Deformable Graph Matching

Feng Zhou,Fernando De La Torre

doi:10.1109/cvpr.2013.376

Abstract

Graph matching (GM) is a fundamental problem in computer science, and it has been successfully applied to many problems in computer vision. Although widely used, existing GM algorithms cannot incorporate global consistence among nodes, which is a natural constraint in computer vision problems. This paper proposes deformable graph matching (DGM), an extension of GM for matching graphs subject to global rigid and non-rigid geometric constraints. The key idea of this work is a new factorization of the pair-wise affinity matrix. This factorization decouples the affinity matrix into the local structure of each graph and the pair-wise affinity edges. Besides the ability to incorporate global geometric transformations, this factorization offers three more benefits. First, there is no need to compute the costly (in space and time) pair-wise affinity matrix. Second, it provides a unified view of many GM methods and extends the standard iterative closest point algorithm. Third, it allows to use the path-following optimization algorithm that leads to improved optimization strategies and matching performance. Experimental results on synthetic and real databases illustrate how DGM outperforms state-of-the-art algorithms for GM. The code is available at http://humansensing.cs.cmu.edu/fgm.

Highlights

Graph matching (GM) has been widely applied in computer vision to solve a variety of problems such as object categorization [10], feature tracking [13, 17], symmetry analysis [12], kernelized sorting [20] and action recognition [3]
This paper proposes deformable graph matching (DGM), an extension of GM for matching points under a global geometric transformation for directed and undirected graphs
The key idea for DGM is a novel factorization of the pairwise affinity matrix

Summary

Introduction

Graph matching (GM) has been widely applied in computer vision to solve a variety of problems such as object categorization [10], feature tracking [13, 17], symmetry analysis [12], kernelized sorting [20] and action recognition [3]. In order to incorporate global transformations, the key idea of our method is to factorize the pairwise affinity matrix into matrices that preserve the local structure of each graph and matrices that encode the similarity between nodes and edges. This factorization is general and can be applied to both directed and undirected graphs. There is no need to compute the costly (in space and time) pair-wise affinity matrix It provides a unified view of many GM methods, which allows to understand the commonalities and differences between them. We illustrate the benefits of DGM in synthetic and real matching experiments on standard databases

Previous works

Factorized graph matching

A path-following algorithm

Objective function

Optimization

Experiments

CMU house image dataset

Car and motorbike image dataset

Fish and character shape dataset

Conclusions