Efficient copyright protection for three CT images based on quaternion polar harmonic Fourier moments

Xia, Zhiqiu; Wang, Xingyuan; Li, Xiaoxiao; Wang, Chunpeng; Unar, Salahuddin; Wang, Mingxu; Zhao, Tingting

doi:10.1016/j.sigpro.2019.06.025

Cited by 57 publications

(31 citation statements)

References 27 publications

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“…Table 1 shows the MSRE values with different L . Compared with Fr‐LMs, Fr‐ZMs, and SOMs, IRHFMs have the smallest reconstruction error in this experiment. EXPERIMENT To further evaluate the performance of the proposed moments, a comparison with certain state‐of‐the‐art orthogonal image moments based on trigonometric functions as basis functions (eg, fast RHFMs, 26 PHFMs 27,28 ) is also depicted, and fair comparison strategies is taken into consideration in this subsection experiment. Experiment 3 is divided into two groups, the first group is conducted using traditional integral method (TIM) that do not involve fast and accurate calculation method (FACM, ie, FFT algorithm) for all image moments including PHFMs and IRHFMs.…”

Section: Resultsmentioning

confidence: 99%

Image analysis by fast improved radial harmonic‐Fourier moments algorithm

Cui

Peng

et al. 2020

Int J Imaging Syst Tech

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Radial harmonic‐Fourier moments (RHFMs) are popular for image reconstruction and invariant pattern recognition due to their properties of translation, scaling and rotation invariant. RHFMs possess lower computation complexity as compared to Zernike moments and Bessel‐Fourier moments. However, they always suffer from discontinuity, numerical instability near the center of image, and reconstruction error, especially have a rise for higher order of moments. In this paper, an improvement of radial harmonic‐Fourier moments (IRHFMs) is proposed for effectively avoiding the above‐mentioned problems.In this paper, a 2D fast Fourier transform algorithm also is applied to the image matrix to obtain the IRHFMs. Simulation experimental results demonstrate the proposed IRHFMs perform better than traditional RHFMs and other classic orthogonal moments including the latest image moments, for example, polar harmonic Fourier moments in terms of the image reconstruction capability and rotation invariant recognition accuracy in noise‐free and noisy conditions.

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Section: Resultsmentioning

confidence: 99%

Image analysis by fast improved radial harmonic‐Fourier moments algorithm

Cui

Peng

et al. 2020

Int J Imaging Syst Tech

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“…The proposed QFr-GLMs demonstrated higher color-image reconstruction capability and invariant recognition accuracy under noise-free, noisy, and smooth filtering conditions. Thus, the proposed QFr-GLMs are potentially useful for color-image description and digital watermarking [37][38][39][40]. However, the only deficiency is that the perfect geometric invariance [41,42] cannot be achieved directly for invariant image recognition since the derivation of these QFr-GLMs invariants are not based on generalized Laguerre polynomials themselves.…”

Section: Discussionmentioning

confidence: 99%

Novel Color Orthogonal Moments-Based Image Representation and Recognition

He¹,

Li²,

Yang³

et al. 2020

Preprint

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Inspired by quaternion algebra and the idea of fractional-order transformation, we propose a new set of quaternion fractional-order generalized Laguerre orthogonal moments (QFr-GLMs) based on fractional-order generalized Laguerre polynomials. Firstly, the proposed QFr-GLMs are directly constructed in Cartesian coordinate space, avoiding the need for conversion between Cartesian and polar coordinates; therefore, they are better image descriptors than circularly orthogonal moments constructed in polar coordinates. Moreover, unlike the latest Zernike moments based on quaternion and fractional-order transformations, which extract only the global features from color images, our proposed QFr-GLMs can extract both the global and local color features. This paper also derives a new set of invariant color-image descriptors by QFr-GLMs, enabling geometric-invariant pattern recognition in color images. Finally, the performances of our proposed QFr-GLMs and moment invariants were evaluated in simulation experiments of correlated color images. Both theoretical analysis and experimental results demonstrate the value of the proposed QFr-GLMs and their geometric invariants in the representation and recognition of color images.

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“…Factorial operations of moments may limit both computational efficiency and resistance to geometric attacks. erefore, zero-watermarking that uses harmonic-based continuous orthogonal moments, such as PCET [19] and PHFM (polar harmonic Fourier moments) [20], has been developed. Considering the relation of the three channels of colour images, quaternion continuous orthogonal moments such as the QPHT (quaternion polar harmonic transform) [21] and QEM (quaternion exponential moment) [22] have been applied to zero-watermarking.…”

Section: Related Workmentioning

confidence: 99%

“…In the selection of the reference value, most schemes select one value as the reference value of all the geometric invariants. For example, [19][20][21]23] select the mean of the geometric invariants, [14,18,24,25] select the median of the geometric invariants, and [22] selects the Otsu threshold as the reference value (Table 1). With the invariants and reference value, schemes construct image features.…”

Section: Related Workmentioning

confidence: 99%

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

Wang

Liu

2021

Security and Communication Networks

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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.

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Efficient copyright protection for three CT images based on quaternion polar harmonic Fourier moments

Cited by 57 publications

References 27 publications

Image analysis by fast improved radial harmonic‐Fourier moments algorithm

Image analysis by fast improved radial harmonic‐Fourier moments algorithm

Novel Color Orthogonal Moments-Based Image Representation and Recognition

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

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