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Pixel clustering is a technique of content-adaptive data embedding in the area of high-performance reversible data hiding (RDH). Using pixel clustering, the pixels in a cover image can be classified into different groups based on a single factor, which is usually the local complexity. Since finer pixel clustering seems to improve the embedding performance, in this manuscript, we propose using two factors for two-dimensional pixel clustering to develop high-performance RDH. Firstly, in addition to the local complexity, a novel factor was designed as the second factor for pixel clustering. Specifically, the proposed factor was defined using the rotation-invariant code derived from pixel relationships in the four-neighborhood. Then, pixels were allocated to the two-dimensional clusters based on the two clustering factors, and cluster-based pixel prediction was realized. As a result, two-dimensional prediction-error histograms (2D-PEHs) were constructed, and performance optimization was based on the selection of expansion bins from the 2D-PEHs. Next, an algorithm for fast expansion-bin selection was introduced to reduce the time complexity. Lastly, data embedding was realized using the technique of prediction-error expansion according to the optimally selected expansion bins. Extensive experiments show that the embedding performance was significantly enhanced, particularly in terms of improved image quality and reduced time complexity, and embedding capacity also moderately improved.

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