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We introduce deep neural networks for the analysis of anatomical shapes thatlearn a low-dimensional shape representation from the given task, instead ofrelying on hand-engineered representations. Our framework is modular andconsists of several computing blocks that perform fundamental shape processingtasks. The networks operate on unordered point clouds and provide invariance tosimilarity transformations, avoiding the need to identify point correspondencesbetween shapes. Based on the framework, we assemble a discriminative model fordisease classification and age regression, as well as a generative model forthe accruate reconstruction of shapes. In particular, we propose a conditionalgenerative model, where the condition vector provides a mechanism to controlthe generative process. instance, it enables to assess shape variationsspecific to a particular diagnosis, when passing it as side information. Nextto working on single shapes, we introduce an extension for the joint analysisof multiple anatomical structures, where the simultaneous modeling of multiplestructures can lead to a more compact encoding and a better understanding ofdisorders. We demonstrate the advantages of our framework in comprehensiveexperiments on real and synthetic data. The key insights are that (i) learninga shape representation specific to the given task yields higher performancethan alternative shape descriptors, (ii) multi-structure analysis is both moreefficient and more accurate than single-structure analysis, and (iii) pointclouds generated by our model capture morphological differences associated toAlzheimers disease, to the point that they can be used to train adiscriminative model for disease classification. Our framework naturally scalesto the analysis of large datasets, giving it the potential to learncharacteristic variations in large populations.

Discriminative and Generative Models for Anatomical Shape Analysison Point Clouds with Deep Neural Networks