Total Generalized Variation (TGV) has recently been proven certainly successful in image processing for preserving sharp features as well as smooth transition variations. However, none of the existing works aims at numerically calculating TGV over triangular meshes. In this paper, we develop a novel numerical framework to discretize the second-order TGV over triangular meshes. Further, we propose a TGV-based variational model to restore the face normal field for mesh denoising. The TGV regularization in the proposed model is represented by a combination of a first- and second-order term, which can be automatically balanced. This TGV regularization is able to locate sharp features and preserve them via the first-order term, while recognize smoothly curved regions and recover them via the second-order term. To solve the optimization problem, we introduce an efficient iterative algorithm based on variable-splitting and augmented Lagrangian method. Extensive results and comparisons on synthetic and real scanning data validate that the proposed method outperforms the state-of-the-art methods visually and numerically.

中文翻译：

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网格总广义降噪

最近，总广义变化量（TGV）在图像处理中无疑得到了成功，可以保留鲜明的特征以及平滑的过渡变化量。但是，现有的工作都没有旨在对三角网格上的TGV进行数值计算。在本文中，我们开发了一个新颖的数值框架来离散三角网格上的二阶TGV。此外，我们提出了基于TGV的变分模型来恢复人脸法线场以进行网格降噪。所提出模型中的TGV正则化由一阶和二阶项的组合表示，可以自动进行平衡。这种TGV正则化功能可以定位尖锐特征并通过一阶项保留它们，同时识别平滑的弯曲区域并通过二阶项恢复它们。为了解决优化问题，我们介绍了一种基于变量分解和增强拉格朗日方法的高效迭代算法。大量的结果以及对合成和真实扫描数据的比较证明，该方法在视觉和数字上均优于最新方法。