GASSF-Net: Geometric Algebra Based Spectral-Spatial Hierarchical Fusion Network for Hyperspectral and LiDAR Image Classification

The field of multi-source remote sensing observation is becoming increasingly dynamic through the integration of various remote sensing data sources. However, existing deep learning methods face challenges in differentiating between internal and external relationships and capturing fine spatial features. These models often struggle to effectively capture comprehensive information across remote sensing data bands, and they have inherent differences in the size, structure, and physical properties of different remote sensing datasets. To address these challenges, this paper proposes a novel geometric-algebra-based spectral–spatial hierarchical fusion network (GASSF-Net), which uses geometric algebra for the first time to process multi-source remote sensing images, enabling a more holistic approach to handling these images by simultaneously leveraging the real and imaginary components of geometric algebra to express structural information. This method captures the internal and external relationships between remote sensing image features and spatial information, effectively fusing the features of different remote sensing data to improve classification accuracy. GASSF-Net uses geometric algebra (GA) to represent pixels from different bands as multivectors, thus capturing the intrinsic relationships between spectral bands while preserving spatial information. The network begins by deeply mining the spectral–spatial features of a hyperspectral image (HSI) using pairwise covariance operators. These features are then extracted through two branches: a geometric-algebra-based branch and a real-valued network branch. Additionally, the geometric-algebra-based network extracts spatial information from light detection and ranging (LiDAR) to complement the elevation data lacking in the HSI. Finally, a genetic-algorithm-based cross-fusion module is introduced to fuse the HSI and LiDAR data for improved classification. Experiments conducted on three well-known datasets, Trento, MUUFL, and Houston, demonstrate that GASSF-Net significantly outperforms traditional methods in terms of classification accuracy and model efficiency.