A Zero-Watermarking Algorithm for Vector Geographic Data Based on Multi-Channel Geometric Representation and a Geometric Encoder

Zero-watermarking technology constructs copyright identifiers by extracting stable features from the original data without modifying the data itself, making it highly suitable for lossless copyright protection of high-precision vector geographic data. However, existing methods rely on topology construction, triangulation, or complex handcrafted features, resulting in high computational overhead and insufficient generalization capability for multiple types of vector data. This paper proposes a zero-watermarking algorithm that combines a geometric encoder with multi-channel geometric representation. The method encodes vector data into a four-channel geometric tensor consisting of an occupancy field, distance field, orientation field, and density field. Then it uses a geometric encoder to extract stable and distinguishable features. Joint training with identity classification, feature consistency, and triplet uniqueness constraints ensures feature stability before and after attacks as well as strong discriminability across different data. Experimental results show that the proposed method remains stable under rotation, translation, and uniform scaling attacks, and still retains a certain level of authentication capability under feature deletion. Meanwhile, the method can effectively distinguish different vector data identities and construct zero-watermarks with relatively low computational overhead, demonstrating good uniqueness and computational efficiency.