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GARIAmark: A Geometric Attack-Resilient Image Adaptive Watermarking Scheme Using Quaternion Wavelet Transform and Nutcracker Optimizer Algorithm.

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Title: GARIAmark: A Geometric Attack-Resilient Image Adaptive Watermarking Scheme Using Quaternion Wavelet Transform and Nutcracker Optimizer Algorithm.
Authors: Kumar, Subodh1 (AUTHOR) skumar.cs.du@gmail.com
Source: Circuits, Systems & Signal Processing. Jul2026, Vol. 45 Issue 7, p5655-5694. 40p.
Subjects: Digital image watermarking, Wavelet transforms, Digital watermarking, Boosting algorithms, Distribution (Probability theory), Optimization algorithms, Copyright
Abstract: As Internet technologies advance rapidly, there has been a significant rise in content authentication and copyright concerns. Conventional digital watermarking methods that rely on a single embedding strength value fail to account for the local attributes of the image, making it challenging to optimally balance between imperceptibility and robustness. Moreover, the vulnerability of these schemes to geometric attacks further limits their effectiveness. To overcome these limitations, we propose GARIAmark—an image-adaptive watermarking scheme based on Nutcracker Optimization Algorithm (NOA) and Quaternion wavelet transform (QWT) that uses multiple watermark embedding strength values optimized locally using NOA to achieve enhanced robustness and visual quality. For watermarking, principal component coefficients are used that are obtained by applying QWT and singular value decomposition, thus mitigating the issue of false positives. Additionally, a novel geometric correction technique is developed using Bessel K-form distribution and an AdaBoost classifier to strengthen the geometric attack-resilience of this scheme. The classifier is trained using scale and location parameters (derived through BKF distribution) of different QWT sub-bands of the training images to accurately categorize geometric attacks and guide correction. Further, to enhance security the watermark is scrambled using a chaotic logistic map prior to embedding. Experimental results confirm that GARIAmark consistently achieves high visual quality while maintaining strong resistance against both image processing and geometric attacks. Comparative analysis with state-of-the-art schemes demonstrates the superior performance of GARIAmark in terms of robustness and imperceptibility, thus making it well-suited for real-world copyright protection applications in domains such as the multimedia industry. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
Description
Abstract:As Internet technologies advance rapidly, there has been a significant rise in content authentication and copyright concerns. Conventional digital watermarking methods that rely on a single embedding strength value fail to account for the local attributes of the image, making it challenging to optimally balance between imperceptibility and robustness. Moreover, the vulnerability of these schemes to geometric attacks further limits their effectiveness. To overcome these limitations, we propose GARIAmark—an image-adaptive watermarking scheme based on Nutcracker Optimization Algorithm (NOA) and Quaternion wavelet transform (QWT) that uses multiple watermark embedding strength values optimized locally using NOA to achieve enhanced robustness and visual quality. For watermarking, principal component coefficients are used that are obtained by applying QWT and singular value decomposition, thus mitigating the issue of false positives. Additionally, a novel geometric correction technique is developed using Bessel K-form distribution and an AdaBoost classifier to strengthen the geometric attack-resilience of this scheme. The classifier is trained using scale and location parameters (derived through BKF distribution) of different QWT sub-bands of the training images to accurately categorize geometric attacks and guide correction. Further, to enhance security the watermark is scrambled using a chaotic logistic map prior to embedding. Experimental results confirm that GARIAmark consistently achieves high visual quality while maintaining strong resistance against both image processing and geometric attacks. Comparative analysis with state-of-the-art schemes demonstrates the superior performance of GARIAmark in terms of robustness and imperceptibility, thus making it well-suited for real-world copyright protection applications in domains such as the multimedia industry. [ABSTRACT FROM AUTHOR]
ISSN:0278081X
DOI:10.1007/s00034-025-03439-5