A Graph Spectral Approach to Consistent Labelling

  • Hongfang Wang
  • Edwin R. Hancock
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4142)


In this paper a new formulation of probabilistic relaxation labeling is developed using the theory of diffusion processes on graphs. Our idea is to formulate relaxation labelling as a diffusion process on the vector of object-label probabilities. According to this picture, the label probabilities are given by the state-vector of a continuous time random walk on a support graph. The state-vector is the solution of the heat equation on the support-graph. The nodes of the support graph are the Cartesian product of the object-set and label-set of the relaxation process. The compatibility functions are combined in the weight matrix of the support graph. The solution of the heat-equation is found by exponentiating the eigensystem of the Laplacian matrix for the weighted support graph with time. We demonstrate the new relaxation process on a toy labeling example which has been studied extensively in the early literature, and a feature correspondence matching problem abstracted in terms of relational graphs. The experiments show encouraging labeling and matching results.


Heat Equation Label Probability Diffusion Kernel Compatibility Function Hazard Rate Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Hongfang Wang
    • 1
  • Edwin R. Hancock
    • 1
  1. 1.Dept. of Computer ScienceUniversity of YorkHeslington, YorkUK

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