Double Robust Zero-Watermarking Algorithms Based on Fractional-Order Jacobi-Fourier Moments and FFST-Schur

• Published in: Circuits, systems, and signal processing Vol. 44; no. 7; pp. 4796 - 4827
• Main Authors: Lu, Yu, Lu, Xin-hui, Yang, Guang-yun, Xiong, Xiang-guang
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.07.2025; Springer Nature B.V
• Subjects: Algorithms; Circuits and Systems; Combinatorial analysis; Copyright; Cryptography; Data encryption; Data integrity; Decomposition; Digital watermarks; Electrical Engineering; Electronics and Microelectronics; Engineering; Image processing; Image reconstruction; Instrumentation; Mean; Multimedia; Robustness; Signal,Image and Speech Processing; Watermarking; Wavelet transforms; Zero-watermarking; Schur decomposition; Fractional-order Jacobi-Fourier moments; Non-extended visual cryptography; Fast finite Shearlet transform
• ISSN: 0278-081X; 1531-5878
• DOI: 10.1007/s00034-025-03014-y

To address the problem that most zero-watermarking algorithms tend to be resistant to some attacks, a dual zero-watermarking algorithm using fractional-order Jacobi-Fourier moments (FrJFMs) and fast finite Shearlet transform and Schur decomposition (FFST-Schur) is proposed. The algorithm constructs two zero-watermarking images separately by utilizing the orthogonal moments and multi-scale transforms with solid robustness to ensure resistance to multiple attacks. On the one hand, the cover image is transformed by FFST, and the low-frequency sub-bands (LSs) are divided into blocks of the same size and decomposed by Schur decomposition. This generates the first feature image by utilizing the magnitude relationship between the maximum value of each block and the overall mean value. Further, the copyright image is encrypted using a non-extended visual cryptography method to generate two encrypted images. The first feature image and one of the encrypted images are subjected to an XOR operation to obtain the first zero-watermarking. On the other hand, the cover image is transformed with a non-subsampled Contourlet transform and the computation of FrJFMs for LSs to construct a second feature matrix. The second feature image is obtained using the magnitude relationship between each feature value and the overall mean value. The second feature image is then subjected to an XOR operation with another encrypted image to obtain the second zero-watermarking. The results show that the mean error of reconstruction of the FrJFMs decreases to 0.02, and the proposed algorithm is highly resistant to image processing and geometric and combinatorial attacks. The algorithm's average performance against attacks is improved by about 2.7%, indicating better robustness of the proposed algorithm.