The Application Of Sparsity Method In Mesh Denoising

With the development of computer technology,3D data has been applied to multiple occasions. The triangular mesh is most common data format used in Computer Graphics when handling the3D data. So, lots of attention has been drawn to the processing of the mesh data. And the mesh denoising, deformation and correspondence are all typical and challenging problems among the field of mesh processing.There have been some methods to hanled the problem of mesh denoising. The key challenge we face in this field is to denoise the mesh and maintain the structure of the mesh at the same time. We propose a global mesh denoising method using l1-sparsity. This method is motivated by the fundamental theory of sparse representation in the field of signal processing. The global optimization of an energy function is employed to remove noises from the mesh while the features are preserved.There are two steps in our method. The first step is the filtering of the face normals. We formulate a global optimization model to optimize the face normals of the noised mesh. Then we use the l1-norm to ensure the sparsity of the solution, which preserves the structures of mesh features. The second step is the reconstruction of the denoised mesh. Given the new filtered face normals, we create a vertex reconstruction model under the least-square sense according to the definition of the face normal. The denoised mesh is updated by the solution of the reconstruction model.Furthermore, our model solves the denoising problem globally, which avoids the problems appeared in existing methods, such as the convergence problem. And we only have one parameter in our model, which is helpful to control the denoising effect. A large number of experiments demonstrate that our method is able to remove noises, at the same time, preserve the features of the mesh, especially for the CAD models.