Traditional prediction error expansion (PEE)-based reversible data hiding (RDH) schemes focus on generating a sharp prediction error histogram (PEH) in order to increase embedding performance, but they neglect the influence of local complexity on embedding performance. When the PEH is partitioned into multiple sub-histograms by means of the local complexity, the embedding performance can be increased by excluding the embedding of data in the sub-histograms located in the texture regions. However, multiple sub-histograms also cause a problem about how to identify the optimal embedding points that can achieve the best visual quality for a given payload. Violent iteration is often used in RDH schemes to traverse all possible values of the embedding points in order to identify the optimal points. Therefore, we conclude that violent iteration is a very time-consuming method and that it leads to unacceptable computational complexity. The traditional multiple sub-histogram methods usually reduce the solution space (i.e., all possible combinations of the embedding points) to decrease the computational complexity. However, the solution that is obtained from the aforementioned methods may significantly deviate from the global optimal solution. Instead of shrinking the solution space by abandoning most solutions, we improve the crisscross optimization algorithm in order to search for the optimal solution in the global solution space. In this paper, the K-means clustering algorithm is used to classify all prediction errors into multiple categories according to the local complexity. Each category would generate a PEH. Subsequently, the problem of selecting the embedding points of multiple sub-histograms is transformed into a typical and multi-choice knapsack problem. The improved crisscross optimization algorithm is used to determine the approximate optimal solution. The experimental results showed that our scheme provided effective performance.

传统的基于预测误差扩展（PEE）的可逆数据隐藏（RDH）方案专注于生成清晰的预测误差直方图（PEH），以提高嵌入性能，但它们忽略了局部复杂度对嵌入性能的影响。当通过局部复杂度将PEH划分成多个子直方图时，可以通过排除数据在位于纹理区域中的子直方图中的嵌入来提高嵌入性能。但是，多个子直方图也引起了一个问题，即如何识别可以为给定有效负载实现最佳视觉质量的最佳嵌入点。RDH方案中经常使用暴力迭代遍历嵌入点的所有可能值，以识别最佳点。因此，我们得出的结论是，剧烈迭代是一种非常耗时的方法，并且它导致无法接受的计算复杂性。传统的多个子直方图方法通常会减少解空间（即嵌入点的所有可能组合），从而降低计算复杂度。但是，从上述方法获得的解决方案可能会明显偏离全局最优解。我们没有放弃大多数解决方案来缩小解决方案空间，而是改进了交叉优化算法，以便在全局解决方案空间中搜索最佳解决方案。在本文中，K-means聚类算法用于根据局部复杂度将所有预测误差分为多个类别。每个类别都会生成一个PEH。后来，选择多个子直方图的嵌入点的问题被转化为典型的多选背包问题。改进的交叉优化算法用于确定近似最优解。实验结果表明我们的方案提供了有效的性能。