# Contextual Learning in Fourier Complex Field for VHR Remote Sensing Images

arXiv: https://arxiv.org/abs/2210.15972 · HTML: https://mlsanity.com/paper/2210.15972/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 78 references that are in the map.
- First posted on arXiv 28 Oct 2022.

## Builds on (most cited first, 30 of 42)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [Encoder-Decoder with Atrous Separable Convolution for Semantic Image Segmentation](https://mlsanity.com/paper/1802.02611/) (2018)
- [SegFormer: Simple and Efficient Design for Semantic Segmentation with Transformers](https://mlsanity.com/paper/2105.15203/) (2021)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Aggregated Residual Transformations for Deep Neural Networks](https://mlsanity.com/paper/1611.05431/) (2016)
- [Pyramid Vision Transformer: A Versatile Backbone for Dense Prediction without Convolutions](https://mlsanity.com/paper/2102.12122/) (2021)
- [MLP-Mixer: An all-MLP Architecture for Vision](https://mlsanity.com/paper/2105.01601/) (2021)
- [MMDetection: Open MMLab Detection Toolbox and Benchmark](https://mlsanity.com/paper/1906.07155/) (2019)
- [Designing Network Design Spaces](https://mlsanity.com/paper/2003.13678/) (2020)
- [Remote Sensing Image Scene Classification: Benchmark and State of the Art](https://mlsanity.com/paper/1703.00121/) (2017)
- [MobileViT: Light-weight, General-purpose, and Mobile-friendly Vision Transformer](https://mlsanity.com/paper/2110.02178/) (2021)
- [DOTA: A Large-scale Dataset for Object Detection in Aerial Images](https://mlsanity.com/paper/1711.10398/) (2017)
- [MetaFormer Is Actually What You Need for Vision](https://mlsanity.com/paper/2111.11418/) (2021)
- [MaxViT: Multi-Axis Vision Transformer](https://mlsanity.com/paper/2204.01697/) (2022)
- [Cascade R-CNN: High Quality Object Detection and Instance Segmentation](https://mlsanity.com/paper/1906.09756/) (2019)
- [AID: A Benchmark Dataset for Performance Evaluation of Aerial Scene Classification](https://mlsanity.com/paper/1608.05167/) (2016)
- [FNet: Mixing Tokens with Fourier Transforms](https://mlsanity.com/paper/2105.03824/) (2021)
- [Object Detection in Optical Remote Sensing Images: A Survey and A New Benchmark](https://mlsanity.com/paper/1909.00133/) (2019)
- [How Do Vision Transformers Work?](https://mlsanity.com/paper/2202.06709/) (2022)
- [Fully Convolutional Siamese Networks for Change Detection](https://mlsanity.com/paper/1810.08462/) (2018)
- [Remote Sensing Image Change Detection with Transformers](https://mlsanity.com/paper/2103.00208/) (2021)

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

- [Deep Learning-Based Anomaly Detection in Spacecraft Telemetry on Edge Devices](https://mlsanity.com/paper/2603.29375/) (2026)

## Abstract (arXiv)

Very high-resolution (VHR) remote sensing (RS) image classification is the fundamental task for RS image analysis and understanding. Recently, transformer-based models demonstrated outstanding potential for learning high-order contextual relationships from natural images with general resolution (224x224 pixels) and achieved remarkable results on general image classification tasks. However, the complexity of the naive transformer grows quadratically with the increase in image size, which prevents transformer-based models from VHR RS image (500x500 pixels) classification and other computationally expensive downstream tasks. To this end, we propose to decompose the expensive self-attention (SA) into real and imaginary parts via discrete Fourier transform (DFT) and therefore propose an efficient complex self-attention (CSA) mechanism. Benefiting from the conjugated symmetric property of DFT, CSA is capable to model the high-order contextual information with less than half computations of naive SA. To overcome the gradient explosion in Fourier complex field, we replace the Softmax function with the carefully designed Logmax function to normalize the attention map of CSA and stabilize the gradient propagation. By stacking various layers of CSA blocks, we propose the Fourier Complex Transformer (FCT) model to learn global contextual information from VHR aerial images following the hierarchical manners. Universal experiments conducted on commonly used RS classification data sets demonstrate the effectiveness and efficiency of FCT, especially on very high-resolution RS images.