Dual Zero-Watermarking Scheme for Two-Dimensional Vector Map Based on Delaunay Triangle Mesh and Singular Value Decomposition

Xu Xi,Weidong Liang,Qinchuan Xin,Pengcheng Zhang,Xinchang Zhang

doi:10.3390/app9040642

Abstract

Digital watermarking is important for the copyright protection of electronic data, but embedding watermarks into vector maps could easily lead to changes in map precision. Zero-watermarking, a method that does not embed watermarks into maps, could avoid altering vector maps but often lack of robustness. This study proposes a dual zero-watermarking scheme that improves watermark robustness for two-dimensional (2D) vector maps. The proposed scheme first extracts the feature vertices and non-feature vertices of the vector map with the Douglas-Peucker algorithm and subsequently constructs the Delaunay Triangulation Mesh (DTM) to form a topological feature sequence of feature vertices as well as the Singular Value Decomposition (SVD) matrix to form intrinsic feature sequence of non-feature vertices. Next, zero-watermarks are obtained by executing exclusive disjunction (XOR) with the encrypted watermark image under the Arnold scramble algorithm. The experimental results show that the scheme that synthesizes both the feature and non-feature information improves the watermark capacity. Making use of complementary information between feature and non-feature vertices considerably improves the overall robustness of the watermarking scheme. The proposed dual zero-watermarking scheme combines the advantages of individual watermarking schemes and is robust against such attacks as geometric attacks, vertex attacks and object attacks.

Highlights

Two-dimensional (2D) vector maps have a broad range of applications, such as engineering construction, urban planning, military affairs, and navigation [1,2,3]
The processing steps include the preprocessing of the vector maps, encryption of watermark information, construction of zero-watermarks based on both feature and non-feature vertices, and watermark extraction and assessment
In the process of extraction, we find that when implementing feature vertex extraction by the Douglas-Peucker algorithm, the random increased vertices cannot be compressed, but as the feature vertices to build Delaunay Triangulation Mesh (DTM), so vertex addition attack has no effect on the non-feature vertex watermark

Summary

Introduction

Two-dimensional (2D) vector maps have a broad range of applications, such as engineering construction, urban planning, military affairs, and navigation [1,2,3]. The production of vector maps is often expensive, and illegal copying, altering, and misuse of the data could result in tremendous losses to data owners. With increasing demands for copyright protection, digital watermarking techniques have been developed rapidly in recent years [4,5,6,7]. Efforts have been made to design various watermark embedding algorithms for digital images to improve the robustness and imperceptibility of the watermark [8,9,10,11,12]. The abundant studies on image watermarking provide valuable information and references for other digital products as well [13,14,15,16], and enhance the development of watermarking for vector maps. Compared with watermarking of digital images, watermarking of

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Conclusion