Linear Anisotropic Mesh Filtering

No algorithm for unconstrained polygon mesh denoising can beat Laplacian smoothing in simplicity and ease of implementation. In this paper we introduce a new algorithm for polygon meshes smoothing with vertex position and face normal interpolatory constraints composed of two phases. First the face normals are filtered independently of vertex positions. Then the vertex positions are filtered integrating the face normals in the least squares sense. Laplacian smoothing is used to smooth both the face normal field and the vertex positions, with a properly defined Laplacian operator in each case. We define isotropic, anisotropic, linear, and non-linear Laplacian operators for signals defined in Euclidean space, and on the unit sphere. In addition to the obvious applications to shape design, our algorithm constitutes a new fast and linear solution to the tangential drift problem, observed in meshes with irregular edge length and angle distribution. We show how classical linear filter design techniques can be applied in both cases, and conclude the paper determining integrability conditions for face normal fields. CR