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l1优化在网格去噪中的应用

DOI: 10.11834/jig.20140419

Keywords: 计算机图形学,网格去噪,全局滤波,l1稀疏性

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Abstract:

目的网格去噪是计算机图形学中的经典问题,而如何在去除噪声的同时保持网格的特征结构是这一研究方向所面临的最大挑战。方法提出一种具有稀疏性的全局网格去噪方法,该方法源于信号处理理论中稀疏表示的基本思想,通过优化全局能量函数来去除网格模型的噪声,同时能够保持网格模型的特征结构。该方法共分为两个步骤,第1步为网格面法向量的滤波,首先建立全局优化模型,对噪声网格的面法向量进行滤波优化,其中引入l1范数来保证解的稀疏性,使得优化后新的面法向量能够保持网格的特征结构;第2步为网格曲面的重建,根据第1步得到的新的面法向量,按照面法向量的定义,建立最小二乘意义下的网格顶点的重建模型,求解得到新的网格曲面。结果由于该模型是全局方法,避免了现有滤波方法可能出现的不收敛等问题,能够取得比较满意的去噪效果。结论大量实验结果表明,本文方法在去除噪声的同时,能较好地保持网格的特征结构,尤其对于CAD模型有很好的实验效果。

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