Implicit spatial-frequency fusion of hyperspectral and lidar data via kolmogorov-arnold networks

The fusion of hyperspectral (HS) and Light Detection and Ranging (LiDAR) data plays a crucial role in enhancing land-cover classification by jointly exploiting spectral, spatial, and structural cues. However, existing multimodal fusion methods still struggle to model long-range dependencies and complex anisotropic interactions while maintaining computational efficiency. This paper introduces M2Heat, a physics-inspired framework that investigates multimodal fusion through the lens of heat conduction. At its core, a physics-driven visual heat conduction module (vHeat) and enhanced Frequency Value Embeddings (FVEs) simulate anisotropic information flow, enabling the capture of global dependencies with sub-quadratic complexity and physical interpretability. This mechanism, combined with a hybrid spatial-frequency fusion strategy named Cross-Frequency Fusion (CFF) module, produces highly discriminative and robust feature representations. M2Heat achieves competitive overall performance on three benchmarks, i.e., Trento, Houston2013, and Augsburg, while providing an interpretable heat-conduction-guided perspective for multimodal feature fusion. These results indicate the potential of heat-conduction-guided neural operators for efficient and interpretable RS multimodal fusion. The source code is publicly available at https: /github.com/Weikan0425/M2Heat_HSI_LiDAR.

Hyperspectral image (HSI) and SAR/LiDAR data offer complementary spectral and structural information for land-cover classification. However, their effective fusion remains challenging due to two major limitations: The spectral redundancy in high-dimensional HSI and the heterogeneous characteristics between multi-source data. To this end, we propose Representative Spectral Correlation Network (RSCNet), a novel multi-source image classification framework specifically designed to address the above challenges through spectral selection and adaptive interaction. The network incorporates two key components: (1) Key Band Selection Module (KBSM) that adaptively selects task-relevant spectral bands from the original HSI under cross-source guidance, thereby alleviating redundancy and mitigating information loss from conventional PCA-based spectral reduction. Moreover, the learned band subset exhibits highly discriminative spectral structures that align with discriminative semantic cues, promoting compact yet expressive representations. (2) Cross-source Adaptive Fusion Module (CAFM) that performs cross-source attention weighting and local-global contextual refinement to enhance cross-source feature interaction. Experiments on three public benchmark datasets demonstrate that our RSCNet achieves superior performance compared with state-of-the-art methods, while maintaining substantially lower computational complexity. Our codes are publicly available at https://github.com/oucailab/RSCNet.

Achieving a coherent integration of spectral richness and spatial fidelity remains a central objective in hyperspectral image fusion. However, existing hyperspectral image fusion methods struggle to effectively model geometric constraints. In the spatial domain, weak spatial-spectral interaction limits geometry-aware feature learning and suppresses high-frequency structural information, resulting in low-frequency bias and structural degradation. In the spectral domain, local manifold structures induced by spectral similarity are insufficiently exploited, limiting intrinsic pixel relationship modeling and fine-grained spectral reconstruction. To address these challenges, we propose a dual-domain manifold modeling (DDMM) framework. Specifically, we introduce a Topology-Aware Transformer (TPFormer) that combines global attention with neighborhood propagation, jointly modeling spatial topology and pixel-level feature manifold relationships to capture intrinsic spatial-spectral structures and improve topology-aware representation learning. Furthermore, a Frequency-Decoupled Spatial-Spectral Collaborative Fusion (FDSCF) module is devised, in which features are projected into the frequency domain via the discrete cosine transform and explicitly decoupled into low- and high-frequency components. Guided by a low-rank structural prior and spectral-driven spatial enhancement, FDSCF selectively enhances geometry-aware high-frequency features, strengthening spatia-spectral coupling and recovering sharper edges and finer textures. Extensive experiments on multiple benchmark datasets demonstrate that DDMM achieves superior overall performance over SoTA methods in terms of spatial structure preservation and spectral reconstruction.