While in the continuous case, statistical models of histogram equalization/specification would yield exact results, their discrete counterparts fail. This is due to the fact that the cumulative distribution functions one deals with are not exactly invertible. Otherwise stated, exact histogram specification for discrete images is an ill-posed problem. Invertible cumulative distribution functions are obtained by translating the problem in a K-dimensional space and further inducing a strict ordering among image pixels. The proposed ordering refines the natural one. Experimental results and statistical models of the induced ordering are presented and several applications are discussed: image enhancement, normalization, watermarking, etc.

Reversible contrast mapping (RCM) is a simple integer transform that applies to pairs of pixels. For some pairs of pixels, RCM is invertible, even if the least significant bits (LSBs) of the transformed pixels are lost. The data space occupied by the LSBs is suitable for data hiding. The embedded information bit-rates of the proposed spatial domain reversible watermarking scheme are close to the highest bit-rates reported so far. The scheme does not need additional data compression, and, in terms of mathematical complexity, it appears to be the lowest complexity one proposed up to now. A very fast lookup table implementation is proposed. Robustness against cropping can be ensured as well.Index Terms-Difference expansion, embedding bit-rate, reversible contrast mapping (RCM), reversible watermarking.

This paper investigates the use of local prediction in difference expansion reversible watermarking. For each pixel, a least square predictor is computed on a square block centered on the pixel and the corresponding prediction error is expanded. The same predictor is recovered at detection without any additional information. The proposed local prediction is general and it applies regardless of the predictor order or the prediction context. For the particular cases of least square predictors with the same context as the median edge detector, gradient-adjusted predictor or the simple rhombus neighborhood, the local prediction-based reversible watermarking clearly outperforms the state-of-the-art schemes based on the classical counterparts. Experimental results are provided.