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The reversible watermarking technique is suitable for vector maps due to its reversibility after watermark extraction. In this paper, a novel reversible watermarking scheme based on the idea of nonlinear scrambling is proposed. It begins with feature point extraction. To avoid the high-precision vector data being illegally used by unauthorized users, the algorithm nonlinearly scrambles the relative position of feature points. Then based on the proposed reversible embedding, both scrambled feature points and nonfeature points are taken as cover data, the coordinates of which are modified to embed both watermark data and feature point identification data. Finally, combined with the scrambling secret key, the original vector data can be exactly recovered with watermark extraction. Comprehensive experimental results validate that the scheme could effectively prevent the high-precision vector data from being illegally used with maintaining the basic shape of each polyline, simultaneously. [ABSTRACT FROM AUTHOR]