This paper deals with reversible contrast enhancement (RCE). Image enhancement is achieved by histogram specification, the most popular contrast enhancement technique. A low bitrate procedure for inverting histogram specification is developed. The data for original image recovery is reversibly embedded into the contrast enhanced version. Very low distortion RDH schemes that exploit the sparse histogram of the contrast enhanced images are also proposed. Their major novelties are: embedding only into the histogram bins that provide room without any pixel shifting or overflow/underflow control, and encoding of embedded data sequence with fewer bits of “1”. The newly proposed RDH can exceed 1 bpp at average square errors per embedded bit between 0.375 and 0.5. It should be stressed that one gets reversibility at the distortion of least significant bit substitution algorithms. Experimental results are presented. With the proposed RCE-HS, reversibility is obtained without any visual distortion.

The reversible data hiding in encrypted images by MSB prediction of P. Puteaux and W. Puesch not only provides high embedding bit-rates, but also entails a very low mathematical complexity. This correspondence investigates its security and shows flaws in embedding imperceptibility, unauthorized detection/removal of embedded data and unauthorized access to image content. Secure solutions are discussed.

Pixel-value-ordering (PVO) appears as an efficient solution for high-fidelity reversible data hiding. State-of-the-art PVO schemes split the host image into blocks, sort pixels within the blocks based on their graylevel and, finally, embed data into some differences between the sorted values. This paper investigates the use of the prediction error instead of the pixel graylevel both for ordering and embedding. The proposed prediction-error-ordering (PEO) scheme also introduces a two-stage procedure by splitting each block in two sets following a chessboard pattern and by processing set by set each block. The pixels of one set are used to classify and predict the ones of the other set and vice-versa. The proposed PEO approach outperforms the state-of-the-art PVO schemes.

This paper proposes a new vacating room after encryption reversible data hiding scheme. Hidden data is embedded into the encrypted host image by bit-flipping a preselected bitplane of a randomly formed pixel group. The major novelty of the paper is the use of multiple predictors in an adaptive procedure for detecting between original and modified pixels. Four predictors are used on a context of four neighbors, namely the average of the four pixels, a weighted average based on local gradients, the median and the midpoint. Experimental results are provided. Compared with the state-of-the-art reserving room after encryption schemes, the proposed approach provides higher embedding bit-rates at lower distortion.

This paper proposes a new vacating room after encryption reversible data hiding scheme developed for color images. The proposed scheme uses standard exclusive-or encryption and inherits the main features of vacating room after encryption schemes, namely joint and separate methods for data embedding. The proposed scheme exploits both the correlation between neighboring pixels and the correlation between color channels by predicting the original pixel values on color channel differences. The experimental results show that the proposed scheme can eliminate the main drawback of the vacating room after encryption framework, namely the large embedding distortions.

Pixel-value-ordering (PVO) appears as an efficient technique for high-fidelity reversible data hiding. This paper proposes a reversible data hiding scheme based on the pairwise PVO framework with improved difference equations. Both the pixel pair selection and the embedding algorithms are also streamlined. The proposed scheme uses a block classification approach based on a local complexity metric. Uniform blocks are processed using the proposed improved pairwise PVO algorithm. Slightly noisy blocks are embedded using a classic PVO scheme and noisy blocks are kept unchanged. The optimal embedding parameters for a given capacity are determined by linear programming. The proposed pairwise PVO approach outperforms other state-of-the-art schemes.

This letter revisits the pairwise reversible watermarking scheme of Ou et al., 2013. An adaptive pixel pairing that considers only pixels with similar prediction errors is introduced. This adaptive approach provides an increased number of pixel pairs where both pixels are embedded and decreases the number of shifted pixels. The adaptive pairwise reversible watermarking outperforms the state-of-the-art low embedding bit-rate schemes proposed so far.

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.

The distortion introduced by reversible watermarking depends on the embedding bit-rate. This paper proposes a fine control of the embedding bit-rate for low capacity histogram shifting reversible watermarking. The basic idea of our approach is to split the prediction error histogram into several histograms and to ensure the fine tuning of the bit-rate by selecting the appropriate bins for each histogram. The splitting is performed as a function of the prediction context. The bins (two for each histogram, one for the right side, another for the left side of the histogram) are selected by linear programming in order to minimize the distortion introduced by the watermarking. The proposed scheme outperforms in terms of embedding distortion the prior state of the art.

This paper proposes a novel predictor, EGBSW (Extended Gradient Based Selective Weighting), and investigates its usefulness in difference expansion reversible watermarking. EGBSW is inspired by GBSW, a causal predictor previously used in lossless image compression and known to outperform well-known predictors as the median edge detector (MED) or the gradient-adjusted predictor (GAP). The proposed predictor operates on a larger prediction context than the one of GBSW, namely a rectangular window of 16 pixels located around the pixel to be predicted. Similar to GBSW, the extended predictor computes the gradients on horizontal, vertical and diagonal directions and selects the smallest two gradients. Opposite to the classical predictor, EGSBW uses a set of four simple linear predictors associated with the four principal directions and computes the output value as a weighted sum between the predicted values corresponding to the selected gradients. The reversible watermarking scheme based on EGBSW appears to outperform not only the ones based on GBSW, MED or GAP, but also some recently proposed schemes based on the average on the rhombus context. Experimental results are provided.

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.

The embedding not only into the current pixel, but also into the prediction context was recently proposed as an improvement of difference expansion reversible watermarking algorithms. So far it was shown that the effect of splitting the data between the current pixel and the prediction context decreases the embedding distortion, but increases the prediction error. This paper revisits the case of context embedding for the case of pixel prediction on the rhombus composed of the two vertical and the two horizontal neighbors. For this case it appears that the context embedding can be used not only to reduce the embedding distortion, but also to improve the prediction. The gain provided by the improvement of the prediction outperforms the one provided by the reduction of the embedding distortion. Experimental results are provided.

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.

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.

This paper continues our researches on high capacity reversible watermarking based on simple transforms. Image pixels obeying some simple constraints are transformed and then, data is embedded by simple additions. The transform induces a congruence equation. At detection, the transformed/not transformed pixels are found by checking the congruence, watermark codes are extracted and original image is recovered. The proposed method is of very low mathematical complexity and does not need additional data compression. The major novelty of the proposed technique is the use of a different transform which allows the embedding of watermark codewords into each transformed pixel. Thus, the improved version provides considerably higher embedding bit-rate. Experimental results for a single embedding level are presented.

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 high capacity low cost reversible watermarking scheme. Image is partitioned in pairs of pixels. In order to satisfy a congruence equation, the pairs obeying some simple constraints are transformed. By adding some correction data, the not transformed pixel pairs are enforced to obey the same equation, too. The payload and the correction data are embedded into the transformed pixels by simple additions. After watermark insertion, only the not transformed pixel pairs satisfy the congruence equation. This allows transformed pairs localization, payload and correction data extraction and, finally, exact recovery of the original image. The proposed scheme can provide, in a single pass, bit-rates greater than 1 bit per pixel without any additional data compression.

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.

The paper proposes a spatial domain watermarking scheme for image authentication and, in case image content has been changed, for localization of the altered area. A pseudo-random set of pixels is selected by using a secret key and is marked with a visually meaningful watermark by exact histogram specification. The exact recovery of the watermark authenticates the image. Specially designed watermarks are used to locate the altered area. Image visual aspect as well as image histogram are preserved. The approach addresses gray level and color images as well.

For graylevel images, the histogram based watermarking approach considers the image histogram as its signature and, by exact histogram specification, images are marked accordingly. This paper extends to color images the histogram based watermarking. Image marking is performed in the hue, saturation, intensity (HSI) space by creating notches in the intensity component histogram. The number of notches and their locations are the features which define each watermark. The detection is blind and of considerably low complexity. Robustness of the proposed method is investigated-tests performed using StirMark show that marking with notches ensures high robustness against many attacks: JPEG compression, geometric distortions (cropping, scaling, rotation, row and column removal, translation, etc.,), linear and nonlinear filtering.

The paper investigates the use of exact histogram specification for robust watermarking. A class of watermarks are selected such that the presence of certain groups of consecutive gray levels is considerably reduced with no visual degradation of images. The proposed technique is proven to be very resistant to many intentional and unintentional attacks.

The paper investigates the definition of strict ordering relations on digital graylevel images. The information needed for strict ordering is extracted by a vectorial operator in the local context of each pixel. The paper focuses on ordering which refines the natural ordering defined on the lattice of integers: pixels having greater graylevel preserve inequality while equal graylevel pixels are differentiated. Applications in exact histogram specification, segmentation and image normalization are discussed.

A general approach for residual representation of one-dimensional (1-D) and two-dimensional (2-D) signals is defined. Signals are reconstructed as a sum of components that are recursively determined by using a constructive transform. Several morphological constructive transforms are proposed and their corresponding representations are discussed. The use of residual representations in signal and image compression is investigated with promising results.

In this paper we propose a new class of filters called Jordan decomposition filters. They are upper and lower bounds of the well-known max and min filters. Our approach is based on a decomposition scheme by representing bounded variation signals as a difference of two increasing functions. Jordan filters are computed as the difference between the local extrema values of the increasing functions. They are faster than max/min filters. The number of operations per sample is constant, regardless the size of the window filter. The computational complexity of the proposed filters decreases with the number of filtering steps needed in an application. Examples are provided and the application in contrast enhancement is investigated.