Joint registration of multiple images using entropie graphs

Registration of medical images (intra- or multi-modality) is the first step before any analysis is performed. The analysis includes treatment monitoring, diagnosis, volumetric measurements or classification to mention a few. While pairwise registration, i.e., aligning a floating image to a fixed reference, is straightforward, it is not immediately clear what cost measures could be exploited for the groupwise alignment of several images (possibly multimodal) simultaneously. Recently however there has been increasing interest in this problem applied to atlas construction, statistical shape modeling, or simply joint alignment of images to get a consistent correspondence of voxels across all images based on a single cost measure. The aim of this paper is twofold, a) propose a cost function - alpha mutual information computed using entropic graphs that is a natural extension to Shannon mutual information for pairwise registration and b) compare its performance with the pairwise registration of the image set. We show that this measure can be reliably used to jointly align several images to a common reference. We also test its robustness by comparing registration errors for the registration process repeated at varying noise levels. In our experiments we used simulated data, applying different B-spline based geometric transformations to the same image and adding independent filtered Gaussian noise to each image. Non-rigid registration was employed with Thin Plate Splines(TPS) as the geometric interpolant.