Robust Reversible Watermarking Algorithm for Vector Maps Based on Virtual Triangle Feature Domain and Improved Quantization Index Modulation

ABSTRACT Existing vector map reversible watermarking algorithms primarily focus on reversibility and watermark capacity, often lacking robustness, especially against geometric and vertex attacks, which limits applicability. To address the issue, this study proposes a highly robust reversible watermarking algorithm for vector maps based on the virtual triangle feature domain. The algorithm extracts the vertices of the vector map, re‐links them linearly, and constructs virtual triangles from consecutive vertices. For any given triangle, the second vertex is used to create a parallel line to the line connecting the first vertex and third vertex . The perpendicular bisector of the midpoint of this line is extended to intersect the parallel line, forming an intersection point . The feature‐length is defined as the distance from to . It is theoretically proven that the ratio of and exhibits strong geometric invariance, making it an ideal watermark embedding domain. The watermark is then embedded into the ratio of and using improved quantization index modulation (IQIM), achieving vertex decoupling and blind watermark extraction, which enhances resistance to vertex attacks. Furthermore, the algorithm incorporates strategies such as watermark re‐encoding and factor amplification to accommodate various types of vector maps. Experimental results demonstrate that the proposed algorithm is robust against translation, rotation, scaling, vertex editing, and cropping, and has a high degree of invisibility while preserving good reversibility.