Velocity Space Representation Learning for GPR Keypoint Detection and Matching

Reliable localization under Global Positioning System-denied or visually degraded conditions remains a fundamental challenge for autonomous systems. Vision- and Light Detection and Ranging (LiDAR)-based approaches often degrade in low illumination, adverse weather, or appearance-changing environments, as they rely on stable surface texture or geometry. In contrast, ground-penetrating radar (GPR) captures subsurface electromagnetic reflections that remain relatively stable across lighting, seasonal, and weather variations, making it a promising complementary sensing modality for long-term localization. However, spatial variability in subsurface dielectric properties induces fluctuations in electromagnetic wave velocity, leading to geometric distortions in GPR echoes and unstable feature extraction. To address this challenge, we propose the Velocity-Invariant Feature Transform (VIFT), a physics-guided self-supervised learning framework for GPR keypoint detection and description. VIFT explicitly models wave-velocity-induced distortions through a continuous velocity space parameterized by a Beta distribution, and leverages velocity-conditioned wavefield migration as physically consistent data augmentation. A Siamese network is trained with velocity-consistency supervision to jointly learn repeatable keypoint score maps and discriminative local descriptors from unlabeled real GPR scans. To further enhance robustness, sparsity-aware, dispersion, distinctiveness, and orthogonality losses are incorporated to improve repeatability, spatial coverage, and descriptor discriminability. Extensive experiments on public benchmarks and large-scale real-world GPR datasets demonstrate that VIFT consistently outperforms traditional handcrafted methods and recent learning-based Vison and GPR methods, achieving a 5–10% improvement in keypoint repeatability over state-of-the-art methods, particularly under extremely sparse keypoint sampling regimes, while also improving matching accuracy and registration robustness under diverse subsurface conditions.