This paper presents frameworks to extend the mean and median filtering schemes in image processing into smoothing noisy 3D shapes given by triangle meshes. The frameworks consist of the application of the mean and median filters to face normals on triangle meshes and the edit of mesh vertex positions to make them fit to the modified normals.

We also give a quantitative evaluation of the proposed mesh filtering schemes and compare them with conventional mesh smoothing methods such as the Laplacian smoothing flow and the mean curvature flow. The quantitative evaluation is performed in error metrics on mesh vertices and normals.

Experimental results demonstrate that our mesh mean and median filtering methods are more stable than the conventional Laplacian and mean curvature flows. We propose those new mesh smoothing methods as one possible solution of a oversmoothing problem.