PM（perona-malik） is a classical nonlinear image diffusion model with adaptive properties of image smoothing and 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 part 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 and 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.