Geometry-Constrained Robust Watermarking for OpenDRIVE High-Definition Maps Exploiting a Similarity-Invariant Curvature–Length Feature

Existing watermarking methods for copyright protection of OpenDRIVE high-definition maps have difficulty balancing robustness and geometric accuracy. This study proposes a geometry-constrained robust watermarking algorithm that exploits the parametric representation of OpenDRIVE. From a symmetry perspective, the signed curvature–length feature used by the geometric carriers is invariant under translation, rotation, and ideal positive uniform scaling. This transformation invariance contributes to stable watermark extraction when the map’s global position, orientation, or scale is changed. A multidimensional carrier pool comprising geometric shapes and road attributes is constructed, and absolute quantization index modulation enables orthogonally decoupled embedding across carrier types. Levenberg–Marquardt optimization and topology-aware chain correction are further used to preserve geometric continuity and topological consistency. Experiments show that the algorithm maintains visual imperceptibility and file-size stability while remaining robust to geometric transformations, cropping, and format sanitization. Scenario simulations conducted in esmini revealed no evident degradation of road smoothness in the test scenarios defined in this study, indicating that the algorithm satisfied the map usability criteria under the experimental conditions.