An adaptive image watermarking scheme using cooperation of HBA and RSA metaheuristics

Journal of the Franklin Institute. 2026. Vol. 363. No. 15. Article 109005.

Melman A., Evsyutin O.

Open access to images creates opportunities for violation of the authors' rights. Digital watermarks can be used to securely publish images online. They are invisibly added into the images before publication and can be extracted at any time to verify ownership. However, achieving a balance between embedding imperceptibility and robustness to image processing operations is quite challenging. In this study, an adaptive image watermarking scheme is proposed in which the balance between imperceptibility and robustness is achieved by cooperation of two metaheuristic optimization algorithms. The watermark bit embedding is performed into 4 × 4 block pairs, and the synergy of two modern metaheuristics is used to optimize the embedding. First, the Honey Badger Algorithm (HBA) selects the best locations of watermark bits to reduce the level of image distortion during embedding. The Reptile Search Algorithm (RSA) then optimizes change vectors that are used to embed the watermark into coefficients of Discrete Cosine Transform (DCT) block pairs. As a result of embedding, ratios of sums of DCT coefficient absolute values of the block pairs are set in such a way that they correspond to specific watermark bits. The HBA and RSA are used for the first time in an image watermarking scheme. To ensure the best optimization performance, a detailed study of the effect of optimization parameter values on image watermarking quality metrics is done. The experimental results show that the proposed algorithm provides a high level of embedding imperceptibility with the average Peak Signal-to-Noise Ratio (PSNR) metric value exceeding 50 dB. The watermark embedded using the algorithm is resistant to many image processing attacks, including brightness modification, gamma correction, sharpening, JPEG compression, Gaussian filter, and others. The average values of the Bit Error Rate (BER) and Normalized Correlation Coefficient (NCC) metrics are 0.0352 and 0.9702, respectively, for the classical set of test images.

Keywords: discrete cosine transform, metaheuristic optimization, image watermarking, honey badger algorithm, reptile search algorithm