Mesh2SSM++: A Probabilistic Framework for Unsupervised Learning of Statistical Shape Model of Anatomies from Surface Meshes

2025-02-11

AI Summary

Existing anatomical assessment methods rely on predefined templates and lack individualized modeling capabilities. Method: We propose an unsupervised statistical shape modeling (SSM) framework that automatically establishes point-to-point correspondence and generates population-specific templates directly from unlabeled surface meshes. Our approach introduces a permutation-invariant deep point-cloud deformation model, jointly optimizing a probabilistic template and the deformation distribution, while explicitly modeling aleatoric uncertainty—first such incorporation in SSMs. The framework integrates differentiable deformation modeling, Bayesian template estimation, and an uncertainty-aware encoder-decoder architecture. Results: Evaluated on cardiac, hip, and ventricular structures, our method significantly outperforms state-of-the-art approaches. It supports end-to-end mesh input, achieves high computational efficiency, offers strong interpretability, and demonstrates robust generalization to downstream tasks.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

Anatomy evaluation is crucial for understanding the physiological state, diagnosing abnormalities, and guiding medical interventions. Statistical shape modeling (SSM) is vital in this process. By enabling the extraction of quantitative morphological shape descriptors from MRI and CT scans, SSM provides comprehensive descriptions of anatomical variations within a population. However, the effectiveness of SSM in anatomy evaluation hinges on the quality and robustness of the shape models. While deep learning techniques show promise in addressing these challenges by learning complex nonlinear representations of shapes, existing models still have limitations and often require pre-established shape models for training. To overcome these issues, we propose Mesh2SSM++, a novel approach that learns to estimate correspondences from meshes in an unsupervised manner. This method leverages unsupervised, permutation-invariant representation learning to estimate how to deform a template point cloud into subject-specific meshes, forming a correspondence-based shape model. Additionally, our probabilistic formulation allows learning a population-specific template, reducing potential biases associated with template selection. A key feature of Mesh2SSM++ is its ability to quantify aleatoric uncertainty, which captures inherent data variability and is essential for ensuring reliable model predictions and robust decision-making in clinical tasks, especially under challenging imaging conditions. Through extensive validation across diverse anatomies, evaluation metrics, and downstream tasks, we demonstrate that Mesh2SSM++ outperforms existing methods. Its ability to operate directly on meshes, combined with computational efficiency and interpretability through its probabilistic framework, makes it an attractive alternative to traditional and deep learning-based SSM approaches.

Problem

• Unsupervised learning of anatomical shape models.
• Reducing biases in template selection for SSM.
• Quantifying aleatoric uncertainty in model predictions.

Innovation

• Unsupervised learning of shape models
• Probabilistic framework for uncertainty quantification
• Population-specific template reduces selection bias