Beyond Euclidean Assumptions: Geometry-Aware Adaptive Routing for Remote Sensing Segmentation

Remote sensing imagery poses a distinct challenge for semantic segmentation due to its inherent fractal complexity and the diversity of geometric structures present in real-world geospatial scenes. Euclidean-based models typically assume spatial uniformity; however, such assumptions often break down when confronted with objects exhibiting markedly different structural characteristics—such as roads versus vegetation—thereby complicating the feature representation process. Hyperbolic space offers a theoretically grounded alternative for modeling such hierarchical and heterogeneous patterns, yet fully replacing Euclidean geometry incurs significant computational overhead. We therefore introduce Geometry-Aware Adaptive Routing (GAAR), a novel module that facilitates geometry-aware routing by dynamically allocating high-level features to either Euclidean or Hyperbolic subspaces through a learnable binary gating mechanism, informed by structural priors learned during training. To further promote routing stability and geometric consistency, we introduce Geometry-Aware Deterministic Regularization (GADR), a regularization strategy that encourages confident, structure-aligned assignments. GAAR is plug-and-play and integrates seamlessly into existing segmentation architectures. Experiments on three challenging Remote Sensing Image Semantic Segmentation (RSISS) benchmarks demonstrate that our approach consistently outperforms state-of-the-art (SOTA) methods, particularly in geometrically complex regions, offering a scalable and effective solution to the limitations of purely Euclidean modeling.

Authors

• Jie Qiu
• Dizuo Cao Fujian Agriculture and Forestry University
• Linwei Dai IFLYTEK
• Xin Li
• Fan Yang Nanyang Technological University
• Dong Yu Tencent AI Lab, Bellevue, WA
• Changying Wang Fujian Agriculture and Forestry University
• Zongheng Wen Xiamen University Tan Kah Kee College
• Youqin Chen Fujian University of Technology
• Jianzhang Chen Fujian Agriculture and Forestry University

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