A Complementary Pivoting Approach to Graph Matching

  • Authors:

  • Alessio Massaro;Marcello Pelillo

  • Affiliations:

  • -;-

  • Venue:
  • EMMCVPR '01 Proceedings of the Third International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition
  • Year:
  • 2001

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Abstract

Graph matching is a problem that pervades computer vision and pattern recognition research. During the past few decades, two radically distinct approaches have been pursued to tackle it. The first views the matching problem as one of explicit search in state-space. A classical method within this class consists of transforming it in the equivalent problem of finding a maximal clique in a derived "association graph." In the second approach, the matching problem is viewed as one of energy minimization. Recently, we have provided a unifying framework for graph matching which is centered around a remarkable result proved by Motzkin and Straus in the mid-sixties. This allows us to formulate the maximum clique problem in terms of a continuous quadratic optimization problem. In this paper we propose a new framework for graph matching based on the linear complementarity problem (LCP) arising from the Motzkin-Straus program. We develop a pivoting-based technique to find a solutions for our LCP which is a variant of Lemke's well-known method. Preliminary experiments are presented which demonstrate the effectiveness of the proposed approach.