Probabilistic relaxation labelling using the Fokker–Planck equation

In this paper we develop a new formulation of probabilistic relaxation labelling using the theory of diffusion processes on graphs. Our aim is to tackle the problem of labelling objects consistently and unambiguously using information concerning label consistency and initial label probabilities. We abstract this problem using a support graph with each graph node an object-label assignment. Initial object-label probabilities then evolve across the graph under the governance of the Fokker–Planck equation in terms of an infinitesimal generator matrix computed from the edge weights of the support graph. In this way we effectively kernelise probabilistic relaxation. Encouraging results are obtained in applying the new relaxation process in the applications of scene labelling, data classification, and feature correspondence matching.