Unbiased Group-wise Alignment by Iterative Central Tendency Estimation

Abstract. This paper introduces a new approach for the joint alignment of a large collection of segmented images into the same system of coordinates while estimating at the same time an opti-mal common coordinate system. The atlas resulting from our group-wise alignment algorithm is obtained as the hidden variable of an Expectation-Maximization (EM) estimation. This is achieved by identifying the most consistent label across the collection of images at each voxel in the com-mon frame of coordinates. In an iterative process, each subject is iteratively aligned with the current probabilistic atlas until convergence of the estimated atlas is reached. Two different transformation models are suc-cessively applied in the alignment process: an affine transformation model and a dense non-rigid deformation field. The metric for both transformation models is the mutual information that is computed between the probabilistic atlas and each subject. This metric is optimized in the affine alignment step using a gradient based stochastic optimization (SPSA) and with a variational ap-proach to estimate the non-rigid atlas to subject transformations. A first advantage of our method is that the computational cost increases linearly with the num-ber of subjects in the database. This method is therefore particularly suited for a large number o