# Laplacian Segmentation Networks Improve Epistemic Uncertainty Quantification

arXiv: https://arxiv.org/abs/2303.13123 · HTML: https://mlsanity.com/paper/2303.13123/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 37 references that are in the map.
- First posted on arXiv 23 Mar 2023.

## Builds on (most cited first, 20 of 20)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [Skin Lesion Analysis Toward Melanoma Detection: A Challenge at the 2017 International Symposium on Biomedical Imaging (ISBI), Hosted by the International Skin Imaging Collaboration (ISIC)](https://mlsanity.com/paper/1710.05006/) (2017)
- [Identifying the Best Machine Learning Algorithms for Brain Tumor Segmentation, Progression Assessment, and Overall Survival Prediction in the BRATS Challenge](https://mlsanity.com/paper/1811.02629/) (2018)
- [Laplace Redux -- Effortless Bayesian Deep Learning](https://mlsanity.com/paper/2106.14806/) (2021)
- [A Probabilistic U-Net for Segmentation of Ambiguous Images](https://mlsanity.com/paper/1806.05034/) (2018)
- [BCN20000: Dermoscopic Lesions in the Wild](https://mlsanity.com/paper/1908.02288/) (2019)
- [PHiSeg: Capturing Uncertainty in Medical Image Segmentation](https://mlsanity.com/paper/1906.04045/) (2019)
- [Quantifying Aleatoric and Epistemic Uncertainty in Machine Learning: Are Conditional Entropy and Mutual Information Appropriate Measures?](https://mlsanity.com/paper/2209.03302/) (2022)
- [PAD-UFES-20: a skin lesion dataset composed of patient data and clinical images collected from smartphones](https://mlsanity.com/paper/2007.00478/) (2020)
- [Stochastic Segmentation Networks: Modelling Spatially Correlated Aleatoric Uncertainty](https://mlsanity.com/paper/2006.06015/) (2020)
- [Learning in an Uncertain World: Representing Ambiguity Through Multiple Hypotheses](https://mlsanity.com/paper/1612.00197/) (2016)
- [Stochastic Multiple Choice Learning for Training Diverse Deep Ensembles](https://mlsanity.com/paper/1606.07839/) (2016)
- [A Hierarchical Probabilistic U-Net for Modeling Multi-Scale Ambiguities](https://mlsanity.com/paper/1905.13077/) (2019)
- [Uncertainty quantification in medical image segmentation with normalizing flows](https://mlsanity.com/paper/2006.02683/) (2020)
- [Laplacian Autoencoders for Learning Stochastic Representations](https://mlsanity.com/paper/2206.15078/) (2022)
- [Distributional Gaussian Process Layers for Outlier Detection in Image Segmentation](https://mlsanity.com/paper/2104.13756/) (2021)

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

- [Out-of-distribution Detection in Medical Image Analysis: A survey](https://mlsanity.com/paper/2404.18279/) (2024)
- [Uncertainty Quantification for Machine Learning in Healthcare: A Survey](https://mlsanity.com/paper/2505.02874/) (2025)
- [Uncertainty Estimation for Safety-critical Scene Segmentation via Fine-grained Reward Maximization](https://mlsanity.com/paper/2311.02719/) (2023)
- [A Review of Bayesian Uncertainty Quantification in Deep Probabilistic Image Segmentation](https://mlsanity.com/paper/2411.16370/) (2024)
- [Aleatoric Uncertainty Medical Image Segmentation Estimation via Flow Matching](https://mlsanity.com/paper/2507.22418/) (2025)
- [Rethinking Uncertainty Quantification and Entanglement in Image Segmentation](https://mlsanity.com/paper/2603.18792/) (2026)
- [L-FUSION: Laplacian Fetal Ultrasound Segmentation & Uncertainty Estimation](https://mlsanity.com/paper/2503.05245/) (2025)
- [Towards Agnostic and Holistic Universal Image Segmentation with Bit Diffusion](https://mlsanity.com/paper/2601.02881/) (2026)
- [It depends: Incorporating correlations for joint aleatoric and epistemic uncertainties of high-dimensional output spaces](https://mlsanity.com/paper/2608.24518/) (2026)

## Abstract (arXiv)

Image segmentation relies heavily on neural networks which are known to be overconfident, especially when making predictions on out-of-distribution (OOD) images. This is a common scenario in the medical domain due to variations in equipment, acquisition sites, or image corruptions. This work addresses the challenge of OOD detection by proposing Laplacian Segmentation Networks (LSN): methods which jointly model epistemic (model) and aleatoric (data) uncertainty for OOD detection. In doing so, we propose the first Laplace approximation of the weight posterior that scales to large neural networks with skip connections that have high-dimensional outputs. We demonstrate on three datasets that the LSN-modeled parameter distributions, in combination with suitable uncertainty measures, gives superior OOD detection.