Robust Image Watermarking Against Geometric Attacks Using Surrogate Model–Based Scaling Factor Optimization and Deep Learning–Based Adaptive Embedding

Abstract

Digital watermarking, as a fundamental approach to copyright protection, has consistently faced the inherent challenge of balancing imperceptibility and robustness, particularly against geometric attacks. This delicate trade-off is strongly influenced by two key factors: the optimal selection of the scaling factor (embedding strength) and the intelligent selection of embedding regions. This article proposes a robust hybrid watermarking framework for color images that strategically integrates intelligent image analysis with accelerated optimization and is specifically designed to withstand rotation attacks. The proposed method incorporates two principal innovations. First, a deep convolutional neural network (CNN) with a U-Net architecture is trained to generate an adaptive weight map. Independently of the embedding process, this network analyzes the content of the host image and automatically identifies regions with high visual complexity, including edges and textures. Second, a particle swarm optimization (PSO) algorithm guided by a regression tree–based surrogate model is employed to determine the optimal scaling factor. By replacing computationally expensive evaluations of the actual objective function with a rapid estimator, this approach substantially accelerates the optimization process. Finally, fully adaptive embedding is performed through the pointwise integration of the optimal scaling factor and the local weight map within the approximation subband of the discrete wavelet transform (DWT). Experimental results obtained using standard benchmark images confirm the strong performance of the proposed method. By achieving an average peak signal-to-noise ratio (PSNR) greater than 38 dB and a normalized correlation (NC) exceeding 98% following the simultaneous application of rotation and JPEG compression attacks, the proposed method demonstrates a substantial improvement over previous approaches and effectively establishes a balance between imperceptibility and robustness.