We propose an auto-encoding network architecture for point clouds (PC) capable of extracting shape signatures without supervision. Building on this, we (i) design a loss function capable of modelling data variance on PCs which are unstructured, and (ii) regularise the latent space as in a variational auto-encoder, both of which increase the auto-encoders descriptive capacity while making them probabilistic. Evaluating the reconstruction quality of our architectures, we employ them for detecting vertebral fractures without any supervision. By learning to efficiently reconstruct only healthy vertebrae, fractures are detected as anomalous reconstructions. Evaluating on a dataset containing $sim$1500 vertebrae, we achieve area-under-ROC curve of $>$75%, without using intensity-based features.
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