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.

FNOSeg3D 模型通过 Fourier 神经算子（FNO）提高了参数效率和分辨率鲁棒性，在 BraTS'19 数据集上表现出优于其他模型的鲁棒性。

FNOSeg3D: 鲁棒分辨率三维图像分割与傅里叶神经算子

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

This paper presents a comprehensive comparison of various machine learning
models, namely U-Net, U-Net integrated with Vision Transformers (ViT), and
Fourier Neural Operator (FNO), for time-dependent forward modelling in
groundwater systems. Through testing on synthetic datasets, it is demonstrated
that U-Net and U-Net + ViT models outperform FNO in accuracy and efficiency,
especially in sparse data scenarios. These findings underscore the potential of
U-Net-based models for groundwater modelling in real-world applications where
data scarcity is prevalent.

通过对合成数据集进行测试，本文对 U-Net、U-Net + ViT 模型以及 Fourier 神经运算器 (FNO) 等不同的机器学习模型进行综合比较，结果表明 U-Net 和 U-Net + ViT 模型在准确性和效率方面优于 FNO，尤其在稀疏数据场景下。这些发现强调了 U-Net 模型在地下水系统中的建模潜力，特别是在数据稀缺的现实应用中。