A NOVEL APPROACH FOR PART BASED OBJECT MATCHING USING DISTANCE METRIC LEARNING WITH GRAPH CONVOLUTIONAL NETWORKS

Abstract. Part-based object representation and part matching problem often appear in various areas of data analysis. A special case of particular interest is when parts are not fully separated, but in relations with each other. The natural way to model such objects are graphs, and part matching problem becomes graph matching problem. Over the years, many methods to solve graph matching problems have been proposed, but it remains relevant due to its complexity. We propose a novel approach to solving graph matching problem based on learning distance metric on graph vertices. We empirically demonstrate that our method outperforms traditional methods based on solving quadratic assignment problem. We also provide an theoretical estimation of computational complexity of proposed method.

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Constrained Nets for Graph Matching and Other Quadratic Assignment Problems

Neural Computation ◽

10.1162/neco.1991.3.2.268 ◽

1991 ◽

Vol 3 (2) ◽

pp. 268-281 ◽

Cited By ~ 57

Author(s):

Petar D. Simić

Keyword(s):

Graph Matching ◽

Optimization Problems ◽

Quadratic Assignment Problem ◽

Semiclassical Approximation ◽

Geometric Optimization ◽

Elastic Net ◽

Physical Models ◽

Quadratic Assignment ◽

Matching Problem ◽

Special Case

Some time ago Durbin and Willshaw proposed an interesting parallel algorithm (the “elastic net”) for approximately solving some geometric optimization problems, such as the Traveling Salesman Problem. Recently it has been shown that their algorithm is related to neural networks of Hopfield and Tank, and that they both can be understood as the semiclassical approximation to statistical mechanics of related physical models. The main point of the elastic net algorithm is seen to be in the way one deals with the constraints when evaluating the effective cost function (free energy in the thermodynamic analogy), and not in its geometric foundation emphasized originally by Durbin and Willshaw. As a consequence, the elastic net algorithm is a special case of the more general physically based computations and can be generalized to a large class of nongeometric problems. In this paper we further elaborate on this observation, and generalize the elastic net to the quadratic assignment problem. We work out in detail its special case, the graph matching problem, because it is an important problem with many applications in computational vision and neural modeling. Simulation results on random graphs, and on structured (hand-designed) graphs of moderate size (20-100 nodes) are discussed.

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Dynamic Programming Bipartite Belief Propagation For Hyper Graph Matching

Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence ◽

10.24963/ijcai.2017/650 ◽

2017 ◽

Cited By ~ 2

Author(s):

Zhen Zhang ◽

Julian McAuley ◽

Yong Li ◽

Wei Wei ◽

Yanning Zhang ◽

...

Keyword(s):

Dynamic Programming ◽

Graphical Models ◽

Belief Propagation ◽

Graph Matching ◽

Matching Problem ◽

Bipartite Matching ◽

Matching Problems ◽

Inference Problems ◽

Order Relations ◽

Traditional Approaches

Hyper graph matching problems have drawn attention recently due to their ability to embed higher order relations between nodes. In this paper, we formulate hyper graph matching problems as constrained MAP inference problems in graphical models. Whereas previous discrete approaches introduce several global correspondence vectors, we introduce only one global correspondence vector, but several local correspondence vectors. This allows us to decompose the problem into a (linear) bipartite matching problem and several belief propagation sub-problems. Bipartite matching can be solved by traditional approaches, while the belief propagation sub-problem is further decomposed as two sub-problems with optimal substructure. Then a newly proposed dynamic programming procedure is used to solve the belief propagation sub-problem. Experiments show that the proposed methods outperform state-of-the-art techniques for hyper graph matching.

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