  Statistical shape modeling is an essential tool for the quantitative analysis
of anatomical populations. Point distribution models (PDMs) represent the
anatomical surface via a dense set of correspondences, an intuitive and
easy-to-use shape representation for subsequent applications. These
correspondences are exhibited in two coordinate spaces: the local coordinates
describing the geometrical features of each individual anatomical surface and
the world coordinates representing the population-level statistical shape
information after removing global alignment differences across samples in the
given cohort. We propose a deep-learning-based framework that simultaneously
learns these two coordinate spaces directly from the volumetric images. The
proposed joint model serves a dual purpose; the world correspondences can
directly be used for shape analysis applications, circumventing the heavy
pre-processing and segmentation involved in traditional PDM models.
Additionally, the local correspondences can be used for anatomy segmentation.
We demonstrate the efficacy of this joint model for both shape modeling
applications on two datasets and its utility in inferring the anatomical
surface.
