  We propose a novel neural deformable model (NDM) targeting at the
reconstruction and modeling of 3D bi-ventricular shape of the heart from 2D
sparse cardiac magnetic resonance (CMR) imaging data. We model the
bi-ventricular shape using blended deformable superquadrics, which are
parameterized by a set of geometric parameter functions and are capable of
deforming globally and locally. While global geometric parameter functions and
deformations capture gross shape features from visual data, local deformations,
parameterized as neural diffeomorphic point flows, can be learned to recover
the detailed heart shape.Different from iterative optimization methods used in
conventional deformable model formulations, NDMs can be trained to learn such
geometric parameter functions, global and local deformations from a shape
distribution manifold. Our NDM can learn to densify a sparse cardiac point
cloud with arbitrary scales and generate high-quality triangular meshes
automatically. It also enables the implicit learning of dense correspondences
among different heart shape instances for accurate cardiac shape registration.
Furthermore, the parameters of NDM are intuitive, and can be used by a
physician without sophisticated post-processing. Experimental results on a
large CMR dataset demonstrate the improved performance of NDM over conventional
methods.
