Manifold learning for shape guided segmentation of cardiac boundaries: application to 3D+t cardiac MRI

In this paper we propose a new method for shape guided segmentation of cardiac boundaries based on manifold learning of the shapes represented by the phase field approximation of the Mumford-Shah functional. A novel distance is defined to measure the similarity of shapes without requiring deformable registration. Cardiac motion is compensated and phases are mapped into one reference phase, that is the end of diastole, to avoid time warping and synchronization at all cardiac phases. Non-linear embedding of these 3D shapes extracts the manifold of the inter-subject variation of the heart shape to be used for guiding the segmentation for a new subject. For validation the method is applied to a comprehensive dataset of 3D+t cardiac Cine MRI from normal subjects and patients.