Local feature-based mutual complexity for pixel-value-ordering reversible data hiding

In reversible data hiding, pixel-value-ordering (PVO) has become a widely used framework benefiting from its high-fidelity under low-capacity requirements. As an essential element in PVO-based methods, complexity could effectively avoid embedded images from unnecessary embedding distortions. There are two main context-pixel-selection strategies in existing complexity methods: inside-block and outside-block pixel selection strategy, which show strong complementarity. To make full use of this characteristic and further mitigate the insufficient feature representation problem in complexity, we propose a multi-complexity mechanism: Mutual Complexity. First, we analyse the relationship between complexity and Capacity-Distortion performance and innovatively regard the complexity problem as a binary classification problem. Then, precision and recall are taken as the optimization objectives and mutual pixels with the best performances could be selected. As a result, our proposed method can leverage different local features represented by various complexities and obtain the best classification result. Furthermore, to solve the block-dependent embedding problem in existing complexities, a simple but effective complexity, named Neighbor Complexity, is designed according to pixel location information. Experimental results show that Mutual Complexity could be easily generalized to different PVO-based methods and the embedding distortions are all effectively controlled.