The mixtures of Student's t-distributions as a robust framework for rigid registration

The problem of registering images or point sets is addressed. At first, a pixel similarity-based algorithm for the rigid registration between single and multimodal images is presented. The images may present dissimilarities due to noise, missing data or outlying measures. The method relies on the partitioning of a reference image by a Student's t-mixture model (SMM). This partition is then projected onto the image to be registered. The main idea is that a t-component in the reference image corresponds to a t-component in the image to be registered. If the images are correctly registered the distances between the corresponding components is minimized. Moreover, the extension of the method to the registration of point clouds is also proposed. The use of SMM components is justified by the property that they have heavier tails than standard Gaussians, thus providing robustness to outliers. Experimental results indicate that, even in the case of low SNR or important amount of dissimilarities due to temporal changes, the proposed algorithm compares favorably to the mutual information method for image registration and to the Iterative Closest Points (ICP) algorithm for the alignment of point sets.