Deformation field interpolation using rotational landmarks

In this paper, we present a novel method for landmark-based deformation field interpolation that incorporates the rotation information for use in curved medical image registration applications. To this end, each Cartesian component of the interpolated deformation field was modeled by a mixture of Gaussian radial basis functions. The mixture coefficients were identified by optimizing an energy functional that seeks to match the landmark positions as well as the orientations of their neighborhoods. Optimization of this functional was carried out via a gradient descent strategy using the closed-form expressions of the partial derivatives with respect to the Gaussian radial basis function coefficients. In the experiments, grater accuracy was observed in the estimation of the unknown deformation fields when the rotation information was incorporated in the interpolation. These results indicate that the proposed scheme can achieve greater accuracy in deformation field interpolation, especially in deformable alignment of multimodality medical images for which the landmarks have to be matched by taking into account the proper orientations of their neighborhoods.