# We Know Where We Don't Know: 3D Bayesian CNNs for Credible Geometric Uncertainty

arXiv: https://arxiv.org/abs/1910.10793 · HTML: https://mlsanity.com/paper/1910.10793/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Oct 2019.

## Built on by (most cited first, 9 of 9)

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- [A Review of Bayesian Uncertainty Quantification in Deep Probabilistic Image Segmentation](https://mlsanity.com/paper/2411.16370/) (2024)
- [Bayesian neural networks for predicting uncertainty in full-field material response](https://mlsanity.com/paper/2406.14838/) (2024)
- [Leveraging Stochastic Predictions of Bayesian Neural Networks for Fluid Simulations](https://mlsanity.com/paper/2205.01222/) (2022)
- [Self-Supervised Learning for Organs At Risk and Tumor Segmentation with Uncertainty Quantification](https://mlsanity.com/paper/2305.02491/) (2023)
- [Comparing Bayesian Models for Organ Contouring in Head and Neck Radiotherapy](https://mlsanity.com/paper/2111.01134/) (2021)
- [Trustworthy Visual Quality Inspection under Data Scarcity in Manufacturing](https://mlsanity.com/paper/2608.21967/) (2026)

## Abstract (arXiv)

Deep learning has been successfully applied to the segmentation of 3D Computed Tomography (CT) scans. Establishing the credibility of these segmentations requires uncertainty quantification (UQ) to identify untrustworthy predictions. Recent UQ architectures include Monte Carlo dropout networks (MCDNs), which approximate deep Gaussian processes, and Bayesian neural networks (BNNs), which learn the distribution of the weight space. BNNs are advantageous over MCDNs for UQ but are thought to be computationally infeasible in high dimension, and neither architecture has produced interpretable geometric uncertainty maps. We propose a novel 3D Bayesian convolutional neural network (BCNN), the first deep learning method which generates statistically credible geometric uncertainty maps and scales for application to 3D data. We present experimental results on CT scans of graphite electrodes and laser-welded metals and show that our BCNN outperforms an MCDN in recent uncertainty metrics. The geometric uncertainty maps generated by our BCNN capture distributions of sigmoid values that are interpretable as confidence intervals, critical for applications that rely on deep learning for high-consequence decisions. Code available at https://github.com/sandialabs/bcnn.