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The conventional histogram-based reversible data-hiding scheme is one-dimensional (1D). In this article, a novel framework that can be used to design 2D reversible data-hiding schemes is presented. Through the flexibility of selecting peaks for each channel, this 2D technique offers higher embedding performance than the conventional 1D techniques. For illustration, the framework is applied to develop two new schemes, C-2D and S-2D. Compared with the 1D schemes that use the predictions individually, the experimental results show that C-2D and S-2D have apparent performance advantages. This framework can be applied to any architecture. Furthermore, it can be easily extended into a multi-dimensional framework. By combining appropriate prediction methods, more reversible data-hiding schemes can be derived.