# FNOSeg3D: Resolution-Robust 3D Image Segmentation with Fourier Neural Operator

arXiv: https://arxiv.org/abs/2310.03872 · HTML: https://mlsanity.com/paper/2310.03872/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 15 references that are in the map.
- First posted on arXiv 5 Oct 2023.

## Builds on (most cited first, 12 of 12)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [UNETR: Transformers for 3D Medical Image Segmentation](https://mlsanity.com/paper/2103.10504/) (2021)
- [Self-Normalizing Neural Networks](https://mlsanity.com/paper/1706.02515/) (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)
- [Deeply-Supervised Nets](https://mlsanity.com/paper/1409.5185/) (2014)
- [CoTr: Efficiently Bridging CNN and Transformer for 3D Medical Image Segmentation](https://mlsanity.com/paper/2103.03024/) (2021)
- [3D Segmentation with Exponential Logarithmic Loss for Highly Unbalanced Object Sizes](https://mlsanity.com/paper/1809.00076/) (2018)
- [3D Segmentation with Fully Trainable Gabor Kernels and Pearson's Correlation Coefficient](https://mlsanity.com/paper/2201.03644/) (2022)

## Built on by (most cited first, 3 of 3)

- [Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning](https://mlsanity.com/paper/2506.10973/) (2025)
- [HNOSeg-XS: Extremely Small Hartley Neural Operator for Efficient and Resolution-Robust 3D Image Segmentation](https://mlsanity.com/paper/2507.08205/) (2025)
- [NOIR: Neural Operator mapping for Implicit Representations](https://mlsanity.com/paper/2603.13118/) (2026)

## Abstract (arXiv)

Due to the computational complexity of 3D medical image segmentation, training with downsampled images is a common remedy for out-of-memory errors in deep learning. Nevertheless, as standard spatial convolution is sensitive to variations in image resolution, the accuracy of a convolutional neural network trained with downsampled images can be suboptimal when applied on the original resolution. To address this limitation, we introduce FNOSeg3D, a 3D segmentation model robust to training image resolution based on the Fourier neural operator (FNO). The FNO is a deep learning framework for learning mappings between functions in partial differential equations, which has the appealing properties of zero-shot super-resolution and global receptive field. We improve the FNO by reducing its parameter requirement and enhancing its learning capability through residual connections and deep supervision, and these result in our FNOSeg3D model which is parameter efficient and resolution robust. When tested on the BraTS'19 dataset, it achieved superior robustness to training image resolution than other tested models with less than 1% of their model parameters.