This paper proposes a new regularization term for optical flow related problems. The proposed regularizer properly handles rotation movements and it also produces good smoothness conditions on the flow field while preserving discontinuities. We also present a dual formulation of the new term that turns the minimization problem into a saddle-point problem that can be solved using a primal-dual a...

Image restoration is one of the most fundamental issues in imaging science. Total variation (TV) regularization is widely used in image restoration problems for its capability to preserve edges. In the literature, however, it is also well known for producing staircase-like artifacts. Usually, the high-order total variation (HTV) regularizer is an good option except its oversmoothing property. I...

We introduce a class of adaptive non-smooth convex variational problems for image denoising in terms of a common data fitting term and a support functional as regularizer. Adaptivity is modeled by a set-valued mapping with closed, compact and convex values, that defines and steers the regularizer depending on the variational solution. This extension gives rise to a class of quasi-variational in...

The fundamental problem of de-noising and de-blurring images is addressed in this study. The great difficulty in this task is due to the ill-posedness of the problem. We suggest to analyze multi-channel images to gain robustness and to regularize it by the Polyakov action which provides an anisotropic smoothing term that use intra-channel information. Blind de-convolution is then solved by addi...

Convex regularizers are often used for sparse learning. They are easy to optimize, but can lead to inferior prediction performance. The difference of `1 and `2 (`1-2) regularizer has been recently proposed as a nonconvex regularizer. It yields better recovery than both `0 and `1 regularizers on compressed sensing. However, how to efficiently optimize its learning problem is still challenging. T...

In this paper we introduce a novel higher-order regularization term. The proposed regularizer is a non-local extension of the popular second-order Total Generalized variation, which favors piecewise affine solutions and allows to incorporate soft-segmentation cues into the regularization term. These properties make this regularizer especially appealing for optical flow estimation, where it offe...

This paper presents a regularized fuzzy c-means clustering method for brain tissue segmentation from magnetic resonance images. A regularizer of the total variation type is explored and a method to estimate the regularization parameter is proposed. 2007 Elsevier B.V. All rights reserved.