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A Probabilistic Approach to Spectral Graph Matching
Jan. 2013 (vol. 35 no. 1)
pp. 18-27
A. Egozi, Dept. of Electr. Eng., Ben Gurion Univ., Beer-Sheva, Israel
Y. Keller, Fac. of Eng., Bar Ilan Univ., Ramat-Gan, Israel
H. Guterman, Dept. of Electr. Eng., Ben Gurion Univ., Beer-Sheva, Israel
Spectral Matching (SM) is a computationally efficient approach to approximate the solution of pairwise matching problems that are np-hard. In this paper, we present a probabilistic interpretation of spectral matching schemes and derive a novel Probabilistic Matching (PM) scheme that is shown to outperform previous approaches. We show that spectral matching can be interpreted as a Maximum Likelihood (ML) estimate of the assignment probabilities and that the Graduated Assignment (GA) algorithm can be cast as a Maximum a Posteriori (MAP) estimator. Based on this analysis, we derive a ranking scheme for spectral matchings based on their reliability, and propose a novel iterative probabilistic matching algorithm that relaxes some of the implicit assumptions used in prior works. We experimentally show our approaches to outperform previous schemes when applied to exhaustive synthetic tests as well as the analysis of real image sequences.
Index Terms:
maximum likelihood estimation,data analysis,graph theory,image matching,image sequences,iterative methods,data analysis,spectral graph matching,SM,pairwise matching problems,NP-hard,PM,maximum likelihood estimation,ML estimation,assignment probabilities,graduated assignment algorithm,GA,maximum a posteriori estimator,MAP estimator,ranking scheme,iterative probabilistic matching algorithm,exhaustive synthetic tests,real image sequences,Probabilistic logic,Vectors,Entropy,Reliability,Maximum likelihood estimation,Kernel,Convergence,point matching,Graphs,spectral matching,probabilistic matching
Citation:
A. Egozi, Y. Keller, H. Guterman, "A Probabilistic Approach to Spectral Graph Matching," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 35, no. 1, pp. 18-27, Jan. 2013, doi:10.1109/TPAMI.2012.51
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