Linear anisotrophic mesh filtering

Abstract

The present invention smoothes a spherical graph signal composed of spherical signal points associated with graph vertices of a graph producing a smoothed spherical graph signal composed of smoothed spherical signal points. Each smoothed spherical signal point is computed by multiplying a vertex rotation matrix by the corresponding spherical signal point. The vertex rotation matrix is computed as a weighted average of neighbor rotation matrices using a local parameterization of the group of rotations. The present invention also filters anisotropically a graph signal composed signal points associated with graph vertices of a graph producing a filtered graph signal composed of filtered signal points. Each filtered signal point is computed as a weighted average of signal points corresponding to the corresponding graph vertices and neighbor graph vertices with neighbor weight matrices. The present invention also denoises the vertex positions of a polygon mesh without tangential drift. The face normals are smoothed on the dual graph of the polygon mesh. The smoothed face normals are used to construct neighbor weight matrices on the primal graph of the polygon mesh. The vertex positions are anisotropically filtered on the primal graph of the polygon mesh. The present invention also filters the vertex positions and face normals of a polygon mesh with interpolatory vertex positions and face normal constraints.