Related papers: Continuous Multiclass Labeling Approaches and Algo…
In this work we show how sublabel-accurate multilabeling approaches can be derived by approximating a classical label-continuous convex relaxation of nonconvex free-discontinuity problems. This insight allows to extend these…
We consider a class of infinite-dimensional optimization problems in which a distributed vector-valued variable should pointwise almost everywhere take values from a given finite set $\mathcal{M}\subset\mathbb{R}^m$. Such hybrid…
In recent years, there has been a growing interest in mathematical models leading to the minimization, in a symmetric matrix space, of a Bregman divergence coupled with a regularization term. We address problems of this type within a…
Motivated by nonconvex, inconsistent feasibility problems in imaging, the relaxed alternating averaged reflections algorithm, or relaxed Douglas-Rachford algorithm (DR$\lambda$), was first proposed over a decade ago. Convergence results for…
We present a novel convex relaxation and a corresponding inference algorithm for the non-binary discrete tomography problem, that is, reconstructing discrete-valued images from few linear measurements. In contrast to state of the art…
We consider a variational convex relaxation of a class of optimal partitioning and multiclass labeling problems, which has recently proven quite successful and can be seen as a continuous analogue of Linear Programming (LP) relaxation…
We present a variational multi-label segmentation algorithm based on a robust Huber loss for both the data and the regularizer, minimized within a convex optimization framework. We introduce a novel constraint on the common areas, to bias…
Graph-based variational methods have recently shown to be highly competitive for various classification problems of high-dimensional data, but are inherently difficult to handle from an optimization perspective. This paper proposes a convex…
Relying on the co-area formula, an exact relaxation framework for minimizing objectives involving the total variation of a binary valued function (of bounded variation) is presented. The underlying problem class covers many important…
In two-phase image segmentation, convex relaxation has allowed global minimisers to be computed for a variety of data fitting terms. Many efficient approaches exist to compute a solution quickly. However, we consider whether the nature of…
We propose a novel spatially continuous framework for convex relaxations based on functional lifting. Our method can be interpreted as a sublabel-accurate solution to multilabel problems. We show that previously proposed functional lifting…
This work proposes a novel convex-non-convex formulation of the image segmentation and the image completion problems. The proposed approach is based on the minimization of a functional involving two distinct regularization terms: one…
We propose a functional lifting-based convex relaxation of variational problems with Laplacian-based second-order regularization. The approach rests on ideas from the calibration method as well as from sublabel-accurate continuous…
This paper explores the role of regularization in data-driven predictive control (DDPC) through the lens of convex relaxation. Using a bi-level optimization framework, we model system identification as an inner problem and predictive…
Convex relaxations of nonconvex multilabel problems have been demonstrated to produce superior (provably optimal or near-optimal) solutions to a variety of classical computer vision problems. Yet, they are of limited practical use as they…
Dual decomposition approaches in nonconvex optimization may suffer from a duality gap. This poses a challenge when applying them directly to nonconvex problems such as MAP-inference in a Markov random field (MRF) with continuous state…
We propose a novel framework for the discretisation of multi-label problems on arbitrary, continuous domains. Our work bridges the gap between general FEM discretisations, and labeling problems that arise in a variety of computer vision…
In this paper, we present a novel deep metric learning method to tackle the multi-label image classification problem. In order to better learn the correlations among images features, as well as labels, we attempt to explore a latent space,…
This article introduces a generalization of the discrete optimal transport, with applications to color image manipulations. This new formulation includes a relaxation of the mass conservation constraint and a regularization term. These two…
In this work, we study complex-valued data detection performance in massive multiple-input multiple-output (MIMO) systems. We focus on the problem of recovering an $n$-dimensional signal whose entries are drawn from an arbitrary…