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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References
Chui, H., Rangarajan, A.: A new point matching algorithm for non-rigid registration. Computer Vision and Image Understanding 89, 114–141 (2003)
Chung, F.R.K.: Spectral Graph Theory. American Mathematical Society, Regional Conference Series in Mathematics 92 (1997)
Doyle, P., Snell, J.: Random walks and electric networks. Mathematical Assoc. of America (1984)
Faber, P.: A theoretical framework for relaxation processes in pattern recognition: application to robust nonparametric contour generalization. IEEE Trans. PAMIÂ 25(8) (2003)
Faugeras, O., Berthod, M.: Improving consistency and reducing ambiguity in stochastic labeling: An optimization approach. IEEE Trans. PAMIÂ 3(4) (1981)
Geman, S., Geman, D.: Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Trans. PAMIÂ 6(6) (1984)
Hummel, R.A., Zucker, S.W.: On the foundations of relaxation labeling processes. IEEE Trans. Pattern Anal. Machine Intell. l.PAMI-5, 267 (1983)
Kittler, J., Hancock, E.R.: Combining evidence in probabilistic relaxation. Intern. J. Pattern Recognition And Artificial Inteligence 3(1), 29–51 (1989)
Kondor, R.I., Lafferty, J.: Diffusion kernels on graphs and other discrete input spaces. In: ICML (2002)
Li, S.Z.: Markov random field modeling in image analysis. Springer, Heidelberg (2001)
Moler, C., van Loan, C.: Nineteen dubious ways to compute the exponential of a matrix. SIAM Review 20, 801–836 (1978)
Pelillo, M., Refice, M.: Learning compatibility coefficients for relaxation labeling processes. IEEE Trans. PAMI 16(9), 933–945 (1994)
Pelillo, M.: Relaxation labeling networks for the maximum clique problem. Journal of Artificial Neural Networks 2(4), 313–328 (1995)
Rosenfeld, A., Hummel, R., Zucker, S.: Scene labeling by relaxation operations. IEEE Trans. System. Man and Cybernetics 6, 420–433 (1976)
Ross, S.: Stochastic Processes. John Wiley & Sons Inc., Chichester (1996)
Smola, A.J., Kondor, R.: Kernels and regularization on graphs. In: Warmuth, M., Schökopf, B. (eds.) Proc. Conf. on Learning Theory and Kernels Workshop (2003)
Vapnik, V.N.: Statistical Learning Theory. John Wiley & Sons, Inc., Chichester (1998)
Waltz, D.L.: Generating semantic descriptions from drawings of scenes with shadows. Technical Report 271, MIT AI Lab (1972)
Wilson, R.C., Hancock, E.R.: A bayesian compatibility model for graph matching. Pattern Recognition Letters 17, 263–276 (1996)
Wilson, R.C., Hancock, E.R.: Structural matching by discrete relaxation. IEEE PAMI 19(6), 634–648 (1997)
Zheng, Y., Doermann, D.: Robust Point Matching for Two-Dimensional Nonrigid Shapes. In: Proceedings IEEE Conf. on Computer Vision (2005)
Zhu, X., Ghahramani, Z., Lafferty, J.: Semi-supervised learning using Gaussian fields and harmonic functions. In: ICML 2003 (2003)
Zucker, S.W.: Relaxation labeling: 25 years and still iterating. In: Davis, L.S. (ed.) Foundations of Image Understanding, Kluwer Academic Publ., Boston (2001)
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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
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