Contextual Learning in Fourier Complex Field for VHR Remote Sensing Images

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 ( ≈ 224 × 224 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 ( ≥ 500 × 500 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 SA (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 datasets demonstrate the effectiveness and efficiency of FCT, especially on VHR RS images. The source code of FCT will be available at https://github.com/Gao-xiyuan/FCT.