Branching medial models for cardiac shape representation

The cm-rep (continuous medial representation) is a powerful shape representation method that models a 3D object by describing its medial axis (skeleton) and boundary as continuous parametric manifolds. It provides parametrization of the entire interior of the object, which can be used for combined statistical analysis of shape and appearance. This paper extends the cm-rep to more complex shapes with multi-figures, i.e., shapes whose skeletons have branches. Along the branching curves, the equality constraints enforced by the medial geometry are implemented as soft penalties in the deformable model. The remaining small violations are corrected by local adjustments. As a proof of concept, the branching continuous medial representation is applied to a 2-chamber heart model data set consisting of 428 cardiac shapes from 90 subjects. The results show that our model can capture the heart shape accurately.