  Statistical shape modeling (SSM) is a powerful computational framework for
quantifying and analyzing the geometric variability of anatomical structures,
facilitating advancements in medical research, diagnostics, and treatment
planning. Traditional methods for shape modeling from imaging data demand
significant manual and computational resources. Additionally, these methods
necessitate repeating the entire modeling pipeline to derive shape descriptors
(e.g., surface-based point correspondences) for new data. While deep learning
approaches have shown promise in streamlining the construction of SSMs on new
data, they still rely on traditional techniques to supervise the training of
the deep networks. Moreover, the predominant linearity assumption of
traditional approaches restricts their efficacy, a limitation also inherited by
deep learning models trained using optimized/established correspondences.
Consequently, representing complex anatomies becomes challenging. To address
these limitations, we introduce SCorP, a novel framework capable of predicting
surface-based correspondences directly from unsegmented images. By leveraging
the shape prior learned directly from surface meshes in an unsupervised manner,
the proposed model eliminates the need for an optimized shape model for
training supervision. The strong shape prior acts as a teacher and regularizes
the feature learning of the student network to guide it in learning image-based
features that are predictive of surface correspondences. The proposed model
streamlines the training and inference phases by removing the supervision for
the correspondence prediction task while alleviating the linearity assumption.
