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In this work, we propose a combinative strategy based on regression and clustering for solving point set matching problems under a Bayesian framework, in which the regression estimates the transformation from the model to the sceneand the clustering establishes the correspondence between two point sets. The point set matching model is illustrated by a hierarchical directed graph, and the matching uncertainties are approximated by a coarse-to-fine variational inference algorithm. Furthermore, two Gaussian mixtures are proposed for the estimation of heteroscedastic noise and spurious outliers, and an isotropic or anisotropic covariance can be imposed on each mixture in terms of the transformed model points. The experimental results show that the proposed approach achieves comparable performance to state-of-the-art matching or registration algorithms in terms of both robustness and accuracy.

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