This article describes how robust error-kernels can be used as smoothness priors in recovering shape-from-shading (SFS). Conventionally, the smoothness error is added to the data-closeness (or brightness-error) as a quadratic regularizer. This leads to over-smoothing of the recovered needle-map or surface, and the loss of important detail provided by surface discontinuities. To solve this probl...

We present a new vectorial total variation (VTV) method that addresses the problem of color consistent image filtering. Our approach combines insights based on the double-opponent cell representation in the visual cortex with state-of-the-art variational modelling using VTV regularization. Existing methods of vectorial total variation regularizers have insufficient (even no) coupling between th...

The Total Variation denoising method, proposed by Rudin, Osher and Fatermi, 92, is a PDE-based algorithm for edge-preserving noise removal. The images resulting from its application are usually piecewise constant, possibly with a staircase eeect at smooth transitions and may contain signiicantly less ne details than the original non-degraded image. In this paper we present some extensions to th...

In this paper we study the decay of solutions to parabolic conservation laws in the Hardy space H 1 and in the total variation norm. We show that solutions to scalar equations and systems decay to zero without a rate in H 1 , and that the total variation of solutions decays to zero at an algebraic rate.

The flow of a Bingham fluid with inertial terms is simplified into a nonlinear hyperbolic scalar conservation law, regularised by the total variation flow operator (or 1-Laplacian). We give an entropy weak formulation, for which we prove the existence and the uniqueness of the solution. The existence result is established using the convergence of a numerical approximation (a splitting scheme wh...

This report relates to the field of image restorations and features extracting from noisy and blurred images. Since their introduction in a classical paper by Rudin, Osher and Fatemi [2], Total Variation (TV) minimising models have become one of the most popular and successful tools for image restorations. Whilst invariance under affine transformations is very important for many image processin...

Let Z > 0 be a random time. The total risk of discovering Z in the next time interval (t, t + dt) is never more variable than an exponential of mean one, which is achieved when the information up to time t is σ(Z ∧ t).

in this paper, we investigate the total variation diminishing property for a class of 2-stage explicit rung-kutta methods of order two (rk2) when applied to the numerical solution of special nonlinear initial value problems (ivps) for (odes). schemes preserving the essential physical property of diminishing total variation are of great importance in practice. such schemes are free of spurious o...