PRISM: A 3D Probabilistic Neural Representation for Interpretable Shape Modeling

2026-02-12

AI Summary

This work proposes a covariate-conditioned probabilistic 3D shape model that integrates implicit neural representations with uncertainty-aware statistical shape analysis to address the dynamic modeling of anatomical shape heterogeneity during development and the quantification of its spatial uncertainty. The method introduces a closed-form Fisher information metric, enabling efficient analytical computation of local temporal uncertainties through automatic differentiation, thereby supporting spatially continuous and interpretable uncertainty modeling. Experiments on three synthetic datasets and one clinical dataset demonstrate that the proposed framework simultaneously achieves high-fidelity shape reconstruction and clinically interpretable uncertainty estimation.

Technology Category

• Reasoning under Uncertainty: Uncertainty Representations
• Machine Learning: Calibration & Uncertainty Quantification
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• User Modeling, Personalization and Recommendation: User model development and evaluation
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

Understanding how anatomical shapes evolve in response to developmental covariates and quantifying their spatially varying uncertainties is critical in healthcare research. Existing approaches typically rely on global time-warping formulations that ignore spatially heterogeneous dynamics. We introduce PRISM, a novel framework that bridges implicit neural representations with uncertainty-aware statistical shape analysis. PRISM models the conditional distribution of shapes given covariates, providing spatially continuous estimates of both the population mean and covariate-dependent uncertainty at arbitrary locations. A key theoretical contribution is a closed-form Fisher Information metric that enables efficient, analytically tractable local temporal uncertainty quantification via automatic differentiation. Experiments on three synthetic datasets and one clinical dataset demonstrate PRISM's strong performance across diverse tasks within a unified framework, while providing interpretable and clinically meaningful uncertainty estimates.

Problem

• shape modeling
• spatial uncertainty
• developmental covariates
• anatomical shapes
• statistical shape analysis

Innovation

• probabilistic neural representation
• statistical shape analysis
• spatially varying uncertainty
• Fisher Information metric
• implicit neural representations