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Mathematical Problems in Engineering

Volume 2012 (2012), Article ID 164869, 14 pages

http://dx.doi.org/10.1155/2012/164869

## Histogram Modification and Wavelet Transform for High Performance Watermarking

^{1}Department of Business Administration, Chung Hua University, Hsinchu 30012, Taiwan^{2}Department of Electrical Engineering, National Central University, Chungli 32001, Taiwan^{3}Department of Electronics Engineering, Chung Hua University, Hsinchu 30012, Taiwan^{4}Department of Computer Science and Information Engineering, National United University, Miaoli 36003, Taiwan

Received 15 September 2012; Accepted 16 October 2012

Academic Editor: Sheng-yong Chen

Copyright © 2012 Ying-Shen Juang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper proposes a reversible watermarking technique for natural images. According to the similarity of neighbor coefficients’ values in wavelet domain, most differences between two adjacent pixels are close to zero. The histogram is built based on these difference statistics. As more peak points can be used for secret data hiding, the hiding capacity is improved compared with those conventional methods. Moreover, as the differences concentricity around zero is improved, the transparency of the host image can be increased. Experimental results and comparison show that the proposed method has both advantages in hiding capacity and transparency.

#### 1. Introduction

Digital watermarking is a technique to embed imperceptible, important data called watermark into the host image for the purpose of copyright protection, integrity check, and/or access control [1–9]. However, it might cause the distortion problem regarding the recovery of the original host image. In order to protect the host image from being distorted, a reversible watermarking technique has been reported in the literature. The reversible watermarking technique does not only hide the secret data but also the host image that can be exactly reconstructed in a decoder. Therefore, it can be used in those applications where the host images, such as medical images, military maps, and remote sensing images, must be completely recovered [10–14].

Recent reversible watermarking techniques can be divided into spatial domain, transform domain, and compressed domain methods. In spatial domain based methods [15–19], the secret data is embedded by pixels’ value modification. In the transform domain methods [20, 21], reversible-guaranteed transforms, such as integer discrete cosine transform and integer wavelet transform, are exploited and data embedding is depending on coefficient modulation. In the compressed domain methods [22, 23], image compression techniques like vector quantization and block truncation coding are involved.

Most spatial domain reversible watermarking techniques are developed based on three principles, they are difference expansion [15, 16] and histogram modification [17–19, 24]. Zhao et al. proposed a reversible data hiding based on multilevel histogram modification [19]. In this scheme, the inverse “S” order is adopted to scan the image pixels for difference generation. The embedding capacity is determined by two factors, the embedding level and the number of histogram bins around 0. However, with a better pixel scan path can provide a higher capacity with the embedding level not changing.

Wavelet transform provides an efficient multiresolution representation with various desirable properties such as subband decompositions with orientation selectivity and joint space-spatial frequency localization. In wavelet domain, the higher detailed information of a signal is projected onto the shorter basis function with higher spatial resolution; the lower detailed information is projected onto the larger basis function with higher spectral resolution. This matches the characteristics of a better situation for scaning the image pixels for difference generation [25, 26].

In this paper, we propose a reversible watermarking technique based on histogram modification and discrete wavelet transform. The remainder of the paper proceeds as follows. In Section 2, the reversible watermarking based on histogram modification is reviewed briefly. Section 3 describes the reversible watermarking based on histogram modification and discrete wavelet transform. Experimental results and comparison are presented in Section 4. Finally, conclusion is given in Section 5.

#### 2. Histogram Modification for Reversible Watermarking

Zhao et al. proposed a reversible data hiding based on histogram modification in [19]. In this scheme, the inverse “S” order is adopted to scan the image pixels for difference generation. The integer parameter called embedding level () controls the hiding capacity and transparency of the marked image. A higher indicates that more watermark can be embedded but leads more distortion to a watermarked image.

The data embedding process of is as follows, and the histogram modification strategy is shown in Figure 1. First, the image is inverse “S” scanned and the difference histogram is constructed. Next, the histogram shifting is performed. The secret bit “1” can be hidden by changing the difference of the pixel value from 0 to 1, and the “0” is hidden by keeping the difference of the pixel value not changed. Each marked pixel can be produced by its left neighbor subtracting the modified difference. Finally, rearrange these marked pixels to produce the watermarked image.

The process of data extraction and image recovery is as follows. The watermarked image is also inverse “S” scanned into a sequence first. As the first pixel value is not changed during embedding, we have the first pixel value. Second, the difference of the first pixel value and second pixel value can be obtained. If the difference is 0, one bit watermark “0” is extracted. If the difference is 1, one bit watermark “1” is extracted and the original difference is 0. Thus the original pixel associated with the difference can be obtained. If the difference is larger than 1, subtract 1 from the difference and recover the original pixel. Repeat these operations for the remained watermarked sequence and all the host pixels are recovered. Finally, rearrange these recovered pixels to produce the original host image.

The embedding capacity is determined by two factors, the embedding level and the number of histogram bins around 0. As mentioned before, a higher indicates that more watermark can be embedded, but leads more distortion to a watermarked image. However, with a better pixel scan path can provide a higher capacity with the embedding level not changing. Thus, we proposed an appropriate method to reach a higher capacity with embedding level .

#### 3. The Proposed Method

In this section, we proposed a novel reversible data hiding based on histogram modification and discrete wavelet transform. According to the similarity of neighbor coefficients’ values in wavelet domain, most differences between two adjacent pixels are close to zero. The histogram is built based on these difference statistics. As more peak points can be used for secret data hiding, the hiding capacity is improved compared with those conventional methods.

##### 3.1. Discrete Wavelet Transform

Discrete wavelet transform (DWT) provides an efficient multiresolution analysis for signals, specifically, any finite energy signal can be written by where denotes the resolution index with larger values meaning coarser resolutions, is the translation index, is a mother wavelet, is the corresponding scaling function, , , is the scaling coefficient representing the approximation information of at the coarsest resolution , and is the wavelet coefficient representing the detail information of at resolution . Coefficients and can be obtained from the scaling coefficient at the next finer resolution by using 1-level DWT, which is given by where , , and denote the inner product. It is noted that and are the corresponding low-pass filter and high-pass filter, respectively. Moreover, can be reconstructed from and by using the inverse DWT, which is given by where and .

For image applications, 2D DWT can be obtained by using the tensor product of 1D DWT. Among wavelets, Haar’s wavelet is the simplest one, which has been widely used for many applications. The low-pass filter and high-pass filter of Haar’s wavelet are as follows Figures 2 and 3 show the row decomposition and the column decomposition using Haar’s wavelet, respectively. Notice that the column decomposition may follow the row decomposition, or vice versa, in 2D DWT.

As a result, 2D DWT with Haar’s wavelet is as follows: where , , , and are pixels values, and , , , and denote the approximation, detail information in the horizontal, and vertical and diagonal orientations, respectively, of the input image. Figure 4 shows 1-level, 2D DWT using Haar’s wavelet.

The subband of an image can be further decomposed into four subbands: , , , and at the next coarser resolution, which together with , , and forms the 2-level DWT of the input image. Thus, higher level DWT can be obtained by decomposing the approximation subband in the recursive manner.

##### 3.2. Watermarking Scheme

Figure 5 shows the proposed embedding process; the details are described below. First, decompose the host image *I* via 2D DWT into four 1-level subbands: , , , and . Then decompose these 1-level subbands again into sixteen 2-level subbands: , , , , , , , , , , , , , , , and , as shown in Figures 5(a) and 5(b). Second, generate a random sequence for these subbands. Third, select a random starting location in the first subbands. Fourth, pick a random scanning direction and scan the first subband into pixel sequence . Next, compute the difference () according to (3.6) and construct a histogram based on ()
Then shift the histogram bins which are larger than 1 rightward one level as
Examine () one by one. Each difference less than 1 can be used to hide one secret bit (pixels with green color in Figure 5(f) of the difference sequence ). If the corresponding watermark bit , it is not changed (pixels with blue color in Figure 5(f) of the difference sequence ). And if , add the difference by 1 (pixels with red color in Figure 5(f) of the difference sequence ). The operation is as
and generate watermarked pixel sequence by this operation:
Rearrange and the first 2-level watermarked subband is obtained. Repeat these operations for the remained subbands.

Pick the 2-level watermarked subbands , , , and and perform the 2D inverse DWT to get the 1-level watermarked subband . Repeat this operation for the remained 2-level watermarked subbands to get the 1-level watermarked subbands , , and . Finally, perform the 2D inverse DWT to get the watermarked image .

The data extraction and image recovery is the inverse process of data embedding, and the process is as follows. First, decompose the watermarked image via 2D DWT into four 1-level watermarked subbands: , , , and . Then decompose these watermarked subbands again into sixteen 2-level watermarked subbands: , , , , , , , , , , , , , , , and . Second, get the subband sequence of the watermark, starting location, and scanning direction of each watermarked subbands. Third, scan the first watermarked subband into watermarked pixel sequence . Then recover the original pixel sequence based on the following: Figure 6 shows an example of secret data extracting and original pixel sequence recovering.

Rearrange the original pixel sequence and the original 2-level subband can be recovered. Repeat those operations until all 2-level subbands are recovered and perform 2D inverse DWT to get the 1-level subbands. Finally, perform 2D inverse DWT again and the original host image can be obtained.

The secret data is extracted as Rearrange these extracted bits and the original watermark can be obtained.

#### 4. Experimental Results

Figure 7 shows our test images, six with 256 gray levels are selected as test images; they are Lena, Baboon, Barbara, Boat, Board, and Peppers. Table 1 lists the average capacity (bit per pixel) and PSNR (db) values of the proposed scheme. The peak signal to noise ratio (PSNR) is used to evaluate the image quality [27], which is defined as where denotes the mean square error.

The six watermarked images obtained by our scheme and Zhao et al.’s method are shown in Figures 8, 9, 10, 11, 12, and 13. Note that all of the bits of the watermarks embedded inside are “1” which leads to a maximum distortion. All these results demonstrate that not only the capacities but also the PSNRs in our method are improved. In other words, even though more secret data embedded in our scheme and leads more distortion, the marked images quality is still better.

#### 5. Conclusion

In this paper, a reversible watermarking based on the histogram modification has been proposed. The transparency of the watermarked image can be increased by taking advantage of the proposed watermarking. As the host image can be exactly reconstructed, it is suitable especially for medical images, military maps, and remote sensing images. The proposed reversible watermarking based on multilevel histogram modification and discrete wavelet transform is preferable and provides a higher capacity and higher transparency compared with other histogram modification based methods.

#### Acknowledgment

This work is supported by the National Science Council of Taiwan, under Grants NSC100-2628-E-239-002-MY2 and NSC100-2410-H-216-003.

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