Geo-ΔSSM: Geometry-Conditioned Δ-Modulated Selective SSM Network for Hyperspectral and LiDAR Joint Classification

Hyperspectral imagery (HSI) and LiDAR-derived elevation data possess distinct and complementary characteristics, making their joint classification essential for precise land-cover interpretation. However, the intrinsic heterogeneity between high-dimensional spectral signatures and geometric structural priors hinders efficient cross-modal interaction. This phenomenon further exacerbates the difficulty in resolving boundary ambiguities, ultimately resulting in suboptimal performance in geometrically complex regions. In this article, a geometry-conditioned Δ-modulated selective state space model network (Geo-ΔSSM) is proposed to solve these challenges. Our core motivation is to explicitly regulate the spectral modeling dynamics of the HSI branch using LiDAR-derived geometric priors at the parameter level. Unlike conventional feature-level fusion, Geo-ΔSSM injects LiDAR-derived geometry into the generation of the selective SSM parameters, including Δ, B , and C , constraining spectral propagation by object boundaries. To further address spectral redundancy and noise, a frequency enhancement module (FrEM) is constructed to fuse static spectral priors with dynamic geometric guidance in the Fourier domain. The whole structure utilizes a weighted dual-modal boundary-aware loss (DBAL) to penalize errors at both material transitions and elevation transitions. Experiments demonstrate that Geo-ΔSSM achieves superior performance on three public benchmarks, effectively balancing accuracy on minority classes and preserving fine-grained details. The datasets and codes are available at https://github.com/bourne159/Geo-SSM