A Zero-Watermark Hybrid Algorithm for Remote Sensing Images Based on DCT and DFT

Remote sensing image has significant advantages such as large detection range and fast acquisition speed, so it has been used in military, environmental, meteorological and other fields. In order to improve the robustness of the digital watermarking technology on the premise that the remote sensing image information is not modified, a remote sensing image zero watermarking algorithm based on Discrete Cosine Transform (DCT) and Discrete Fourier Transform (DFT) is proposed in this paper. First of all, the color remote sensing image is converted into grayscale image. The transformed coefficient matrix is obtained by DFT, to the grayed host image. Secondly, in order to compress the amount of information and improve the efficiency of the algorithm, the high frequency coefficient image is transformed by DCT transform. The low frequency coefficient image which is consistent with the size of the watermark image after DCT is selected as the feature image of the host image. After that, the watermark information is scrambled by Arnold transform to improve the security of the watermark information. Finally, the zero-watermark image is obtained by XOR operation between the scrambled watermark information and the feature image. The zero-watermark image is saved in a third-party database for copyright verification. In order to verify the robustness of digital watermarking, this paper carries out sharpening, histogram equalization, Karma transform, noise, filtering and geometric attacks on the host image, and compares it with other algorithms. The NC value between the extracted watermark image and the original watermark image after attacking the host image show that the algorithm has a strong ability to resist common attacks.


Introduction
The rapid development of digital media communication technology has increased the ways of image acquisition, accelerated the speed of image transmission, and brought a lot of convenience to people's life. However, it also leads to the proliferation of image copyright problems such as illegal acquisition and illegal embezzlement. Digital watermarking technology is an effective method to protect the rights of copyright owners. Without affecting the visual effect of the image, the digital watermark

Hybrid watermarking algorithm
In order to meet the robustness requirements of digital watermarking, the researchers combine single watermarking algorithm and propose a hybrid digital watermarking algorithm based on transform domain. Ying et al [9] proposed a robust digital watermarking algorithm for color images based on DFT and dual-tree complex wavelet transform (DTCWT). The algorithm divides the image into three channels: Y, U and V, and transforms the host image on different channels. Experiments show that this method has significant advantages in resisting geometric attacks.
With the continuous development of intelligent algorithms, particle swarm optimization algorithm [10] and machine learning [11] also have some applications in digital watermarking.

Zero watermarking algorithm
Medical images and remote sensing images contain important information, and the security and protection of their information put forward higher requirements for digital watermarking algorithms. Liu et al. [12] firstly encrypt medical images through DWT, DCT and chaotic maps. Secondly, the 3 encrypted image is transformed by SIFT-DCT transform, and 32 bits are selected as the feature sequence in the transformed coefficients. Finally, zero watermark is generated by distinguishing the feature sequence of the encrypted watermark image and the host image. The watermarking algorithm shows good robustness to common attacks.
Wang [13] proposed a zero-watermarking algorithm for color images against rotation attacks based on Nonsubsampled Pyramidde Composition and DCT.

Zero watermarking algorithm for remote sensing image
In order to protect the copyright of remote sensing image without modifying remote sensing image data, zero watermarking is introduced into the digital watermarking algorithm of remote sensing image.
Zhao et al. [14] uses Nonsubsampled Contourlet Transform to decompose the grayed host image, and then divides the low frequency subband into block DCT transform. The feature image of the host image is constructed according to the stable relationship of direct current coefficient on the average value of each block and all blocks after DCT. Atoany [15] proposed a robust zero watermarking algorithm based on convolution neural network (CNN) and depth learning algorithm for remote sensing images with less distortion. The characteristic images constructed by Li et al. [16] are the lowfrequency coefficient image after the DWT of the host image and the logarithmic polar mapping image of the host image.
The robustness of the above algorithm is passable, but the ability to resist some attacks does not meet the requirements of copyright protection. In this paper, a robust zero watermarking algorithm is proposed for remote sensing images.

Discrete Fourier transform (DFT)
Discrete Fourier transform (DFT) converts the image signal from time domain to frequency domain, that is, the gray distribution function of the image is transformed into the frequency distribution function. The amplitude and phase parts can be obtained by DFT decomposition. DFT is widely used in image enhancement, denoising, edge detection, feature extraction and so on. The DFT transform formula of an image of MN  size is as follows: 11 2 Where ( , ) F u v is the result of discrete Fourier transform of image matrix ( , ) f x y , and u and v can be used to determine the frequency of sine and cosine.

Discrete cosine transforms (DCT)
Discrete cosine transform (DCT) is one of the commonly used transforms in image watermarking, which is separable and energy-concentrated. Separability means that two-dimensional DCT can be divided into two one-dimensional DCT transforms. After DCT transform, the energy of the image is mainly concentrated in the low frequency part, so embedding the watermark in the low frequency component of DCT has good stability. DCT transform is widely used in image processing and data compression, such as common JPEG still image coding, MJPEG, MPEG dynamic coding and other standards. The formula of DCT transform is as follows.
The inverse DCT is:

Arnold transform
Arnold transform realizes image scrambling through finite elementary matrix transformation of image matrix. After the Arnold transform, the pixels of the image will be redistributed, and the image will become disorganized, so as to realizing the hiding of image information [17]. The Arnold transform is periodic, and the continuous transformation of the image can finally restore the original image. This characteristic of Arnold transform can realize the encryption and decryption of the image. The Arnold transform formula of the M-order image is: Where n is the degree of the current transformation, 11 ( , ),( , ) n n n n x y x y ++ is the position of the corresponding pixel before and after the transformation respectively.

The Algorithm
Based on DCT and DFT, this paper proposes a zero-watermarking algorithm for remote sensing image. In this section, Baboon (128×128) is used as the watermark image to show the algorithm of this work.

Zero-watermark generation
Firstly, the original host image is grayscale processed. The RGB image is converted into grayscale image to reduce the amount of data and improve the processing speed. The principle of image graying is as follows: Secondly, perform DFT on the grayed host image, to get the high frequency part which represents the details of the image and the low frequency part that represents the outline information of the image.
In order to enhance the robustness of the watermark, the DCT is computed on the high frequency coefficient image after DFT. DCT concentrates most of the energy of the image on the upper left corner of the transformed coefficient matrix. The coefficient matrix which is consistent with the size of the watermark is selected from the upper left corner, and the mean value is used as the threshold for binarization. The binarized image is used as the feature image of the host image.

4.1.2.
Processing watermark image. In order to improve the security of the watermark, Arnold transform is used to scramble the binary watermark image. The number of scrambles is used as the key .
Key The purpose of scrambling is that even if the feature information of the image is extracted correctly, the original watermark image cannot be restored without grasping the key. Figure 1 shows the course of processing the original watermark image. The zero watermark can be obtained by XOR operation between the final feature image and the watermark image.
The overall process of constructing a zero-watermark image is as follows: Step1. If the host image I is a RGB image or a color image, convert it to a grayscale image G I .
Step2. Perform DFT on G I to obtain the corresponding DFT coefficient Step4. In order to make the size of the feature image consistent with that of the watermark image, the mn  part of the upper left corner of the _ coefficient DCT is extracted as the feature image Feature of the host image.
Step5. Select the mean value as the threshold value to perform binarization processing on Feature , and mark the image after binarization as . Feature Step6. After binarizing the original watermark image W of size mn  , perform Arnold transform according to the key Key to obtain the scrambled watermark image A W .
Step7. The zero-watermark image _ zero watermarking is obtained by XOR operation between the feature image Feature and A W . The zero watermark is saved in the third-party database for copyright verification.

Watermark extraction
Extracting the watermark image needs to use the zero-watermark image saved in the third-party database. Firstly, extract the feature image from the attacked host image. Then the extracted watermark image can be obtained by XORing the feature image with the zero-watermark stored in the third-party database. The specific algorithm flow of extracting watermark image is as follows: Step1. Enter image I  to be detected, which is the host image after attack.
Step2. Perform DFT on the image I  to get the coefficient matrix _ coefficient DFT .
Step3. Perform DCT on the high-frequency part in _ coefficient DFT , and get the DCT coefficient _.

coefficient DCT
Step4. Extract the low-frequency part _ low DCT from _.

coefficient DCT
Step5. Binarize the _ low DCT with the mean value as the threshold to obtain the image Feature .
Step6. Perform XOR on Feature and zero watermarking image _ zero watermarking to get the extracted watermark image G W . Step7

Experimental Results
The experimental samples used in this section are mainly 20 color remote sensing images. Figure 2 shows the image data set of this article, and the number and size of the image are given at the bottom of each image.

Evaluation index
In this work, the performance of digital watermarking is quantitatively evaluated by Normalized Correlation (NC).
The normalized correlation coefficient is able to measure the degree of similarity between the images. The robustness of the digital watermark can be tested by calculating the NC value between the extracted watermark and the original watermark. The calculation formula of NC value is: Where mn  represents the size of the watermark image, , WW represents the embedded watermark and the extracted watermark respectively.

Parameter Setting
Before carrying out the experiment, some experimental parameters need to be set. The main parameters used in this algorithm are the block size of DFT, the threshold of binarization after DFT and the times of Arnold scrambling. Considering the efficiency of time and space and the accuracy of the results, the block size of DFT is set to 8×8, the mean value as the threshold, and the times of Arnold scrambling is 5.
Before the XOR operation between the feature image of the host image and the watermark information, it is necessary to binarize the feature image. For the threshold in binarization, the mean, median, mode, 3/4 digits and 1/4 digits are selected to test. Table 1 shows the average NC values of 20 images. It can be seen from the table 1 that the average NC of all test images is the lowest when the mean is used as the threshold, which verifies the rationality of the mean as the threshold.

Noise Attack and Filtering Attack
In order to test the performance of watermark, compare the similarity between the original watermark information and the watermark extracted from the attacked host image. The types of attacks selected  Figure 3 shows the visualization result of the host image after being attacked by filtering and noise. Table 2 shows the NC value of the image 4, 7, 10, 11, 14 as the host image.
Filtering attacks include Gaussian low-pass filtering, median filtering, Wiener filtering and Average filtering. Noise attacks include salt and pepper noise, speckle noise and Gaussian noise. These attacks have caused varying degrees of damage to the visual effect of the image. Among them, salt and pepper noise and Gaussian noise damage the image the most. However, from the NC value of 20 images, 80% of the NC value is greater than 0.95. The results show that the extracted watermark is not greatly affected, which indicating that the algorithm is robust to filtering and noise attack.

Geometric Attack
The geometric attacks used in this paper include cropping and rotation. Figure 4 shows  In the rotation attack experiment, the host image is rotated 5° and 10° clockwise and counterclockwise. Rotation results in the dislocation between the position of the extracted watermark and the watermark information. With the increase of the rotation angle, the more error information is extracted at the position where the watermark is constructed, which leads to the decrease of the NC value. When the rotation angle is 10 degrees, the NC value is still above 0.8, indicating that the algorithm has a strong ability to resist rotation attacks.

Other Attacks
Other types of attacks selected in this paper are sharpening, histogram equalization and gamma correction. Figure 5 shows the watermark image extracted from the host image after being attacked. When the sharpening intensity increases from 3 to 7, the NC value of the image decreases from 0.978 to 0.955. The NC value is still greater than 0.95 under the strong sharpening attack, which indicates that the algorithm in this paper is robust to the sharpening attack.
With the decrease of the number of equalization bits in the histogram, the contrast of the image decreases, and the similarity between the image and the original host image is lower. Under 16-bit histogram equalization, the NC value of the watermark image is still greater than 0.85. For gamma transformation, the gamma values of less than 1 and greater than 1 are tested respectively. When the gamma values are 1.

Comparative experiment with other algorithms
In order to quantitatively measure the advantages of this algorithm, images 4,10,11 are used as host images to compare with other algorithms.   Figure 6 shows the NC values of the above algorithms under noise, filtering, geometry and other attacks.
As can be seen from the figure 6, the DCT+DFT hybrid algorithm is better than the single algorithm. The NC value can reach more than 95% under most attacks, and the curve trend is the most stable. For a single algorithm, the NC value of DCT algorithm under partial attack is close to 0.5, so the extracted watermark image may not be recognized.

5.6.2.
Compared with previous literature. This section compares the robustness of the algorithm proposed in reference [18] and reference [19] with that of this algorithm under filtering, noise, cropping and rotation attacks. Although the algorithms in references [18] and [19] can resist noise and filtering attacks, they are not robust to geometric attacks. As can be seen from table 3, the robustness of this algorithm in cropping and rotation attacks is much higher than that in references [18] and [19]. The algorithm in this work also has some advantages under filtering and noise attacks.  Figure 7 shows the FPR value of the data set image. The average FPR of 20 images is 0.063 as the final total FPR value. Therefore, the probability of false positive problem of the zero-watermark constructed by this algorithm is very small, which makes the accuracy of copyright verification very high.

Conclusions
In this paper, a zero-watermarking algorithm for remote sensing images is proposed based on DCT and DFT. The innovation of this algorithm lies in: (1) The host image is not modified. (2) The watermarking algorithm has high robustness. (3) The possibility of the false positive problem is very small.
In the experiment of testing the performance of the algorithm, after the host image is attacked with high intensity, even if the image is visually unrecognizable, the algorithm in this paper can still extract the feature image with high accuracy. For all kinds of attacks, the increase in attack intensity has little effect on the visual effect of the extracted watermark. Experimental results show that the watermark has good invisibility and high robustness.