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.

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.

This paper aims at reducing the embedding distortion of prediction error expansion reversible watermarking. Instead of embedding the entire expanded difference into the current pixel, the difference is split between the current pixel and its prediction context. The modification of the context generates an increase of the following prediction errors. Global optimization is obtained by tuning the amount of data embedded into context pixels. Prediction error expansion reversible watermarking schemes based on median edge detector (MED), gradient-adjusted predictor (GAP), and a simplified GAP version, SGAP, are investigated. Improvements are obtained for all the predictors. Notably good results are obtained for SGAP-based schemes. The improved SGAP appears to outperform GAP-based reversible watermarking.

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

This paper proposes a low-distortion transform for prediction-error expansion reversible watermarking. The transform is derived by taking a simple linear predictor and by embedding the expanded prediction error not only into the current pixel but also into its prediction context. The embedding ensures the minimization of the square error introduced by the watermarking. The proposed transform introduces less distortion than the classical prediction-error expansion for complex predictors such as the median edge detector or the gradient-adjusted predictor. Reversible watermarking algorithms based on the proposed transform are analyzed. Experimental results are provided.

The use of local prediction in difference expansion reversible watermarking provides very good results, but at the cost of computing for each pixel a least square predictor in a square block centered on the pixel. This correspondence investigates the reduction of the mathematical complexity by computing distinct predictors not for pixels, but for groups of pixels. The same predictors are recovered at detection. Experimental results for the case of prediction on the rhombus defined by the four horizontal and vertical neighbors are provided. It is shown that by computing a predictor for a pair of pixels, the computational cost is halved without any loss in performance. A small loss appears for groups of three and four pixels with the advantage of reducing the mathematical complexity to a third and a fourth, respectively.