Correspondence-based statistical shape modeling (SSM) stands as a powerful technology for morphometric analysis in clinical research. SSM facilitates population-level characterization and quantification of anatomical shapes such as bones and organs, aiding in pathology and disease diagnostics and treatment planning. Despite its potential, SSM remains under-utilized in medical research due to the significant overhead associated with automatic construction methods, which demand complete, aligned shape surface representations. Additionally, optimization-based techniques rely on bias-inducing assumptions or templates and have prolonged inference times as the entire cohort is simultaneously optimized. To overcome these challenges, we introduce Point2SSM++, a principled, self-supervised deep learning approach that directly learns correspondence points from point cloud representations of anatomical shapes. Point2SSM++ is robust to misaligned and inconsistent input, providing SSM that accurately samples individual shape surfaces while effectively capturing population-level statistics. Furthermore, we present extensions of Point2SSM++ tailored for dynamic spatiotemporal and multi-anatomy scenarios, showcasing the broad versatility of the framework. Through extensive validation across diverse anatomies, evaluation metrics, and clinically relevant downstream tasks, we demonstrate Point2SSM++’s superiority over existing state-of-the-art deep learning models and the traditional approach. Point2SSM++ substantially enhances the feasibility of SSM generation and significantly broadens its array of potential clinical applications. • Self-supervised approach for predicting anatomical correspondences from point clouds. • Outperforms statistical shape modeling methods on bones and organ populations. • Validation on downstream clinical tasks: craniosynostosis and femur pathology. • Extends to multi-anatomy learning such as full spine vertebrae. • Extends to 4D spatiotemporal data for longitudinal studies and dynamic shape analysis.

We present Point2SSM, a novel unsupervised learning approach for constructing correspondence-based statistical shape models (SSMs) directly from raw point clouds. SSM is crucial in clinical research, enabling population-level analysis of morphological variation in bones and organs. Traditional methods of SSM construction have limitations, including the requirement of noise-free surface meshes or binary volumes, reliance on assumptions or templates, and prolonged inference times due to simultaneous optimization of the entire cohort. Point2SSM overcomes these barriers by providing a data-driven solution that infers SSMs directly from raw point clouds, reducing inference burdens and increasing applicability as point clouds are more easily acquired. While deep learning on 3D point clouds has seen success in unsupervised representation learning and shape correspondence, its application to anatomical SSM construction is largely unexplored. We conduct a benchmark of state-of-the-art point cloud deep networks on the SSM task, revealing their limited robustness to clinical challenges such as noisy, sparse, or incomplete input and limited training data. Point2SSM addresses these issues through an attention-based module, providing effective correspondence mappings from learned point features. Our results demonstrate that the proposed method significantly outperforms existing networks in terms of accurate surface sampling and correspondence, better capturing population-level statistics. The source code is provided at https://github.com/jadie1/Point2SSM.

Statistical shape modeling (SSM) is an enabling tool in medical image analysis as it allows for population-based quantitative analysis. The traditional pipeline for landmark-based SSM from images requires painstaking and cost-prohibitive steps. My thesis aims to leverage probabilistic deep learning frameworks to streamline the adoption of SSM in biomedical research and practice. The expected outcomes of this work will be new frameworks for SSM that (1) provide reliable and calibrated uncertainty quantification, (2) are effective given limited or sparsely annotated/incomplete data, and (3) can make predictions from incomplete 4D spatiotemporal data. These efforts will reduce required costs and manual labor for anatomical SSM, helping SSM become a more viable clinical tool and advancing medical practice.

The cosmic microwave background (CMB) is a significant source of knowledge about the origin and evolution of our universe. However, observations of the CMB are contaminated by foreground emissions, obscuring the CMB signal and reducing its efficacy in constraining cosmological parameters. We employ deep learning as a data-driven approach to CMB cleaning from multi-frequency full-sky maps. In particular, we develop a graph-based Bayesian convolutional neural network based on the U-Net architecture that predicts cleaned CMB with pixel-wise uncertainty estimates. We demonstrate the potential of this technique on realistic simulated data based on the Planck mission. We show that our model ac- accurately recovers the cleaned CMB sky map and resulting angular power spectrum while identifying regions of uncertainty. Finally, we discuss the current challenges and the path forward for deploying our model for CMB recovery on real observations.