# Data Hiding Method for Color AMBTC Compressed Images Using Color Difference
## 5 Experimental Results  
In this section, we experiment and evaluate the proposed DH method based on color AMBTC with five test images such as Lena, Pepper, Airplane, Lake, and Baboon (Figure 6). The size of the images used in the experiment is \(512\times 512\) and the size of a block is \(4\times 4\). For evaluation, we use a Color Difference (CD) to compare the performance and use PSNR and SSIM as a reference. Figure 6: Original image used in the experiment; (**a**) Lena, (**b**) Pepper, (**c**) Airplane, (**d**) Lake, and (**e**) Baboon. The quality of the image was measured by the PSNR defined as  
\[PSNR=10 log_{10}\frac{255^{2}}{(MSE_{R}+MSE_{G}+MSE_{B})/3} \tag{18}\]  
PSNR is calculated as \(10 log\) (signal power/noise power), and signal power and noise power are calculated using peak power. The \(MSE_{R}\), \(MSE_{G}\), and \(MSE_{B}\) used for PSNR calculation is the difference in mean intensity between the marked image and the reference image, and a low MSE value can be evaluated as good image quality. In other words, the MSE is the mean of the squares of the errors \((p_{i}-p_{i}^{\prime})^{2}\), where \(p\) and \(p^{\prime}\) are reference and distorted images, respectively. The MSE is calculated as follows:  
\[MSE_{R,G,B}(p,p^{\prime})=\frac{1}{n\times n}\sum_{i=1}^{n\times n}(p_{i}-p_{i }^{\prime})^{2}. \tag{19}\]  
Here, the allowable pixel intensity is \(255^{2}\). SSIM [24] is a multiplicative model for three similarity components i.e., luminance, contrast and structure similarity components, and it is formulated as  
\[\phi(p,p^{\prime})=l(p,p^{\prime})^{\theta_{1}}\cdot c(p,p^{\prime})^{\theta_{ 2}}\cdot s(p,p^{\prime})^{\theta_{3}} \tag{20}\]  
where \(l(\cdot)\), \(c(\cdot)\) and \(s(\cdot)\) indicate luminance, contrast and structure similarity components, respectively, and exponents \(\theta_{1}\), \(\theta_{2}\) and \(\theta_{3}\) are set to 1 in [25]. \(l(\cdot)\) in Equation (20) measures similarity of mean pixel intensity between \(p\) and \(p^{\prime}\), which is expressed as  
\[l(p,p^{\prime})=\frac{2\mu_{p}\mu_{p^{\prime}}+C_{1}}{\mu_{p}^{2}+\mu_{p^{ \prime}}^{2}+C_{1}} \tag{21}\]  
where \(\mu_{p}\) and \(\mu_{p^{\prime}}\) are mean pixel intensity for \(p\) and \(p^{\prime}\), respectively, and \(C_{1}\) is a parameter to avoid unstable results when the denominator in Equation (21) is close to zero. The overall measured quality value of the SSIM for the whole distorted image \(p^{\prime}\) compared to the original image \(P\) is calculated as  
\[F(P,P^{\prime})=\frac{1}{n\times n}\sum_{j=1}^{n\times n}\phi(p_{j},p_{j}^{ \prime}) \tag{22}\]  
where \(n\times n\) is the number of local image regions of an whole image and \(j\) is an index of local image regions, \(p_{j}\) and \(p_{j}^{\prime}\). The quality measurement of the color image we proposed is by the Color Difference (CD) defined as  
\[CD(p,p^{\prime})=\sum_{i=1}^{n\times n}\mathcal{D}(p_{i})-\mathcal{D}(p_{i}^{ \prime}). \tag{23}\]  
CD measures similarity by color difference. In case of the measurement of CD, it is the use of weighted R, G, and B values to better fit human perception. A color difference in each pixel is calculated by  
\[D(x)=\sqrt{2\times 0.3x_{R}^{2}+4\times 0.59x_{G}^{2}+3\times 0.11x_{B}^{2}}. \tag{24}\]  
where the R, G, and B components are weighted by 30%, 59%, and 11%, respectively. Unlike the other measurement methods, the CD can differentiate and compare feelings of the images' surface and textures that humans can perceive by the visual system. Table 1 shows the comparison of compression performance and image quality of traditional AMBTC and our proposed AMBTC methods by using CD, SSIM, and PSNR. From an image compression point of view, when compressing with traditional AMBTC, it compresses at 96 bits per block. On the contrary, our proposed method can compress at about 95 bits per block. Here, 2Q/B means that two quantization levels are used per block, and 3Q/B means that three quantization levels are used per block.