Altun H Oktay, Orsdemir Adem, Sharma Gaurav, Bocko Mark F
Electrical and Computer Engineering Department, University of Rochester, Rochester, NY 14627-0126, USA.
IEEE Trans Image Process. 2009 Feb;18(2):371-87. doi: 10.1109/TIP.2008.2008222. Epub 2009 Jan 6.
We consider optimal formulations of spread spectrum watermark embedding where the common requirements of watermarking, such as perceptual closeness of the watermarked image to the cover and detectability of the watermark in the presence of noise and compression, are posed as constraints while one metric pertaining to these requirements is optimized. We propose an algorithmic framework for solving these optimal embedding problems via a multistep feasibility approach that combines projections onto convex sets (POCS) based feasibility watermarking with a bisection parameter search for determining the optimum value of the objective function and the optimum watermarked image. The framework is general and can handle optimal watermark embedding problems with convex and quasi-convex formulations of watermark requirements with assured convergence to the global optimum. The proposed scheme is a natural extension of set-theoretic watermark design and provides a link between convex feasibility and optimization formulations for watermark embedding. We demonstrate a number of optimal watermark embeddings in the proposed framework corresponding to maximal robustness to additive noise, maximal robustness to compression, minimal frequency weighted perceptual distortion, and minimal watermark texture visibility. Experimental results demonstrate that the framework is effective in optimizing the desired characteristic while meeting the constraints. The results also highlight both anticipated and unanticipated competition between the common requirements for watermark embedding.
我们考虑扩频水印嵌入的最优公式，其中水印的常见要求，如带水印图像与载体的感知接近度以及在存在噪声和压缩情况下水印的可检测性，被作为约束条件，同时优化与这些要求相关的一个指标。我们提出一种算法框架，通过多步可行性方法来解决这些最优嵌入问题，该方法将基于凸集投影（POCS）的可行性水印与二分参数搜索相结合，以确定目标函数的最优值和最优带水印图像。该框架具有通用性，能够处理水印要求采用凸和拟凸公式的最优水印嵌入问题，并确保收敛到全局最优解。所提出的方案是集合论水印设计的自然扩展，为水印嵌入的凸可行性和优化公式之间提供了联系。我们在提出的框架中展示了许多最优水印嵌入，分别对应于对加性噪声的最大鲁棒性、对压缩的最大鲁棒性、最小频率加权感知失真以及最小水印纹理可见性。实验结果表明，该框架在满足约束条件的同时，能够有效地优化所需特性。结果还突出了水印嵌入常见要求之间预期和未预期的竞争。
