Denoising, Based On The Surface Of The Level Set Method

Variational level set methods is a new modeling method that is used in 3D-reconstruction and Surface Processing. It is used to represent the surface by level set implicitly. It allows us to process surface with arbitrary shapes and changing topology, Level set method is used in surface smoothing by filtering the normals of the surface in this paper, rather than filtering the positions on a mesh. Energy functions of surface-smoothing model can be formulated as functions on the surface normals. Fourth-order flows could be solved by a couple of second-order PDEs efficiently. Experimental results indicate that this method could denoise and smooth surface efficiently. PM (Perona-Malik) is a classical nonlinear image diffusion model with adaptive properties of image smoothing, edge preserving. It is transformed to geometric surface smoothing, edge preserving variational model using variational level set method based on the analogue of normal vector of surface and general image intensity in this paper. The energy functional includes three parts, the first one is a data term using the square of the difference between the Heaviside function of initial level set function and the one of the evolved level set function, the second part is a regularizing term based on geometric curvature, the third part is a penalty term enforcing the level set function to satisfy the property of signed distance functions. Numerical examples validate its abilities of surface smoothing and edge preserving.