Mesh denoising is a fundamental yet open problem in geometry processing. The main challenge is to remove noise while recovering the shape of the underlying surface as accurately as possible. In this paper, we propose a novel joint bilateral filter on the face normal field. The key is to estimate a reliable guidance normal field by constructing a shape-aware consistent patch for accurately describing the local shape of each face. To this end, we first select a candidate patch for each face by using a newly defined consistent metric considering both patch flatness and face-to-patch orientation similarity. Then, spectral analysis is used in combination with ${\ell }_0$ minimization to refine the candidate patches in a shape-aware manner. The refined patches do not contain any features, and therefore they can accurately describe the local shape of the underlying surface. After smoothing the face normal field, vertex positions are reconstructed to match the filtered face normals. Our mesh denoising method is theoretically rooted and practical for dealing with the meshes containing corners with low sampling rates, multi-scale features, or narrow structure regions. Extensive experimental results demonstrate that our method can significantly improve the feature preserving capability of joint normal filter and outperforms state-of-the-art methods visually and quantitatively.

网格去噪是几何处理中一个基本但开放的问题。主要挑战是在尽可能准确地恢复下垫面形状的同时去除噪声。在本文中，我们在面部法线场上提出了一种新的联合双边滤波器。关键是通过构建形状感知一致的补丁来准确描述每个人脸的局部形状，从而估计出可靠的引导法向场。为此，我们首先通过使用新定义的一致度量为每个人脸选择一个候选补丁，同时考虑补丁平坦度和面部到补丁方向的相似性。然后，光谱分析结合使用${\ell }_0$最小化以形状感知的方式细化候选补丁。细化的补丁不包含任何特征，因此它们可以准确地描述下垫面的局部形状。在平滑面部法线场后，顶点位置被重建以匹配过滤后的面部法线。我们的网格去噪方法在处理包含低采样率、多尺度特征或狭窄结构区域的角点的网格方面具有理论根基和实用性。大量的实验结果表明，我们的方法可以显着提高联合法线滤波器的特征保留能力，并在视觉和定量上优于最先进的方法。