Abstract: In this study, a reversible data hiding for natural images are proposed. It exploits the technique of orthogonal prediction error modification and multilevel histogram shifting. The proposed orthogonal prediction error modification strategy uses the sets of basic pixels to predict the value of non-basic pixels. A histogram is constructed based on the sequences of prediction errors, and a multilevel histogram shifting mechanism is designed for embedding secret data. In decoder, the cover image pixels and secret data are perfectly recovered. The experimental results show the effectiveness of the proposed scheme. As more embedding levels are used in data hiding, the capacity can be enhanced to about 1.0 bit per pixel. Meanwhile, the visual quality can be achieved as larger than 30 dB.
INTRODUCTION
Recently, the technique of reversible data hiding (Ahmed et al., 2010; Hong et al., 2009a; Li et al., 2011; Liu et al., 2010; Luo et al., 2011; Mohammad et al., 2011; Phadikar et al., 2007; Qureshi and Tao, 2006; Wang et al., 2008) has attracted increasing interests. Its key advantage is not only the secret data but also the host image can be accurately recovered in decoder. Because the reversibility of this technique, it plays an important role in some specific scenarios such as military, medical diagnosis, law enforcement and so on, where the cover images must be accurately reconstructed after data extraction.
Currently, research in reversible data hiding has become quite important. A lot of reversible data hiding schemes have been proposed in literatures. These schemes can be classified into frequency domain, compressed domain and spatial domain based schemes. Generally, the spatial domain schemes are the basis of other transform and compressed domain schemes; it can be divided into two effective ways to accomplish reversible data hiding categories. One is based on Difference Expansion (DE) and the other is based on histogram shifting.
Tian (2003) firstly proposed DE scheme. Its principle is to expand the differences of a pair of pixels and embed secret bits into the LSB of the expanded difference. Alattar (2004) developed Tian’s method by using four neighboring pixels to carry more of secret data to improve the embedded capacity and image quality. Hong et al. (2009b) introduced a novel difference expansion scheme based on modification of prediction errors. This scheme firstly predicts pixel values and then obtains error values. Secret bits are embedded reversibly by modifying the values of prediction errors, which provides higher embedding capacity with better image quality.
Ni et al. (2006) proposed a reversible data hiding scheme based on the histogram shifting technique. In their scheme, the zero and peak points of an image histogram are shifted to vacate an empty bin for data embedding and achieved reversibility. Their scheme achieves low computational cost and high visual quality; however, the embedding capacity is low and mainly depends on the distribution of image histogram Li et al. (2010) a proposed histogram shifting scheme based on the Adjacent Pixels Differences (APD). This scheme employs the histogram of the pixel difference sequence to increase the embedding capacity. Zhao et al. (2011) proposed a reversible data hiding scheme based on multilevel histogram shifting, the differences histogram is constructed and employed multilevel histogram shifting mechanism for data embedding, and their method greatly improved the capacity. Generally, performance of a data hiding scheme is evaluated in terms of embedding capacity and the marked image quality. The DE based schemes can provide a higher capacity for secret data embedding, while the histogram shifting based schemes can obtain a better quality marked images. Nowadays, many efforts are committed to improving the overall performance.
Thodi and Rodriguez (2007) firstly combined the difference expansion and histogram shifting methods and proposed a new embedding method to improve the distortion performance and achieve reversibility. Although their method effectively improves the embedding capacity, the compressibility of the location map is undesirable for some images. Hong et al. (2010) designed a high capacity reversible data hiding scheme using orthogonal projection and prediction error modification, an orthogonal projection technique is used to compute the best weights for a predictor, so that prediction errors can be significantly reduced to achieve high capacity and better image quality.
RELATED WORK
Hong et al. (2010). exploited the Orthogonal Projection Technique (OPT) to predict pixel values and modify the error values using the histogram shifting technique. In this method, the orthogonal projection technique is an weighted linear predictor. The value of current processing pixel pj is predicted by a weighted sum of its three neighboring pixels, as shown in Fig. 1. And the prediction of pj are computed as:
| (1) |
where, n is the weight of neighboring pixels mj(1), mj(2), mj(3) of the current processing pixel pj .
The best weights for an linear predictor which minimize the prediction error can be computed as:
| (2) |
The above equation can be rewritten as the matrix form.
| (3) |
| Fig. 1: | The relationship of pj and it’s neighboring pixels |
where, M = [m(1), m(2), m(3)]' and N = [n1, n2, n3]. The weights N can be calculated as:
| (4) |
And then compute the predication value of pj one by one according to Eq. 1 and 4. The histogram of prediction errors is shifted to embed secret data.
Zhao et al. (2011) proposed a reversible data hiding method based on multilevel histogram shifting and sequential recovery. The data embedding and data extraction is based on a multi level histogram shifting mechanism. A higher capacity is obtained using Zhao et al. (2011) method.
PROPOSED SCHEME
Generally, an integer parameter g named the embedding level in which the multilevel histogram shifting strategy is used to control the hiding capacity, a larger g indicates the more predicted errors provided, the more secret data can be embedded.
The method of Hong et al. (2010) was adopted to predict pixel values in residue image, and then the predication errors are achieved. Secret data is embedded into the histogram of prediction errors using histogram shifting. However, Hong et al. method only select one pair of peak bin and zero bins in the process of histogram shifting. As a result, the capacity is not excellent.
In this study, a novel multilevel histogram shifting strategy based on OPT was proposed. The more pairs of peak-zero points can be utilized; our method designed a multilevel histogram shifting mechanism for a large capacity data hiding.
Data embedding: Given a cover image I sized MxN and secret data S, the data embedding details are described as follows:
| • | Step 1: Compute weights N of linear predictor according to Eq. 4. | ||
| • | Step 2: The first row and first column of I is selected as the
basic pixel for predicted image I', the prediction values of the rest elements
are computed according to Eq. 1. the predicted image I'
can be obtained. Calculate the prediction errors e as:
|
||
| • | Step 3: Construct the histogram of these prediction errors with the exception of the first row and first column. Suppose the bins of histogram from left to right are denoted by h-255, h-254… h-1, h0, h1… h254, h255. Given an integer parameter g named embedding level is used to control the embedding capacity, the multilevel histogram mechanism is exploited in the data embedding stage: | ||
| • | Step 4: The prediction errors e is modified into the shifted
differences e' (2≤i≤MxN) as:
|
||
| • | Step 5: Next, embed the secret data s into the shifted differences
e', compute marked difference e''i as:
|
||
| • | Step 6: Compute the capacity Cap (bit) as:
|
||
| • | Step 7: Generate the marked pixel Is(i, j) as:
|
where, 2≤i ≤m, 2≤j≤n.
| • | Step 8: Repeat Steps 1-7, the marked image Is is obtained |
Data extraction and Image recovery: In this process, the details of the data extraction and image recovery are described as follows:
| • | Step 1: Initialize the first row and first column of the marked image Is as left-and-top-most one of the recovered cover image I |
| • | Step 2: Compute the predicted values Iij’ of the recovered cover image I according to the following Equation: |
| (10) |
where, round (●) represents rounding the element to the nearest integers. and 1≤i≤m-1, 1≤j≤n-1.
EXPERIMENTAL RESULTS AND COMPARISONS
As shown in Fig. 2, six 512x512 gray level natural images are selected as test image. The secret data is binary sequences generated by pseudo-random number generator.
Our scheme is compared with Hong et al. (2010) method, As the results shown in Table 1, 2.The Tables list the capacity and PSNR values of Hong et al.’s method and the proposed scheme with g = 1, ….9. Hong et al.’s method only provides one pair of peak-zero bins in histogram shifting but our scheme exploits the multilevel histogram shifting of many pairs of peak-zero bins. Obviously, our scheme can provide a higher capacity than Hong et al.’s method.
The six marked images obtained by our scheme and Hong et al. scheme are shown in Fig. 3-8. All results demonstrate the capacities are improved in our scheme, the average PSNR value is larger than 30 dB even when g = 9. As human eyes are not sensitive to distortions when PSNR>30 dB, the visual quality of the marked images are acceptable.
| Table 1: | Comparison of PSNR and capacity for Hong et. al’s method and our method on Elaine, Goldhill, Couple images |
| Table 2: | Comparison of PSNR and capacity for Hong et al. (2009a,b) method and our method on Airplane, Frog, Barbara images |
| Fig. 2(a-f): | Test images (a) Elaine (b) Goldhill (c) Couple (d) Aerial (e) Frog (f) Barbara |
| Fig. 3(a-b): | Visual quality comparison for two methods: (a) Marked Elaine images obtained by Hong et al.’s method (17773 bits hidden, 51.13 dB) and (b) Marked Elaine images obtained by our method with g = 9 (203984 bits hidden, 32.47 dB) |
| Fig. 4(a- b): | Visual quality comparison for two methods: (a) Marked Goldhill images obtained by Hong et al.’s method (19496 bits hidden, 51.06 dB) and (b) Marked Goldhill images obtained by our method with g = 9 (115580 bits hidden, 33.20 dB) |
| Fig. 5 (a-b): | Visual quality comparison for two methods: (a) Marked Couple images obtained by Hong et al.’s method (26840 bits hidden, 51.04 dB) and (b) Marked Couple images obtained by our method with g = 9 (230171 bits hidden, 34.32 dB) |
| Fig. 6 (a-b): | Visual quality comparison for two methods: (a) Marked Airplane images obtained by Hong et al.’s method (40134 bits hidden, 51.04 dB) and (b) marked Airplane images obtained by our method with g = 9 (236813 bits hidden, 35.53 dB) |
| Fig. 7(a-b): | Visual quality comparison for two methods: (a) Marked Frog images obtained by Hong et al.’s method (8570 bits hidden, 51.03 dB) and (b) marked Frog images obtained by our method with g = 9 (115580 bits hidden, 30.15 dB) |
| Fig. 8 (a-b): | Visual quality comparison for two methods: (a) Marked Barbara images obtained by Hong et al.’s method (22419 bits hidden, 50.84 dB) and (b) Marked Barbara images obtained by our method with g = 9 (193291 bits hidden, 32.73 dB) |
CONCLUSIONS
This study proposes a novel reversible data hiding scheme based on orthogonal prediction modification (OPT). OPT technique can obtain the best weights of a predictor. As a result, the most prediction errors also are concentrated around zero. The multilevel histogram shifting strategy can provide higher embedding capacity is compared with one level histogram shifting method. Experimental results show our proposed method outperforms Hong et al.’s method. Therefore, our method is efficient.
ACKNOWLEDGMENT
This study is supported by the project from Zhejiang University of Media and Communications with No. 2C11XJ045.