# A Bayesian Approach to Segmentation with Noisy Labels via Spatially Correlated Distributions

arXiv: https://arxiv.org/abs/2504.14795 · HTML: https://mlsanity.com/paper/2504.14795/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 50 references that are in the map.
- First posted on arXiv 21 Apr 2025.

## Builds on (most cited first, 22 of 22)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Co-teaching: Robust Training of Deep Neural Networks with Extremely Noisy Labels](https://mlsanity.com/paper/1804.06872/) (2018)
- [Making Deep Neural Networks Robust to Label Noise: a Loss Correction Approach](https://mlsanity.com/paper/1609.03683/) (2016)
- [Combating noisy labels by agreement: A joint training method with co-regularization](https://mlsanity.com/paper/2003.02752/) (2020)
- [Dual T: Reducing Estimation Error for Transition Matrix in Label-noise Learning](https://mlsanity.com/paper/2006.07805/) (2020)
- [OpenEarthMap: A Benchmark Dataset for Global High-Resolution Land Cover Mapping](https://mlsanity.com/paper/2210.10732/) (2022)
- [Confidence Scores Make Instance-dependent Label-noise Learning Possible](https://mlsanity.com/paper/2001.03772/) (2020)
- [Adaptive Early-Learning Correction for Segmentation from Noisy Annotations](https://mlsanity.com/paper/2110.03740/) (2021)
- [Disentangling Human Error from the Ground Truth in Segmentation of Medical Images](https://mlsanity.com/paper/2007.15963/) (2020)
- [Superpixel-guided Iterative Learning from Noisy Labels for Medical Image Segmentation](https://mlsanity.com/paper/2107.10100/) (2021)
- [Labeling instructions matter in biomedical image analysis](https://mlsanity.com/paper/2207.09899/) (2022)
- [Learning to Segment from Noisy Annotations: A Spatial Correction Approach](https://mlsanity.com/paper/2308.02498/) (2023)
- [An Empirical Study into Annotator Agreement, Ground Truth Estimation, and Algorithm Evaluation](https://mlsanity.com/paper/1307.0426/) (2013)
- [Robust T-Loss for Medical Image Segmentation](https://mlsanity.com/paper/2306.00753/) (2023)
- [Classification of Large-Scale High-Resolution SAR Images with Deep Transfer Learning](https://mlsanity.com/paper/2001.01425/) (2020)
- [Cascaded Robust Learning at Imperfect Labels for Chest X-ray Segmentation](https://mlsanity.com/paper/2104.01975/) (2021)
- [Distilling effective supervision for robust medical image segmentation with noisy labels](https://mlsanity.com/paper/2106.11099/) (2021)
- [AIO2: Online Correction of Object Labels for Deep Learning with Incomplete Annotation in Remote Sensing Image Segmentation](https://mlsanity.com/paper/2403.01641/) (2024)
- [Impact of imperfect annotations on CNN training and performance for instance segmentation and classification in digital pathology](https://mlsanity.com/paper/2410.14365/) (2024)

## Built on by (most cited first, 1 of 1)

- [VoxelFix: Post-Hoc Semantic Correction of Completed 3D Voxel Maps](https://mlsanity.com/paper/2609.05114/) (2026)

## Abstract (arXiv)

In semantic segmentation, the accuracy of models heavily depends on the high-quality annotations. However, in many practical scenarios, such as medical imaging and remote sensing, obtaining true annotations is not straightforward and usually requires significant human labor. Relying on human labor often introduces annotation errors, including mislabeling, omissions, and inconsistency between annotators. In the case of remote sensing, differences in procurement time can lead to misaligned ground-truth annotations. These label errors are not independently distributed, and instead usually appear in spatially connected regions where adjacent pixels are more likely to share the same errors. To address these issues, we propose an approximate Bayesian estimation based on a probabilistic model that assumes training data include label errors, incorporating the tendency for these errors to occur with spatial correlations between adjacent pixels. However, Bayesian inference for such spatially correlated discrete variables is notoriously intractable. To overcome this fundamental challenge, we introduce a novel class of probabilistic models, which we term the ELBO-Computable Correlated Discrete Distribution (ECCD). By representing the discrete dependencies through a continuous latent Gaussian field with a Kac-Murdock-Szeg"o (KMS) structured covariance, our framework enables scalable and efficient variational inference for problems previously considered computationally prohibitive. Through experiments on multiple segmentation tasks, we confirm that leveraging the spatial correlation of label errors significantly improves performance. Notably, in specific tasks such as lung segmentation, the proposed method achieves performance comparable to training with clean labels under moderate noise levels. Code is available at https://github.com/pfnet-research/BayesianSpatialCorr.