Robust zero-watermarking algorithm based on polar complex exponential transform and logistic mapping

2016 ◽  
Vol 76 (24) ◽  
pp. 26355-26376 ◽  
Author(s):  
Chun-peng Wang ◽  
Xing-yuan Wang ◽  
Xing-jun Chen ◽  
Chuan Zhang
Keyword(s):  
Logistic Mapping ◽  
Exponential Transform ◽  
Zero Watermarking ◽  
Polar Complex Exponential Transform ◽  
Complex Exponential

scholarly journals A Polar Complex Exponential Transform-Based Zero-Watermarking for Multiple Medical Images with High Discrimination

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Wenbing Wang ◽  
Yan Li ◽  
Shengli Liu
Keyword(s):  
Medical Images ◽  
Computation Time ◽  
Image Features ◽  
Computational Time ◽  
Geometric Attacks ◽  
Exponential Transform ◽  
Zero Watermarking ◽  
Polar Complex Exponential Transform ◽  
The Stability ◽  
Complex Exponential

Zero-watermarking is one of the solutions for image copyright protection without tampering with images, and thus it is suitable for medical images, which commonly do not allow any distortion. Moment-based zero-watermarking is robust against both image processing and geometric attacks, but the discrimination of watermarks is often ignored by researchers, resulting in the high possibility that host images and fake host images cannot be distinguished by verifier. To this end, this paper proposes a PCET- (polar complex exponential transform-) based zero-watermarking scheme based on the stability of the relationships between moment magnitudes of the same order and stability of the relationships between moment magnitudes of the same repetition, which can handle multiple medical images simultaneously. The scheme first calculates the PCET moment magnitudes for each image in an image group. Then, the magnitudes of the same order and the magnitudes of the same repetition are compared to obtain the content-related features. All the image features are added together to obtain the features for the image group. Finally, the scheme extracts a robust feature vector with the chaos system and takes the bitwise XOR of the robust feature and a scrambled watermark to generate a zero-watermark. The scheme produces robust features with both resistance to various attacks and low similarity among different images. In addition, the one-to-many mapping between magnitudes and robust feature bits reduces the number of moments involved, which not only reduces the computation time but also further improves the robustness. The experimental results show that the proposed scheme meets the performance requirements of zero-watermarking on the robustness, discrimination, and capacity, and it outperforms the state-of-the-art methods in terms of robustness, discrimination, and computational time under the same payloads.

Novel quaternion polar complex exponential transform and its application in color image zero-watermarking

2021 ◽  
pp. 103130
Author(s):  
Zhiqiu Xia ◽  
Xingyuan Wang ◽  
Chunpeng Wang ◽  
Bin Ma ◽  
Hao Zhang ◽  
...  
Keyword(s):  
Color Image ◽  
Exponential Transform ◽  
Zero Watermarking ◽  
Polar Complex Exponential Transform ◽  
Complex Exponential

Geometrically Invariant NSCT–GPCET-Based Image Watermarking with Accurate Moment Calculation

2021 ◽  
pp. 2150284
Author(s):  
Wenbing Wang ◽  
Shengli Liu ◽  
Liu Feng
Keyword(s):  
Calculation Method ◽  
Image Watermarking ◽  
Robust Watermarking ◽  
Exponential Transform ◽  
Computational Simplicity ◽  
Polar Complex Exponential Transform ◽  
Watermarking Scheme ◽  
Complex Exponential ◽  
Grid Division ◽  
Geometrical Attacks

Generic polar complex exponential transform (GPCET), as continuous orthogonal moment, has the advantages of computational simplicity, numerical stability, and resistance to geometric transforms, which make it suitable for watermarking. However, errors in kernel function discretization can degrade these advantages. To maximize the GPCET utilization in robust watermarking, this paper proposes a secondary grid-division (SGD)-based moment calculation method that divides each grid corresponding to one pixel into nonoverlapping subgrids and increases the number of sampling points. Using the accurate moment calculation method, a nonsubsampled contourlet transform (NSCT)–GPCET-based watermarking scheme with resistance to image processing and geometrical attacks is proposed. In this scheme, the accurate moment calculation can reduce the numerical error and geometrical error of the traditional methods, which is verified by an image reconstruction comparison. Additionally, NSCT and accurate GPCET are utilized to achieve watermark stability. Subsequent experiments test the proposed watermarking scheme for its invisibility and robustness, and verify that the robustness of the proposed scheme outperforms that of other schemes when its level of invisibility is significantly higher.

Copy Move Forgery Image Detection via Discrete Radon and Polar Complex Exponential Transform-Based Moment Invariant Features

2017 ◽  
Vol 31 (02) ◽  
pp. 1754005 ◽  
Author(s):  
Junliu Zhong ◽  
Yanfen Gan ◽  
Janson Young ◽  
Peiyu Lin
Keyword(s):  
Background Information ◽  
Moment Invariant ◽  
Geometric Distortions ◽  
Invariant Features ◽  
Geometrical Features ◽  
Exponential Transform ◽  
Polar Complex Exponential Transform ◽  
Circular Template ◽  
Scaling Invariant ◽  
Complex Exponential

Copy move forgery with geometric distortions such as the rotational operation, the scaling operation, the mirror operation and the additive noise operation became more common. Existing methods are not competent for the detection of the copy move forgery with these distortions. In fact, the most critical issue for the detection of the forgery is the determination of the geometric features. This paper proposes an efficient Discrete Radon Polar Complex Exponential Transform (DRPCET)-based method for the extraction of the rotational and the scaling invariant features for the copy move forgery detection. First, the features obtained by the Radon transform (RT) and the Polar Complex Exponential Transform (PCET) are fused together. Then, these features are normalized. In order to achieve the scaling invariant property, an auxiliary circular template is introduced. With the auxiliary circular template, the translational moment invariant features, the rotational moment invariant features and the scaling moment invariant features are constructed for the extraction of the planar geometrical features. By further extracting some useful features for the representation of the image background, the interference of the background information can be reduced. After extracting the geometrical features, the lexicographic sorting is applied. Then, a correlation between the same part or similar parts of the image which are copied and moved to another image is computed. Based on the obtained correlations, these forgery parts can be identified and their composed positions can be located. Finally, these images are denoted as the forgery image. Extensive computer numerical simulations have been performed. The obtained results show that the proposed method can detect the copy move region in the forgery image precisely even though the forgery regions are suffered from the mixed geometric distortions.

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