DS-DPSO: A dual surrogate approach for intelligent watermarking of bi-tonal document image streams

Intelligent watermarking (IW) techniques employ population-based evolutionary computing in order to optimize embedding parameters that trade-off between watermark robustness and image quality for digital watermarking systems. Recent advances indicate that it is possible to decrease the computational burden of IW techniques in scenarios involving long heterogeneous streams of bi-tonal document images by recalling embedding parameters (solutions) from a memory based on Gaussian Mixture Model (GMM) representation of optimization problems. This representation can provide ready-to-use solutions for similar optimization problem instances, avoiding the need for a costly re-optimization process. In this paper, a dual surrogate dynamic Particle Swarm Optimization (DS-DPSO) approach is proposed which employs a memory of GMMs in regression mode in order to decrease the cost of re-optimization for heterogeneous bi-tonal image streams. This approach is applied within a four level search for near-optimal solutions, with increasing computational burden and precision. Following previous research, the first two levels use GMM re-sampling to recall solutions for recurring problems, allowing to manage streams of heterogeneous images. Then, if embedding parameters of an image require a significant adaptation, the third level is activated. This optimization level relies on an off-line surrogate, using Gaussian Mixture Regression (GMR), in order to replace costly fitness evaluations during optimization. The final level also performs optimization, but GMR is employed as a costlier on-line surrogate in a worst-case scenario and provides a safeguard to the IW system. Experimental validation were performed on the OULU image data set, featuring heterogeneous image streams with a varying levels of attacks. In this scenario, the DS-DPSO approach has been shown to provide comparable level of watermarking performance with a 93% decline in computational cost compared to full re-optimization. Indeed, when significant parameter adaptation is required, fitness evaluations may be replaced with GMR.