An Adaptive Watermark Detection Algorithm for Vector Geographic Data

Abstract

With the rapid development of computer and communication techniques, copyright protection of vector geographic data has attracted considerable research attention because of the high cost of such data. A novel adaptive watermark detection algorithm is proposed for vector geographic data that can be used to qualitatively analyze the robustness of watermarks against data addition attacks. First, a watermark was embedded into the vertex coordinates based on coordinate mapping and quantization. Second, the adaptive watermark detection model, which is capable of calculating the detection threshold, false positive error (FPE) and false negative error (FNE), was established, and the characteristics of the adaptive watermark detection algorithm were analyzed. Finally, experiments were conducted on several real-world vector maps to show the usability and robustness of the proposed algorithm.

1. Introduction

Vector geographic data are fundamental achievements of national information infrastructure and earth science research and have been widely used in cartography, navigation, spatial analysis and many other areas. With the rapid development of computer and communication technology, vector geographic data can be conveniently replicated and distributed. The acquisition of vector geographic data is a costly process; therefore, the copyright protection of vector geographic data has become a hot issue in the geospatial data security domain.

As an effective algorithm for copyright protection, watermarking for vector geographic data has been studied for more than ten years [1]. A number of watermarking algorithms for vector geographic data have been proposed. Generally, digital watermark techniques for vector geographic data contain three parts: watermark generation, embedding, and detection. The first step is selecting a watermark, which could be an image, character, binary sequence, or voice. Preprocessing is performed when necessary, and examples include watermark encryption and watermark compression. The second step is to hide the watermark in the cover data used to embed the watermark. A watermark may be contained in the cover data or not. According to the different embedded domains, digital watermarking is categorized as spatial and transform domain watermarking. Spatial watermarking hides the watermark in the spatial domain component, and transform domain watermarking hides the watermark in the discrete cosine transform (DCT) [2]-[3], discrete Fourier transform (DFT) [4]-[6], or discrete wavelet transform (DWT) domain [7]-[8]. To date, many studies on digital watermark embedding for vector graphic data have been undertaken [9]-[16]. The third step of the digital watermark technique includes extracting and detecting the watermark. Extraction is mostly the inverse operation of the embedding process, and it is used to extract the embedded watermark. The detection step employs various methods to judge the specific content of the watermark. If the original data are not available for detection, the process is called “blind detection”, whereas if the data are available, then the process is called “informed detection.” Compared with research on embedding, the research on detection algorithms is limited [17]-[23]. For most existing watermarking algorithms, robustness has been qualitatively analyzed rather than quantitatively analyzed. However, the detection algorithm is an important part of digital watermark techniques and affects the robustness, reliability, and practicability of the watermark system. A better detection algorithm is useful for improving the robustness and capability of the watermark system.

Data deletions and data additions are the most common types of data processing performed in geographic information systems (GIS), and quantitatively analyzing the robustness of the watermark against data deletion and data addition attacks is a critical process. Therefore, we focus on the detection algorithm, and the design of a watermark detection algorithm based on statistical characteristics is presented. This paper proposes an adaptive watermark detection algorithm that a) can calculate the detection threshold, false positive error (FPE) and false negative error (FNE), b) is robust to data deletions and data additions and c) can qualitatively analyze the robustness of watermarks against data adding attacks.

The remainder of the paper is organized as follows. Section 2 briefly describes the watermark generation and embedding algorithms. Section 3 presents the fixed watermark detection process and establishes the adaptive watermark detection. Section 4 analyzes the characteristics of the proposed watermark detection method. Section 5 describes the experiments and results, and Section 6 presents the conclusions of the paper.

2. Watermark Generation and Embedding

2.1 Watermark Generation

Research manuscripts reporting on large datasets deposited in a publicly available database should specify where the data have been deposited and provide the relevant accession numbers. If the accession numbers have not yet been obtained at the time of submission, a note should be included stating that the numbers will be provided during review. The numbers must be provided prior to publication.

Watermark information can be classified into two main categories: significant watermarks and insignificant watermarks. A significant watermark is usually represented as a binary logo, and this logo is extracted to detect the presence of the watermark by visual inspection by a third entity, whereas an insignificant watermark is usually represented as a pseudo-random sequence. The presence of the watermark is detected using statistical correlations so that the detection of an insignificant watermark is more objective [11]. Moreover, the length of an insignificant watermark is usually much shorter than that of a significant watermark; thus, an insignificant watermark is more suitable for small datasets, which are common in vector geographic data. To establish the watermark detection model and quantitatively analyze the robustness of the proposed watermarking algorithm, we used a pseudo-random sequence as a watermark for this paper.

Let the watermark information be \(W=\{w[i], 0 \leq i<N\}, \text { where } w[i]\) is the watermark bit, \(i\) is the watermark bit index, \(N\) is the length of the watermark, and \(w[i] \in\{-1,1\}\) . The statistical characteristics of \(w[i]\) are \(P(w[i]=-1)=1 / 2\) and \(P(w[i]=1)=1 / 2\) , which means that the probabilities that \(w[i]\) are equal to -1 or 1 are the same. We set N to 200 for this paper.

The steps used to generate watermark information are as follows: first, a random integer is generated and used as a watermark seed; second, according to the watermark seed, the watermark is generated by the pseudo-random sequence generator; and third, the watermark seed is saved for the potential watermark detection. A one-to-one relationship is observed between the watermark seed and the corresponding watermark; therefore, we only need to save the watermark seed for the potential watermark detection.

In the subsequent section, the terms watermark seed, watermark, watermark bit, and watermark bit index are frequently referenced. The relationships among the watermark, watermark bit, and watermark bit index are shown in Fig. 1, in which N is the length of the watermark.

Fig. 1. Relationships among the watermark seed, the watermark, the watermark bits, and the watermark bit index

2.2 Watermark Embedding

The vector geographic data consist of the vertex coordinates. Vertex coordinates are the fundament units of points, polylines, and polygons that describe geographical objects, such as wells, rivers, and residential areas. To obtain a watermarking algorithm that is robust against the most common watermarking attacks such as data cropping, data reordering, data simplification, vertex adding and vertex deleting, we establish the mapping relationships between the vertex coordinates and the watermark bit index [23], and the watermark bits are then embedded into the corresponding vertex coordinates according to the mapping relationships.

In this paper, let the vertex coordinates of the vector geographic data be the set \(V C, V C=\left\{v c_{i} \mid\left(x_{i}, y_{i}\right), 0 \leq i<M\right\}\), where \(v c_{i}\) is the \(ith \) vertex, \(\left(x_{i}, y_{i}\right)\) is the coordinate of the ith vertex, and \(M \) is the number of vertex coordinates. The details of the steps for establishing mapping relationships are as follows.

1) The vertex coordinates \(VC\) are mapped to region \(R \) , which has a size of \(R_ x \times R_ y\) as shown as equation (1):

\(\left\{\begin{array}{l} x_{i}^{\prime}=\left\lfloor x_{i} * s\right\rfloor \% R_{-} x \\ y_{i}^{\prime}=\left\lfloor y_{i} * s\right\rfloor \% R_{-} y \end{array}\right.\),    (1)

where \(\left(x_{i}^{\prime}, y_{i}^{\prime}\right)\) is the mapped coordinate and \(s\) is a scaling factor used to control the data distortions in the watermark embedding.

distortions in the watermark embedding.

2) The region R is divided into NcNr _ _ × grid cells and by establishing the mapping relationships between coordinate (, ) i i x y ′ ′ and the grid cell index (,) ic ir , which are shown in equation (2), where N r _ ， N c _ ， LD x _ ， and LD y _ are all positive integers, R x _ can be divided by N c _ , and R y _ can be divided by N r _ . Additionally, N r R y LD y _ __ / _ = ， N c R x LD x _ _/ _ = ， and NcNr N _ _ × = .