  We introduce deep neural networks for the analysis of anatomical shapes that
learn a low-dimensional shape representation from the given task, instead of
relying on hand-engineered representations. Our framework is modular and
consists of several computing blocks that perform fundamental shape processing
tasks. The networks operate on unordered point clouds and provide invariance to
similarity transformations, avoiding the need to identify point correspondences
between shapes. Based on the framework, we assemble a discriminative model for
disease classification and age regression, as well as a generative model for
the accruate reconstruction of shapes. In particular, we propose a conditional
generative model, where the condition vector provides a mechanism to control
the generative process. instance, it enables to assess shape variations
specific to a particular diagnosis, when passing it as side information. Next
to working on single shapes, we introduce an extension for the joint analysis
of multiple anatomical structures, where the simultaneous modeling of multiple
structures can lead to a more compact encoding and a better understanding of
disorders. We demonstrate the advantages of our framework in comprehensive
experiments on real and synthetic data. The key insights are that (i) learning
a shape representation specific to the given task yields higher performance
than alternative shape descriptors, (ii) multi-structure analysis is both more
efficient and more accurate than single-structure analysis, and (iii) point
clouds generated by our model capture morphological differences associated to
Alzheimers disease, to the point that they can be used to train a
discriminative model for disease classification. Our framework naturally scales
to the analysis of large datasets, giving it the potential to learn
characteristic variations in large populations.
