Open Access


A Zero-Watermark Scheme Based on Quaternion Generalized Fourier Descriptor for Multiple Images

Baowei Wang1,2,3,*, Weishen Wang1, Peng Zhao1, Naixue Xiong4
1 School of Computer Science, Nanjing University of Information Science and Technology, Nanjing, 210044, China
2 Jiangsu Collaborative Innovation Center of Atmospheric Environment and Equipment Technology (CICAEET), Nanjing, 210044, China
3 Engineering Research Center of Digital Forensics, Ministry of Education, Nanjing, 210044, China
4 Department of Mathematics and Computer Science, Northeastern State University, Tahlequah, OK, 74464, USA
* Corresponding Author: Baowei Wang. Email:

Computers, Materials & Continua 2022, 71(2), 2633-2652.

Received 03 August 2021; Accepted 16 September 2021; Issue published 07 December 2021


Most of the existing zero-watermark schemes for medical images are only appropriate for a single grayscale image. When they protect a large number of medical images, repeating operations will cause a significant amount of time and storage costs. Hence, this paper proposes an efficient zero-watermark scheme for multiple color medical images based on quaternion generalized Fourier descriptor (QGFD). Firstly, QGFD is utilized to compute the feature invariants of each color image, then the representative features of each image are selected, stacked, and reshaped to generate a feature matrix, which is then binarized to get a binary feature image. Copyright information can be converted into the copyright image by using QR code technology, which contains more information. Finally, the zero-watermark image is constructed by executing the XOR operation on the copyright image and the feature image scrambled by the Cat map. In the experiment, different parameters are selected to determine the maximum number of images that the proposed scheme can protect simultaneously while achieving good robustness. The experimental results demonstrate that the proposed scheme can effectively resist common attacks, geometric attacks and joint attacks, and effectively improve the operation efficiency of the algorithm, thus effectively decreasing the time and storage cost of copyright protection for lots of medical images.


Copyright protection; color medical image; zero-watermark; QGFD

Cite This Article

B. Wang, W. Wang, P. Zhao and N. Xiong, "A zero-watermark scheme based on quaternion generalized fourier descriptor for multiple images," Computers, Materials & Continua, vol. 71, no.2, pp. 2633–2652, 2022.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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