Feature Guided Biased Gaussian Mixture Model for image matching

In this article we propose a Feature Guided Biased Gaussian Mixture Model (FGBG) for image matching. We formulate the matching task as a Maximum a Posteriori (MAP) problem by seeing one point set as the centroid of a Gaussian Mixture Model (GMM) and the other point set as the data. A Thin Plate Spline (TPS) transformation between the two point sets is learnt so that the GMM can best fit the data. Our main contribution is to assign each Gaussian mixture component a different weight. This is where our model differs from the traditional Self Governed Balanced Gaussian Mixture Model (SGBG), whose Gaussian mixture components have equal coefficients. The new weight is defined as a value related to feature similarity, which can be computed by simply decomposing a distance matrix in the feature space. In this way, both feature similarity and spatial arrangement are considered. The feature descriptor is introduced as a reasonable prior to guide the matching, and the spatial transformation offers a global constraint so that local ambiguity can be alleviated. We solve this MAP problem in a framework similar to [16], in which Deterministic Annealing and the Expectation Maximization (EM) algorithms are used. We show that our FGBG algorithm is robust to outliers, deformation and rotation. Extensive experiments on self-collected and the latest open access data sets show that FGBG can boost the number of correct matches.