Most of current watermarking algorithms for GIS vector data embed copyright information by means of modifying the coordinate values, which will do harm to its quality and accuracy. To preserve the fidelity of vector line data and protect its copyright at the same time, a lossless watermarking algorithm is proposed based on storage feature in this paper. Firstly, the superiority of embedding watermark based on storage feature is demonstrated theoretically and technically. Then, the basic concepts and operations on storage feature have been defined including length and angle of the polyline feature. In the process of embedding watermark, the watermark information is embedded into directions of polyline feature by the quantitative mechanism, while the positions of embedding watermark are determined by the feature length. Hence, the watermark can be extracted by the same geometric features without original data or watermark. Finally, experiments have been conducted to show that coordinate values remain unchanged after embedding watermark. Moreover, experimental results are presented to illustrate the effectiveness of the method.

The existing commutative encryption and watermarking (CEW) methods based on feature invariants can achieve both the robustness of the watermarking algorithm and the security of the encryption algorithm. However, they are only applicable to the raster data such as images, videos, etc. In particular, the organization structure and storage structure of vector map have not been considered in these methods. Therefore, they cannot be used for vector map. This paper derives two feature invariants to solve this problem, which are the sum of inner angles and the storage direction of two adjacent objects according to the inherent characteristics of vector map. Based on these two feature invariants, a new CEW method is proposed in this paper, which includes the feature invariants based watermarking algorithm and the perceptual stream cipher based encryption algorithm on coordinates. Since the coordinate values used in encryption and the feature invariants used in watermarking are independent of each other, the commutativity is achieved for the proposed CEW method. The experiments are given to verify that the proposed CEW method can achieve the commutativity between encryption and watermarking without deteriorating accuracy of data. Besides, it has been verified that the proposed method is more robust to rotate, scaling, translation, and projection transformation compared with the existing CEW methods and has high security. The proposed algorithm has good scalability of encryption, and arbitrary encryption methods based on encrypting the coordinate values can be applied without affecting the extracted feature invariants.INDEX TERMS Commutative encryption and watermarking, feature invariant, vector map, perceptual stream cipher, lossless.

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Various watermarking algorithms have been studied to better enable the copyright protection of remote sensing images. The robustness of such algorithms against image cropping attacks has subsequently been verified mainly by various experiments. However, to date, the experimental results are subject to the differences in experimental factors and computational resource costs. Hence, the study presented in this paper proposes a robustness computation model of watermarking remote sensing images in terms of the image cropping attack. The robustness computation model consists of three parts: analysis principles, an evaluation index, and a computation method. The robustness analysis principles are provided based on the salient features of watermarking remote sensing images and attacking properties. A probability-based evaluation index is then defined to more comprehensively measure the robustness of different algorithms. The computation method developed in this study is based on permutations and the inclusion-exclusion principle to theoretically calculate robustness. The experiments conducted to verify the effectiveness of the computation model, revealed true closeness between both the calculated and experimental results. Finally, the relationships between the robustness and the different parameters used in the watermarking algorithms are investigated by using the proposed computation model.