An iterative method for fast mesh denoising

A new approach for removing noises from a corrupted 3D model (mesh or surface) of arbitrary topology is presented. The basic idea is to transform a space domain model into a frequency-like domain representation and achieve denoising by low pass filtering. The transformation from space domain to frequency domain is done by decomposing the 3D model into an infinite series of meshes of the same topology but less magnitude so that each mesh represents part of the information of the given model, with some meshes containing more information on overall shape while others containing more on subtle details. The transformation process does not require setting up any linear systems, nor any matrix computation, but is done by iteratively moving vertices of the given mesh locally until a smooth model with noises properly removed is reached. The iterative process converges at an exponential rate. Therefore the new iterative method is very fast and can be used for meshes with large number of vertices. The mesh decomposition scheme is obtained using the concept of Catmull-Clark subdivision surfaces, but the same idea can be applied to other subdivision schemes as well. Some test results obtained using this method are included. They show that the iterative method can achieve visually pleasant resulting models with noises properly removed.