Degenerative spinal pathologies are highly prevalent among the elderly population. Timely diagnosis of osteoporotic fractures and other degenerative deformities facilitates proactive measures to mitigate the risk of severe back pain and disability. In this study, we specifically explore the use of shape auto-encoders for vertebrae, taking advantage of advancements in automated multi-label segmentation and the availability of large datasets for unsupervised learning. Our shape auto-encoders are trained on a large set of vertebrae surface patches, leveraging the vast amount of available data for vertebra segmentation. This addresses the label scarcity problem faced when learning shape information of vertebrae from image intensities. Based on the learned shape features we train an MLP to detect vertebral body fractures. Using segmentation masks that were automatically generated using the TotalSegmentator, our proposed method achieves an AUC of 0.901 on the VerSe19 testset. This outperforms image-based and surface-based end-to-end trained models. Additionally, our results demonstrate that pre-training the models in an unsupervised manner enhances geometric methods like PointNet and DGCNN. Our findings emphasise the advantages of explicitly learning shape features for diagnosing osteoporotic vertebrae fractures. This approach improves the reliability of classification results and reduces the need for annotated labels. This study provides novel insights into the effectiveness of various encoder-decoder models for shape analysis of vertebrae and proposes a new decoder architecture: the point-based shape decoder.

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