Abstract
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.
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Wang, H., Hancock, E.R. (2006). A Graph Spectral Approach to Consistent Labelling. In: Campilho, A., Kamel, M. (eds) Image Analysis and Recognition. ICIAR 2006. Lecture Notes in Computer Science, vol 4142. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11867661_6
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DOI: https://doi.org/10.1007/11867661_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-44894-5
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