Fast correspondences for statistical shape models of brain structures

Statistical shape models based on point distribution models are powerful tools for image segmentation or shape analysis. The most challenging part in the generation of point distribution models is the identification of corresponding landmarks among all training shapes. Since in general the true correspondences are unknown, correspondences are frequently established under the hypothesis that correct correspondences lead to a compact model, which is mostly tackled by continuous optimisation methods. In favour of the prospect of an efficient optimisation, we present a simplified view of the correspondence problem for statistical shape models that is based on point-set registration, the linear assignment problem and mesh fairing. At first, regularised deformable point-set registration is performed and combined with solving the linear assignment problem to obtain correspondences between shapes on a global scale. With that, rough correspondences are established that may not yet be accurate on a local scale. Then, by using a mesh fairing procedure, consensus of the correspondences on a global and local scale among the entire set of shapes is achieved. We demonstrate that for the generation of statistical shape models of deep brain structures, the proposed approach is preferable over existing population-based methods both in terms of a significantly shorter runtime and in terms of an improved quality of the resulting shape model.