Image registration using radial basis functions with adaptive radius

Purpose: Deformable registration of medical images often requires initial rigid alignment. Because of variations in the articulation of bony structures, rigid alignment can capture only limited regions of the image. We propose a method that allows us to compensate for misalignment of mobile parts, which leads to improved accuracy of deformable registration. The method is based on matching landmarks using radial basis functions (RBF) with adaptive radius. Methods: Based on the assumption that the compactly positioned landmarks likely delineate an anatomic structure whose position needs to be corrected, the algorithm incorporates unsupervised clustering of landmarks based on their positions within the reference image. It calculates an appropriate RBF radius based on the set of pairwise distances between landmarks within the cluster. The algorithm distinguishes between clusters of different size and between clusters of spherical and elongated shape, and assigns the optimal RBF radius for each cluster in order to restrict the deformation field to the closest vicinity of the structure of interest. Results: Experiments with synthetic images demonstrate sensitivity of registration results to the choice of the radius of RBF support. We have statistically validated the methods on a large set of pulmonary landmarks. We also tested the method on medical use cases that show that it is potentially advantageous for initial registration of images with large spatial dislocations. Conclusions: The results of registration of CT images demonstrate that an automated selection of the RBF radius simplifies the registration routine and improves the registration quality. The selection is based on two criteria of preserving diffeomorphism of deformation and localization of the deformation within a desired area of the image.