Elsevier

Signal Processing

Volume 92, Issue 3, March 2012, Pages 819-828
Signal Processing

Reducing location map in prediction-based difference expansion for reversible image data embedding

https://doi.org/10.1016/j.sigpro.2011.09.028Get rights and content

Abstract

In this paper, we present a reversible data embedding scheme based on an adaptive edge-directed prediction for images. It is known that the difference expansion is an efficient data embedding method. Since the expansion on a large difference will cause a significant embedding distortion, a location map is usually employed to select small differences for expansion and to avoid overflow/underflow problems caused by expansion. However, location map bits lower payload capacity for data embedding. To reduce the location map, our proposed scheme aims to predict small prediction errors for expansion by using an edge detector. Moreover, to generate a small prediction error for each pixel, an adaptive edge-directed prediction is employed which adapts reasonably well between smooth regions and edge areas. Experimental results show that our proposed data embedding scheme for natural images can achieve a high embedding capacity while keeping the embedding distortion low.

Highlights

► We present a reversible data embedding scheme based on difference expansion. ► We use an adaptive edge-directed prediction to generate small prediction errors. ► Edge detectors are used to reduce location map bits. ► Less location maps may improve PSNR-payload performance and justified by experiments.

Introduction

Data embedding, or digital watermarking, refers to the process of embedding watermark bits into a host media signal like audio, images and video without modifying or distorting the host signal significantly [1], [2]. A variety of embedding techniques, e.g., high capacity selected-feature modification or transform-domain spread spectrum methods have been used in various applications such as authentication, secret communications, and content-protection. Most multimedia data-embedding techniques modify and distort the host signal in order to insert the additional information. The distortion induced on the host signal by the data embedding technique is called the embedding distortion. The embedding distortion is generally designed to be as small as possible. Depending on the loss of host signal fidelity after the data extraction, data embedding techniques can be classified into two categories: lossy data embedding and lossless (or reversible) data embedding techniques. In many applications, the loss of host signal fidelity is permissible as long as original and modified signals are perceptually equivalent [3], [4]. The lossless data embedding techniques enable the removal of embedding distortions and the exactly lossless recovery of the original host signal after extraction of embedded information, which makes it suitable in military, legal and medical imaging applications.

In this paper, we investigate into reversible data embedding on natural images. A general block diagram representing reversible data-embedding schemes is shown in Fig. 1. The lossless embedding step takes the host and watermark signals and produces a watermarked host signal. The data extraction and recovery process attempts to extract the embedded watermarked host signal and recover the original host signal exactly. Note that although the recovery process allows lossless reconstruction of the original host signal, it is still necessary or highly desirable to keep the embedding distortion to a minimum.

The earliest references to reversible data embedding can be found in the patents [5], [6]. De Vleeschouwer et al. [7] proposed a reversible data-embedding algorithm by circular interpretation of bijective transformations. Many other data embedding algorithms are to embed information bits by modifying the selected features of the host signal, e.g., overwriting least significant bits (LSBs). Taking an area in an image for data embedding, the watermark payload P, original selected features O (e.g., LSBs) together with some possible additional information L are embedded. The total amount of these data should be smaller than the embedding capacity C of the area, that is, |P|+|O|+|L|<|C|. O and L are usually compressed losslessly to save space for the embedding of more payloads P. Fridrich et al. [8] developed a high capacity reversible data-embedding technique by embedding message bits in the status of group of pixels. Celik et al. [9] presented a high capacity, low distortion reversible data-embedding algorithm by compressing quantization residues. The lossless image compression algorithm context-based adaptive lossless image coding (CALIC) [10] is employed to efficiently compress quantization residues with the quantized values as side-information and a high embedding capacity is obtained.

Tian proposed a difference expansion method for data embedding in [11]. The image pixels are divided to pairs and the difference values between two neighboring pixels are computed for the purpose of hiding data. A location map bit is assigned to each pair to indicate whether the pair is embedded by the watermark bits or not. Location map bits are the main part of the L. Since the location map has a large size (i.e., half of image resolution), compression has to be done before embedding it. Location map bits can be compressed well using some efficient lossless compression algorithms such as arithmetic coding. Alattar improved the difference expansion method using other integer transforms, which increase the units of data embedding from pair to triplet [12] and quad [13]. In [12] three pixels are used to hide two bits in each triplet, so that the size of location map is equal to one-third of the size of host image. The location map compression performance places an important rule in the overall efficiency of the methods [11], [12], [13]. The reversible embedding method in [14] has produced a smaller size of location map and it is independent on the lossless compression algorithm. This simplified location map only contains the information of those intersected cells (for pairs, triplets or quads) after embedding. Kamstra and Heijmans [15] also improved Tian's difference expansion technique. They proposed a method to reduce the size of location map by sorting pairs based on correlation measures to facilitate compression.

Lee et al. [16] used an advanced watermarking technique based on integer wavelet transform. In their method, an image is firstly divided into non-overlapping blocks. For each block, expandability and changeability over high-frequency wavelet coefficients are defined. A data hiding technique is then applied on each block based on these definitions. Thodi and Rodriguez [17] proposed a histogram shift method for embedding data in JPEG-LS prediction errors. The location map used in the scheme covers all ambiguous cells. Ambiguous cells include all cells that cannot be decoded without a location map. Also in [17], Thodi and Rodriguez proposed advanced methods based on difference expansion technique. Their methods exploit the histogram shift technique for embedding data, which combines the difference expansion with histogram shifting. In [18], Sachnev et al. proposed a reversible watermarking technique which employs prediction errors to embed data into an image. They used the idea of sorting technique in [15] to record prediction errors based on magnitudes of their local variances. Using sorted prediction errors and a reduced size location map can embed more data into the image with less distortion. Coltuc [19], [20] developed high capacity reversible embedding schemes based on simple transforms. The transforms induce a congruence equation to avoid using location map bits in the extraction and recovery process. However, a larger embedding distortion is presented in these high capacity schemes, compared with those based on location maps [11], [12], [13]. In [21] Weng et al. introduced a novel reversible data hiding scheme based on invariability of the sum of pixel pairs and pairwise difference adjustment.

In this paper, we develop an efficient reversible data embedding method for natural images, which embeds watermark bits in the prediction error between an original pixel value and its prediction. To minimize the embedding distortion, small prediction errors (we consider their absolute values) need to be generated and selected for difference expansion. On one hand, the small prediction errors are achieved by the edge-directed prediction (EDP) method in [22], which is one of the least-square (LS) based prediction methods for lossless image compression. On the other hand, an edge detector is used to select small errors for embedding. Since the edge detector can predict the small prediction error well, the corresponding location map bit can be saved. Specifically, the small prediction errors usually lie in the smooth regions of the image, we can use edge detectors to foresee these regions and try to avoid using the location map bit for each pixel. As a result the scheme we proposed is able to achieve high embedding capacity with small embedding distortion, only with cost of a few bits on locations where the overflow/underflow problems occur.

The rest of the paper is organized as follows. Section 2 describes the concepts of difference expansion and LS-based adaptive prediction. The proposed data embedding method is described in Section 3. Experimental results are included in Section 4 followed by conclusions in Section 5.

Section snippets

Difference expansion

In difference expansion based data embedding schemes, reversible integer transforms can be used to set up a one-to-one mapping between two pairs (x,y) and (l,h). If the Haar wavelet transform is used for this mapping, thenl=x+y2,h=xywhere h is the difference between x and y.

The inverse transform of (1) isx=l+h+12,y=lh2For an 8-bit grayscale-valued pair (x,y) with 0x,y255, the following condition should be held to restrict x and y in the range of [0, 255] to prevent overflow/underflow

Data embedding

The difference expanding process in the proposed scheme is simple at the sender side. To embed a watermark bit in the current pixel X(n), we consider the prediction errore(n)=X(n)X^(n)=hThen the expanded prediction error e(n) ise(n)=h=2×h+b=2×e(n)+bTo avoid overflow/underflow problems, e(n) has to satisfy (10). It is known that difference expansion is a good method for data embedding to achieve embedding capacity with low embedding distortion in image quality [11], [12], [14]. Location map

Experimental results

To validate the effectiveness of the proposed data embedding scheme, we consider coding four 512×512 8-bit images as shown in Fig. 6. “Lena” is an image with large smooth regions while “Barbara”, “Baboon” and “Boat” contain textured regions. The performance of PSNR vs. payload is used for comparison. PSNR is calculated byPSNR=10·log102552MSEwhere MSE (mean square error) is calculated byMSE=i=1512j=1512(I(i,j)I(i,j))2512·512with I being the original image and I being the watermarked image.

Conclusion

In this paper, a novel reversible data embedding scheme has been proposed for natural images. An edge-directed prediction method has been used to generate small prediction errors for all pixels. A gradient-based edge detector only using causal pixels has been employed to predict whether the prediction error for the current pixel location is small enough and suitable for embedding. As a result, the amount of location map bits is reduced and the capacity of payloads increases accordingly. Our

Acknowledgments

This work has been supported by the National Research Foundation grant, which is administered by the Media Development Authority Interactive Digital Media Programme Office, MDA (IDMPO).

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