Grayscale-invariant reversible data hiding (GI-RDH) in color images is a data embedding framework in which the grayscales of a marked color image must be identical to those of the host color image. Recently, some state-of-the-art GI-RDH schemes were proposed. However, their performance in embedding distortion is unsatisfactory. In order to obtain better image quality, a well-known histogram-shifting-based RDH method called multiple histograms modification (MHM) is considered. In this paper, we propose an MHM-based GI-RDH scheme. First, we modified our previous GI-RDH scheme using a multiple-histogram-shifting approach instead of a difference expansion approach. Next, we designed a procedure to select expansion–bin pairs for generated histograms to achieve low embedding distortion through further data embedding. Specifically, we analyzed the expected embedding distortion of our MHM-based GI-RDH scheme given any set of expansion–bin pairs. We then formulated an optimization problem called the GI-MHM minimization problem to identify the optimal expansion–bin pairs for further embedding tasks. Finally, we generated an approximated solution for the GI-MHM minimization problem and conducted the embedding task with these selected expansion–bin pairs. The experimental results revealed that the proposed GI-RDH scheme outperformed previous methods when the embedding capacity was small.

中文翻译：

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基于多重直方图修正的灰度不变可逆数据隐藏


彩色图像中的灰度不变可逆数据隐藏（GI-RDH）是一种数据嵌入框架，其中标记彩色图像的灰度必须与主彩色图像的灰度相同。最近，提出了一些最先进的 GI-RDH 方案。然而，它们在嵌入失真方面的表现并不令人满意。为了获得更好的图像质量，考虑了一种著名的基于直方图平移的 RDH 方法，称为多重直方图修改（MHM）。在本文中，我们提出了一种基于 MHM 的 GI-RDH 方案。首先，我们使用多重直方图移动方法而不是差异扩展方法修改了之前的 GI-RDH 方案。接下来，我们设计了一个程序来为生成的直方图选择扩展箱对，以通过进一步的数据嵌入来实现低嵌入失真。具体来说，我们分析了给定任何一组扩展箱对的基于 MHM 的 GI-RDH 方案的预期嵌入失真。然后，我们制定了一个称为 GI-MHM 最小化问题的优化问题，以确定进一步嵌入任务的最佳扩展箱对。最后，我们生成了 GI-MHM 最小化问题的近似解，并使用这些选定的扩展箱对执行嵌入任务。实验结果表明，当嵌入容量较小时，所提出的 GI-RDH 方案优于以前的方法。