ABSTRACT
In this work, we investigate the computation on a shape manifold for atlas generation and application to atlas propagation and segmentation. We formulate the computation of Fr´echet mean via the constant velocity fields and Log-Euclidean framework for Nadaraya-Watson kernel regression modeling. In this formulation, we directly compute the Fr´echet mean of shapes via fast vectorial operations on the velocity fields. By using image similarity metric to estimate the distance of shapes in the assumed manifold, we can estimate a close shape of an unseen image using Naderaya-Watson kernel regression function. We applied this estimation to generate subject-specific atlases for whole heart segmentation of MRI data. The segmentation results on clinical data demonstrated an improved performance compared to existing methods, thanks to the usage of subject-specific atlases which had more similar shapes to the unseen images.
