In this paper, we propose a variational approach for the affine point set matching problems under the Bayesian probabilistic framework. A directed acyclic graph is provided for the representation of the joint probability over affine transformation, random variables and the point sets. Based on the directed graph, a variational iterative algorithm is derived to approximate the posteriors of the random variables and the anisotropic Gaussian mixtures are used for the estimation of the spurious outliers instead of the frequently-used uniform distribution. Experimental results demonstrate that our method achieves good performance in terms of both robustness and accuracy and is comparable to other state-of-the-art point registration algorithms especially in the case of complicated outliers.
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