A Dual Ascent Framework for Lagrangean Decomposition of Combinatorial Problems

Swoboda, Paul; Kuske, Jan; Savchynskyy, Bogdan

doi:10.1109/cvpr.2017.526

Cited by 25 publications

(35 citation statements)

References 61 publications

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“…Hence, for solving QAPs in practice, existing approaches either resort to (expensive) branch and bound methods [6], or to approximations, e.g. based on spectral methods [35,18], dual decomposition [57], linear relaxations [54,55], convex relaxations [71,46,23,22,30,1,21,7], path following [70,72,29], or alternating directions [33].…”

Section: Related Workmentioning

confidence: 99%

Synchronisation of partial multi-matchings via non-negative factorisations

Bernard

Thunberg

Theobalt

2019

Pattern Recognition

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In this work we study permutation synchronisation for the challenging case of partial permutations, which plays an important role for the problem of matching multiple objects (e.g. images or shapes). The term synchronisation refers to the property that the set of pairwise matchings is cycle-consistent, i.e. in the full matching case all compositions of pairwise matchings over cycles must be equal to the identity. Motivated by clustering and matrix factorisation perspectives of cycle-consistency, we derive an algorithm to tackle the permutation synchronisation problem based on non-negative factorisations. In order to deal with the inherent non-convexity of the permutation synchronisation problem, we use an initialisation procedure based on a novel rotation scheme applied to the solution of the spectral relaxation. Moreover, this rotation scheme facilitates a convenient Euclidean projection to obtain a binary solution after solving our relaxed problem. In contrast to state-of-the-art methods, our approach is guaranteed to produce cycle-consistent results. We experimentally demonstrate the efficacy of our method and show that it achieves better results compared to existing methods.

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Section: Related Workmentioning

confidence: 99%

Synchronisation of partial multi-matchings via non-negative factorisations

Bernard

Thunberg

Theobalt

2019

Pattern Recognition

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“…In this section we will first present the multi-graph matching problem with quadratic costs. Next, we review the Lagrange decomposition framework [34] and show how it can be applied to decompose the MGM into efficiently solvable subproblems. We also review the message passing algorithm from [34] for general decompositions and detail how our MGM decomposition can be optimized by this method.…”

Section: Lagrangian Mgm Relaxationmentioning

confidence: 99%

A Convex Relaxation for Multi-Graph Matching

Swoboda

Kainmüller²,

Mokarian

et al. 2019

2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)

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We present a convex relaxation for the multi-graph matching problem. Our formulation allows for partial pairwise matchings, guarantees cycle consistency, and our objective incorporates both linear and quadratic costs. Moreover, we also present an extension to higher-order costs. In order to solve the convex relaxation we employ a message passing algorithm that optimizes the dual problem. We experimentally compare our algorithm on established benchmark problems from computer vision, as well as on large problems from biological image analysis, the size of which exceed previously investigated multi-graph matching instances.

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“…In this section we define a general algorithm for IRPS-LP problems (5), which is applicable to the decompositions (R1)-(R5) of the graph matching problem considered in Section 3.1. Our algorithm is a simplified version of the algorithm [49], where we fixed several parameters to the values common to the relaxations (R1)-(R5).…”

Section: General Algorithmmentioning

confidence: 99%

“…Since Algorithm 2 reparametrizes the problem by Procedure 1 only and the latter is guaranteed to not decrease the dual, so is Algorithm 2. We refer to [49] for further theoretical properties of Algorithm 2.…”

Section: Dualmentioning

confidence: 99%

A Study of Lagrangean Decompositions and Dual Ascent Solvers for Graph Matching

Swoboda

Rother

Alhaija

et al. 2017

2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)

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We study the quadratic assignment problem, in computer vision also known as graph matching. Two leading solvers for this problem optimize the Lagrange decomposition duals with sub-gradient and dual ascent (also known as message passing) updates. We explore this direction further and propose several additional Lagrangean relaxations of the graph matching problem along with corresponding algorithms, which are all based on a common dual ascent framework. Our extensive empirical evaluation gives several theoretical insights and suggests a new state-of-the-art anytime solver for the considered problem. Our improvement over state-of-the-art is particularly visible on a new dataset with large-scale sparse problem instances containing more than 500 graph nodes each.

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A Dual Ascent Framework for Lagrangean Decomposition of Combinatorial Problems

Cited by 25 publications

References 61 publications

Synchronisation of partial multi-matchings via non-negative factorisations

Synchronisation of partial multi-matchings via non-negative factorisations

A Convex Relaxation for Multi-Graph Matching

A Study of Lagrangean Decompositions and Dual Ascent Solvers for Graph Matching

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