The Split Bregman Method for Image Diffusion on Implicit Surfaces

Image diffusion on implicit surfaces is solved by the concepts of intrinsic gradient and intrinsic divergence along with the expression of implicit surfaces using zero level set of a continuous signed distance function. But the finite difference scheme of the relevant gradient descent equations is complex and its computation efficiency is low. The Split Bregman algorithm for the nonlinear variational image diffusion on implicit surfaces is designed by introducing auxiliary variables and Bregman iterative parameters, which transforms the previous energy functional minimization problem to solving some simple Poisson equations and some soft threshold formulas. The generalized TV model, PM model and Char bonnier model are implemented as examples to validate the proposed algorithm in image denoising and in painting on implicit surfaces and demonstrate its simplicity and efficiency.