<![CDATA[This study introduces a novel digital image watermarking method that integrates Möbius transformations with the Discrete Cosine Transform (DCT) to enhance both resilience and imperceptibility. The primary objective is to address the challenges of watermark embedding in digital images, ensuring robustness against geometric distortions, noise, and compression while maintaining high visual quality. The method employs a genetic algorithm to optimize the Möbius transformation parameters for effective watermark embedding in the DCT domain. Experimental results demonstrate the robustness of the proposed technique, with peak signal-to-noise ratio (PSNR) values consistently above 40 dB, ensuring minimal perceptual distortion. The bit error rate (BER) is significantly lower than that of traditional methods, demonstrating the technique's resilience against a wide range of attacks, including rotation, scaling, Gaussian noise, JPEG compression, and cropping. Compared to existing watermarking schemes, this approach consistently outperforms them in visual quality and resistance to tampering, with the PSNR reaching 60.94 dB for Lena images and achieving an SSIM value close to 1, indicating superior imperceptibility. The novelty of this approach lies in its combination of Möbius transformations with the DCT domain, offering a robust, efficient, and scalable solution for digital rights management and secure media transmission. This technique’s efficiency in terms of computational complexity and potential scalability for broader applications like video and audio watermarking highlights its practical advantages.]]>
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