A Robust Authentication Algorithm for Medical Images Based on Fractal Brownian Model and Visual Cryptography

In this paper, we aimed to discuss the security authentication requirements of medical images in the medical network, and a security authentication method is designed based on fractal and visual cryptography. Based on the discrete fractal Brownian random ﬁeld model, the gray-level statistical information and spatial structure information of medical images is fully mined. The gray distribution of medical images is expressed in the form of fractal features. By using the spatial data mining methods, the data of fractal structure space is analyzed, and by using the stability of the energy structure, the authentication features are formed. Using the visual cryptography (VC), the robustness of the authentication method is further enhanced. Through the centralized test of common medical images and the comparison analysis with existing methods, it is further veriﬁed that the method is eﬀective against common attacks such as JPEG compression, scaling, rotation operation, clipping, added noise, ﬁltering, and blurring.


Introduction
e rapid development of 5G technology provides a strong technical guarantee for the popularization and application of medical networking. Under the current novel coronavirus pneumonia epidemic situation, the utilization rate of telemedicine and teleconsultation is increasing day by day. While digital medical images such as CT, MRI, US, and other diagnosis and treatment information are rapidly distributed and disseminated on the medical networking platform, the authentication of the integrity, authenticity, and validity of medical information has also become a hot issue that needs to be solved urgently. e rapid development of digital watermarking technology provides a solution for the authentication of medical information. However, the traditional watermarking technology often modifies the original carrier information to some extent. Any nonmedical changes of medical information may affect the diagnosis of doctors, which may lead to medical disputes. erefore, without any modification to the original medical information, starting from the original data, analyzing and mining the inherent stable characteristics of the carrier information, and using the stable characteristics as the basis for security certification has become a feasible solution for medical information security certification.
In recent years, many scholars at home and abroad have done a lot of research to meet the needs of medical image security authentication [1][2][3][4][5][6][7][8][9][10][11][12]. Using perceptual hashing, DTCWT-DCT, and Hénon mapping, Jing et al. proposed a multiwatermarking method for medical image authentication, which is robust against common geometric attacks [1]. Tzuo et al. used the significant difference of cellular automata coefficient to realize the lossless authentication of medical images [2]. Hu and Zhu used the key to control the logistic chaotic map and used a certain strategy to search for the similar binary sequences as the watermark information to achieve authentication [3]. Kavitha and Sakthivel implemented a medical image copyright protection scheme in hybrid domain by using the mechanism of fast response code [4]. Arsalan et al. used compression function to reduce the embedding distortion and realized the reversibility of medical image authentication [5]. Fatahbeygi and Akhlaghian combined support vector machine and visual cryptography to propose a high-security image authentication method [6]. Elham combined entropy analysis and discrete firefly algorithm to achieve image security authentication [7]. Hsieh and Huang proposed an authentication scheme based on DWT and visual cryptography. e scheme was based on the mean value and variance of the wavelet coefficients to achieve authentication [8]. Qingtang and Beijing made full use of the distribution characteristics of the DC coefficients of DCT transform to implement a copyright authentication scheme suitable for color images in the spatial domain [9].
On the basis of previous research, combined with fractal Brownian model and visual cryptography, an authentication scheme suitable for medical image is proposed. is method maps medical image information from gray-scale space to fractal dimension space and uses the stability of fractal data to form authentication features. e initial authentication features are scrambled and confused by visual cryptography, which further enhances the robustness of the method. ere is no noise added in the authentication process. A series of experiments reveal that the method is robust against common attacks, such as JPEG compression, scaling, angle rotation, clipping, noise, filtering, blurring, and so on.

Fractional Brownian Random Field Model.
e concept of fractal was first introduced by Hausdorff in 1919 and then developed by Mandelbrot in 1975. e basic characteristic of fractal is scale invariance. Mandelbrot thinks that fractal has three elements: form, chance, and dimension. Fractal dimension is a basic parameter to describe fractal quantitatively. It is an important feature of geometric object scale transformation. According to different definitions and calculation methods, the commonly used fractal dimensions include Hausdorff dimension, box dimension, information dimension, and fractal Brownian random field model [10]. e gray value of the image is processed in random walk mode, and the gray value at (x, y) is marked as I (x, y). According to the model of fractal Brownian random field, the following results are obtained: Let Formula (1) can be simplified as By taking the logarithm of both sides of (2), the following can be obtained: where C is a constant. By using least squares method, the data points (ln E(ΔI Δr ), ln(Δr)) are fitted. e slope of the straight line is the Hurst exponent H of the fractal Brownian model. For two-dimensional medical images, its fractal dimension D is equal to 3 minus H.
rough research on natural images, Pentland proved that the anisotropy of gray images conformed to the discrete fractional Brownian random field model. Pentland and other scholars first introduced the concept of fractal dimension into signal processing and pointed out that the shape and texture information of objects can be obtained by fractal analysis of images. Fractal information not only reflects the change of gray amplitude but also reflects the change of gray level at different scales. In the edge region of the image, the value of fractal characteristic parameters will undergo singular change. After experimental analysis, under a series of attack modes such as translation, rotation, affine transformation, and JPEG compression, the structure ordering of the edge area has good regularity and the change of fractal dimension value is not obvious, so it has strong robustness. In this paper, we make full use of the fine-grained stable relationship in the edge area to form a stable extremum structure in the fractal dimensional structure as copyright authentication information.

Visual Cryptography.
In 1994, the visual cryptography was proposed by Naor and Shamir. It is actually a secret sharing scheme (n, k) [11]. is method provides a scheme of dividing a secret image into n subimages. Without any cryptographic calculations, the original secret image can be recovered through k subimages. Even an attacker with infinite computing power cannot obtain any information about the secret image when the number of subsecrets is less than a given value (k). Figure 1 shows the structure of a (2, 2) visual cryptography. Figure 2 shows an application example of (2, 2) visual cryptography.

The Authentication Scheme
is section presents the authentication scheme. e scheme consists of two phases: one is the ownership construction phase and the other is the ownership verification phase.

Ownership Construction Phase.
e medical image is divided into blocks. Based on the fractal Brownian random field model, the fractal dimension of the subimage is calculated one by one. e original carrier information is mapped from the gray space to the fractal dimension space. e fractal dimension features of the subimages are formed. e fractal dimension features are connected together for analysis and normalization to form the stable feature which is regarded as the key point of copyright authentication. Figure 3 shows the ownership construction phase. e details of this phase are described as follows.   Figure 4 shows the ownership verification phase. e details of this phase are described as follows. at is to say, im_share1_1 � (dw_copyright) XOR (FD1). (vi) Step 6: Fetch im_share2 from the third-party certification center. e shared image im_share is restored according to the sharing of im_share1_1 and im_share2 as the following rule: im_share � (im_share1_1) OR (im_share2). (vii) Step 7: Divide the share image im_share into nonoverlapping 2 × 2 blocks. Calculate the sum of each small block (i); if the sum is less than or equal to 2, the im1 (i) is equal to 0; otherwise, im1 (i) is equal to 1. at is to say,

Ownership Verification Phase.
where im1 is the recovered authentication information.

Experimental Results
In order to verify the robustness of the algorithm some experiments are carried out in this section. Figure 5 shows six 512 × 512 medical images named "abdomen," "heart," "lung," "breast," "adrenal," "head" and one 32 × 32 logo image. All the images have been tested using this algorithm.
In order to describe the effectiveness and robustness of the algorithm, the peak signal-to-noise ratio (PSNR) is used to measure the visual changes of the image after a series of attacks. e larger the PSNR value is, the less damage the image will have [3]. e normalized similarity (NC) value is used to measure the similarity between the extracted copyright information and original copyright information.
e larger the NC value, the higher the similarity between the two. e PSNR and NC are defined by the following rules: where M and N are the size of the test image. H ij and H ij ′ are the original image and the attacked image.
where w b , w b ′ are the original copyright information and recovered copyright information. B is the size of copyright information.

Correlation Test of the Carrier Images.
e authentication information stored in the authentication center is closely related to the inherent characteristics of the carrier image, so the feature information of different carrier images should be independent of each other. e correlation data between the tested images is given in Table 1. From Table 1, it can be seen that the correlation data between different images are mostly concentrated around 0.6, which indicates that the feature information extracted from different images has significant differences.

Common Attack Test.
Medical images are prone to geometric and nongeometric attacks in the process of network transmission. e robustness test is carried out after the common attacks such as JPEG compression (compression factor 50%), salt and pepper noise (0.001), Gaussian noise (0.001), image rotation (10°), scaling attack (reduced to 50%), sharpening, multiplicative noise (0.01), cropping attack (1/5), median filtering (7 × 7), contrast enhancement, and brightness enhancement. Figures 6-16 show the results obtained by performing the proposed scheme on the "abdomen" image.
From Figures 6-16, it can be seen that the algorithm shows strong robustness against both conventional geometric attacks and nongeometric attacks, and the NC value of the authentication image is mostly close to 1. For medical images, any visible changes will cause special attention. In the attack test given in Figures 6-16, there are many attacks that make the carrier image change significantly. For example, as shown in Figure 13, the carrier image is cut by 1/5 and its PSNR value is much lower than 30 dB. However, the obtained authentication image still performs well. e NC of the authentication image extracted from Figure 13(a) is equal to 0.9971. Tables 2 and 3 show the performance comparison between this algorithm and other security authentication algorithms. From the comparison data, the algorithm shows strong robustness in resisting geometric attacks and conventional attacks.

Conclusion
Based on the discrete fractal Brownian random field model, the medical image is transformed from gray space to fractal space without adding any noise. In the fractal space, the fractal dimension data is analyzed and mined to form stable features. Based on the stable features, the copyright information of the medical image is authenticated. e security of the method is further enhanced by using the visual cryptography scheme. In the extraction process, the knowledge of probability statistics is applied to further improve the accuracy of the authentication. e scheme has the following characteristics. (1) e fractal dimension reflects the inherent attribute of the image, which is the energy property rather than the visual property. e attribute still shows good intrinsic stability under the affine transformation modes, such as rotation, shearing, size adjustment, and compression transformation. A series of attack tests have proved the robustness of scheme. (2) e meaningful binary image is used as authentication information. is scheme differs from the traditional authentication algorithms simply judge the similarity of the threshold. (3) e security of the algorithm is further enhanced by visual cryptography obfuscation operation. Meanwhile, to improve the accuracy of information detection, the probability and statistics knowledge is applied. At the same time, the algorithm has a good universality, especially suitable for medical images and military images, and has a good theoretical significance and popularization value [18][19][20][21][22][23][24][25][26][27][28][29][30][31].
Data Availability e tested images are available at http://peir.path.uab.edu/ library.

Conflicts of Interest
e authors declare no conflicts of interest.

Authors' Contributions
Xingyuan Wang was responsible of the formal analysis. Bin Ding was responsible of the funding acquisition. Daihong Jiang and Dan Li were responsible of the investigation. Tiankai Sun was responsible of the methodology.