We present a semi-sparsity model for 3D triangular mesh denoising, which is motivated by the success of semi-sparsity regularization in image processing applications. We demonstrate that such a regularization model can be also applied for graphic processing and gives rise to similar simultaneous-fitting results in preserving sharp features and piece-wise smoothing surfaces. Specifically, we first describe the piecewise constant function spaces associated with the differential operators on triangular meshes and then show how to extend the semi-sparsity model to meshes denoising. To verify its effectiveness, we present an efficient iterative algorithm based on the alternating direction method of multipliers (ADMM) technique and show the experimental results on synthetic and real scanning data against the state-of-the-arts both visually and quantitatively.

翻译：我们提出了一种用于三维三角网格去噪的半稀疏模型，该模型的灵感源于半稀疏正则化在图像处理应用中的成功。我们证明了此类正则化模型同样可应用于图形处理，并在保持尖锐特征与分段平滑表面方面产生类似的联合拟合效果。具体而言，我们首先描述了三角网格上伴随微分算子的分段常数函数空间，进而展示了如何将半稀疏模型扩展至网格去噪。为验证其有效性，我们提出了一种基于交替方向乘子法（ADMM）的高效迭代算法，并在合成数据与真实扫描数据上，从视觉和量化两个维度与现有最优方法进行了实验对比。