# Hybrid Data Hiding Based on AMBTC Using Enhanced Hamming Code
## 4 Experimental Results  
In this section, we prove the performance of our proposed scheme by comparing with the existing methods, such as [PERSON] [30], [PERSON] [33], and [PERSON] et al. [28]. As shown in Figure 7, six grayscale images sized \(512\times 512\) are used for our experiments. In addition, the block size of AMBTC is set to \(4\times 4\), and the secret bits are generated by a pseudo-random number generator. Embedding Capacity (EC) and the Peak Signal-to-Noise Ratio (PSNR) are widely used as objective image evaluation indices. Here, EC is used as an indicator for the number of secret bits that can be embedded in a cover pixel. The relatively high PSNR value means that the quality of the stego image is good. The DH capacity is the size of the secret bit that is embedded in the cover image. The quality of the image is measured by the PSNR defined as:  
\[PSNR=10 log_{10}\frac{255^{2}}{MSE} \tag{11}\]  
Figure 6: Illustration of data embedding. The Mean-Squared Error (MSE) used in the PSNR denotes the average intensity difference between the stego and reference images. The lower the MSE value of a stego image, the better the quality of the image. The MSE is calculated using the reference image \(p\) and the distorted image \(p^{{}^{\prime}}\) as follows. \[MSE=\frac{1}{N\times N}\sum_{i=1}^{N}\sum_{j=1}^{N}(p_{ij}-p_{ij}^{{}^{\prime} })^{2} \tag{12}\]  
The error value \(\epsilon=p_{ij}-p_{ij}^{{}^{\prime}}\) indicates the difference between the original and the distorted pixels. The \(255^{2}\) means the allowable pixel intensity in Equation (11). A typical value for the PSNR in a lossy image is from 30 dB to 50 dB for an eight bit depth; the higher the better. Structural SIMilarity (SSIM) [39] estimates whether changes such as image brightness, photo contrast, and other residual errors are identified as structural changes. The SSIM values is limited to a range between zero and one. If the SSIM value is close to one, it means that the stego image is similar to the cover image and of high quality. The equation of SSIM is as follows:  
\[SSIM(x,y)=\frac{(2\mu_{x}\mu_{y}+c_{1})(2\sigma_{xy}+c_{2})}{(\mu_{x}^{2}\mu_{ y}^{2}+c_{1})(\mu_{x}^{2}\mu_{y}^{2}+c_{2})} \tag{13}\]  
where \(\mu_{x},\mu_{y}\) are the mean values of the cover image (\(x\)) and stego image (\(y\)), \(\sigma_{x},\sigma_{y},\sigma_{x}^{2},\sigma_{y}^{2}\), and \(\sigma_{xy}\) are the standard deviation, variances, and covariance of the cover image and stego image, and \(c_{1},c_{2},c_{3}\) are constant values to avoid the division by zero problem. The Normalized Cross-Correlation (NCC) has been commonly used as a metric to evaluate the degree of similarity (or dissimilarity) between two compared images. The main advantage of the NCC  
Figure 7: Test images: (**a\(\sim\)**f**) \(512\times 512\). is that it is less sensitive to linear changes in the amplitude of illumination in the two compared images. Furthermore, the NCC is confined to the range between \(-1\) and one. NCC is calculated by the formula given in Equation (14). \[NCC=\frac{\sum_{x=1}^{M}\sum_{y=1}^{N}(S(x,y)\times C(x,y))}{\sum_{x=1}^{M}\sum_ {y=1}^{N}(S(x,y))^{2}} \tag{14}\]  
Table 1 represents the comparison of EC and PSNR between the proposed scheme and existing methods, i.e., [PERSON] and [PERSON] [29], [PERSON] and [PERSON] [30], and [PERSON] et al. [33]. Specifically, we compare the performance between our scheme and the existing methods using six images when the threshold value \(T(=b-a)\) is 5, 10, and 20. The evaluation of EC and the PSNR based on threshold values is necessary for objectivity and fairness for comparative evaluation of the performance; that is, the data measured under the same threshold value may be evaluated as a more meaningful comparison. One important point for EC and PSNR is that there is a trade-off between the two assessments. That is, if EC is higher, the PSNR is reduced, and vice versa. However, in the case that the proposed method has very good performance, the deviation from the trade-off may not be large.