  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. Additionally, we present principled extensions of
Point2SSM++ to adapt it for dynamic spatiotemporal and multi-anatomy use cases,
demonstrating the broad versatility of the Point2SSM++ framework. 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 traditional approaches.
Point2SSM++ substantially enhances the feasibility of SSM generation and
significantly broadens its array of potential clinical applications.
