Total variation regularization has been proven very useful in image processing and computer graphics applications.Recently many efforts have been contributed to e ciently solve this type of problems which are non-di erentiable.Augmented Lagrangian method is one of the most e cient methods.In this talk,we will dis-cuss this method for total variantion related problems over triangulated surfaces,including image denoising and segmentation on surfaces,as well as surface de-noising.