Fractal-domain Vision Graph Neural Network for Remote Sensing Ground Target Classification

To the best of our knowledge, this paper is the first to integrate fractal signal processing with vision graph neural networks, establishing a new graph representation learning paradigm consistent with fractal dynamics. Building on this foundation, we propose a Fractal-domain Vision Graph Neural Network (FD-ViG). Specifically, FD-ViG includes: (i) a Fractal-Domain Learning Module that maps images into the fractal-domain using local Hölder exponents and the Singularity Power Spectrum (SPS), enabling fractal-spatial feature fusion; (ii) a Fractal Graph Construction Module that adaptively generates a topology by combining semantic attention with fractal similarity in the fractal feature space; and (iii) a Graph Propagation Module with power-law multi-scale propagation to realize cross-scale diffusion and aggregation, enabling coupled texture-structure learning. Experiments on UCMerced, RSSCN7, and SIRI-WHU achieve overall accuracies of 91.75%, 89.52%, and 92.78%, respectively. Compared with representative vision graph models such as ViG, WiGNet, and ViHGNN, our method achieves consistent improvements over prior methods across all three datasets, while remaining lightweight (2.6M parameters). Moreover, despite having far fewer parameters than ResNet-18, our model yields competitive or better performance on two datasets, and further demonstrates strong generalization ability in cross-dataset evaluation on SAR imagery. This work provides a principled and effective bridge between fractal theory and graph deep learning, benefiting interpretable remote sensing scene understanding under complex textures and structures.