Joint seminar CVGI - OGRE - Discrete Total Variation: New Definition and Minimization

A new definition for the gradient field of a discrete image is proposed. The differentiation mapping from the image to its gradient field, defined on a twice finer grid, is nonlinear and is viewed as the inverse operation of linear integration. Then, the total variation of an image is simply defined as the l1 norm of its gradient field amplitude. This new definition of the total variation yields sharp edges and has better isotropy than the classical definition.