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

arXiv: https://arxiv.org/abs/2602.11467 · HTML: https://mlsanity.com/paper/2602.11467/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 56 references that are in the map.
- First posted on arXiv 12 Feb 2026.

## Builds on (most cited first, 25 of 25)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation](https://mlsanity.com/paper/1606.06650/) (2016)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [On the Pitfalls of Heteroscedastic Uncertainty Estimation with Probabilistic Neural Networks](https://mlsanity.com/paper/2203.09168/) (2022)
- [Deformed Implicit Field: Modeling 3D Shapes with Learned Dense Correspondence](https://mlsanity.com/paper/2011.13650/) (2020)
- [A-SDF: Learning Disentangled Signed Distance Functions for Articulated Shape Representation](https://mlsanity.com/paper/2104.07645/) (2021)
- [Deep Implicit Templates for 3D Shape Representation](https://mlsanity.com/paper/2011.14565/) (2020)
- [Assessing Reliability and Challenges of Uncertainty Estimations for Medical Image Segmentation](https://mlsanity.com/paper/1907.03338/) (2019)
- [Reliable training and estimation of variance networks](https://mlsanity.com/paper/1906.03260/) (2019)
- [textttGradICON: Approximate Diffeomorphisms via Gradient Inverse Consistency](https://mlsanity.com/paper/2206.05897/) (2022)
- [Gaussian Process Morphable Models](https://mlsanity.com/paper/1603.07254/) (2016)
- [ICON: Learning Regular Maps Through Inverse Consistency](https://mlsanity.com/paper/2105.04459/) (2021)
- [CINA: Conditional Implicit Neural Atlas for Spatio-Temporal Representation of Fetal Brains](https://mlsanity.com/paper/2403.08550/) (2024)
- [A numerical approximation method for the Fisher-Rao distance between multivariate normal distributions](https://mlsanity.com/paper/2302.08175/) (2023)
- [Human Mesh Modeling for Anny Body](https://mlsanity.com/paper/2511.03589/) (2025)
- [Learning distributions of shape trajectories from longitudinal datasets: a hierarchical model on a manifold of diffeomorphisms](https://mlsanity.com/paper/1803.10119/) (2018)
- [NAISR: A 3D Neural Additive Model for Interpretable Shape Representation](https://mlsanity.com/paper/2303.09234/) (2023)
- [Dynamic Neural Surfaces for Elastic 4D Shape Representation and Analysis](https://mlsanity.com/paper/2503.03132/) (2025)
- [CINeMA: Conditional Implicit Neural Multi-Modal Atlas for a Spatio-Temporal Representation of the Perinatal Brain](https://mlsanity.com/paper/2506.09668/) (2025)

## Abstract (arXiv)

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 - from modeling shape evolution to personalized shape prediction and anomaly detection - within a unified framework, while providing interpretable and clinically meaningful uncertainty estimates.