EM-ICP strategies for joint mean shape and correspondences estimation: Applications to statistical analysis of shape and of asymmetry

In this paper, we propose a new approach to compute the mean shape of unstructured, unlabelled point sets with an arbitrary number of points. This approach can be seen as an extension of the EM-ICP algorithm, where the fuzzy correspondences between each point set and the mean shape, the optimal non-linear transformations superposing them, and the mean shape itself, are iteratively estimated. Once the mean shape is computed, one can study the variability around this mean shape (e.g. using PCA) or perform statistical analysis of local anatomical characteristics (e.g. cortical thickness, asymmetry, curvature). To illustrate our method, we perform statistical shape analysis on human osseous labyrinths and statistical analysis of global cortical asymmetry on control subjects and subjects with situs inversus.