Related papers: Fast Convex Relaxations using Graph Discretization…

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…

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…

Motivated by a geometric problem, we introduce a new non-convex graph partitioning objective where the optimality criterion is given by the sum of the Dirichlet eigenvalues of the partition components. A relaxed formulation is identified…

Dense image matching is a fundamental low-level problem in Computer Vision, which has received tremendous attention from both discrete and continuous optimization communities. The goal of this paper is to combine the advantages of discrete…

Semi-supervised clustering is a basic problem in various applications. Most existing methods require knowledge of the ideal cluster number, which is often difficult to obtain in practice. Besides, satisfying the must-link constraints is…

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…

Graph matching---aligning a pair of graphs to minimize their edge disagreements---has received wide-spread attention from both theoretical and applied communities over the past several decades, including combinatorics, computer vision, and…

We address the problem of minimizing a class of energy functions consisting of data and smoothness terms that commonly occur in machine learning, computer vision, and pattern recognition. While discrete optimization methods are able to give…

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…

The most commonly used method to tackle the graph partitioning problem in practice is the multilevel approach. During a coarsening phase, a multilevel graph partitioning algorithm reduces the graph size by iteratively contracting nodes and…

Given a connected undirected weighted graph, we are concerned with problems related to partitioning the graph. First of all we look for the closest disconnected graph (the minimum cut problem), here with respect to the Euclidean norm. We…

We propose a convex-concave programming approach for the labeled weighted graph matching problem. The convex-concave programming formulation is obtained by rewriting the weighted graph matching problem as a least-square problem on the set…

This paper introduces a discrete relaxation for the class of combinatorial optimization problems which can be described by a set partitioning formulation under packing constraints. We present two combinatorial relaxations based on computing…

This work combines three paradigms of image processing: i) the total variation approach to denoising, ii) the superior structure of hexagonal lattices, and iii) fast and exact graph cut optimization techniques. Although isotropic in theory,…

Graphs provide an efficient tool for object representation in various computer vision applications. Once graph-based representations are constructed, an important question is how to compare graphs. This problem is often formulated as a…

This paper proposes a new algorithm for simultaneous graph matching and clustering. For the first time in the literature, these two problems are solved jointly and synergetically without relying on any training data, which brings advantages…

In this paper we derive a moment relaxation for large-scale nonsmooth optimization problems with graphical structure and spherical constraints. In contrast to classical moment relaxations for global polynomial optimization that suffer from…

A common way of partitioning graphs is through minimum cuts. One drawback of classical minimum cut methods is that they tend to produce small groups, which is why more balanced variants such as normalized and ratio cuts have seen more…

In the constraint programming framework, state-of-the-art static and dynamic decomposition techniques are hard to apply to problems with complete initial constraint graphs. For such problems, we propose a hybrid approach of these techniques…

Exact solution of hard combinatorial optimization problems often relies on strong convex relaxations, but solving these relaxations repeatedly inside a branch-and-bound algorithm can be prohibitively expensive. Hence, we consider this…