to 2D signal and 3D spherical surface signal processing;Secondly,map the mesh to the spherical surface with parameterization,resample the spherical mesh and decompose the spherical signals by local wave analysis;Thirdly,propose the coordinate smoothing and radical radius smoothing methods,the former filters the mesh points＇ coordinates by local wave,and the latter filters the radical radius from their geometric center to mesh points by local wave;Finally,remove the high-frequency component of spherical signal,and obtain the smooth mesh model with inversely mapping from the spherical signal.Several mesh models with Gaussian noise are processed by local wave based method and other compared methods.The results show that local wave based method can obtain better smoothing performance,and reserve more original geometric features at the same time.As the mesh models usually contain noise data,it is necessary to eliminate the noises and smooth the mesh.But existed methods always lose geometric features during the smoothing process.Hence,the noise is considered as a kind of random signal with high frequency,and then the mesh model smoothing is operated with signal processing theory.Local wave analysis is used to deal with geometric signal,and then a novel mesh smoothing method based on the local wave is proposed.The proposed method includes following steps：Firstly,analyze the principle of local wave decomposition for 1D signal,and expand it to 2D signal and 3D spherical surface signal processing;Secondly,map the mesh to the spherical surface with parameterization,resample the spherical mesh and decompose the spherical signals by local wave analysis;Thirdly,propose the coordinate smoothing and radical radius smoothing methods,the former filters the mesh points＇ coordinates by local wave,and the latter filters the radical radius from their geometric center to mesh points by local wave;Finally,remove the high-frequency component of spherical signal,and obtain the smooth mesh model with inversely mapping from the spherical signal.Several mesh models with Gaussian noise are processed by local wave based method and other compared methods.The results show that local wave based method can obtain better smoothing performance,and reserve more original geometric features at the same time.

关 键 词：mesh models local wave analysis noise SMOOTHING 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术] TN911.6[自动化与计算机技术—计算机科学与技术]