A robust non-rigid point set registration method based on inhomogeneous Gaussian mixture models

In this paper, we propose a novel robust non-rigid point set registration method adopting a new probability model called inhomogeneous Gaussian mixture models (IGMM), where we regard one point set as the centroids of a Gaussian mixture model and the other point set as the data. The IGMM is defined by applying local features and Gaussian mixture models. Considering the local relationship among neighboring points is stable, a neighborhood structural descriptor, named as local shape context, is first presented. On the basis of local descriptors, we can obtain a measure of compatibility between local features in the point sets. Then, the similarity of the local structure of point neighborhoods can be calculated on the basis of the matching scores. Each Gaussian mixture component is assigned a different weight depending on the feature similarity, which differs from the traditional Gaussian mixture model where each Gaussian mixture component has the same weight. The proposed IGMM makes point pairs with more similar features have bigger probability to formulate a match, while in algorithms based on GMMs, all point pairs have the same probability to construct correspondence points. Finally, we support our claims through regularization theory and formulate registration as a likelihood maximization problem, which is solved by updating transformation parameters and outlier ratios using the expectation maximization algorithm. Extensive comparison and evaluation experiments on synthetic point-sets datasets demonstrate that the proposed approach is robust and achieves superior performance in the presence of non-rigid deformation, noise, outliers and occlusion. In addition, a number of experiments on real images reveal that our proposed algorithm is more applicable than state-of-the-art algorithms.