**4. Experimental Results**

In the following, the experimental results of the proposed scheme will be presented and compared with the related works. As shown in Figure 10, this study uses eight standard 512 × 512 grayscale images and four standard 512 × 512 true color images as the cover image *P* for secret data embedding. All experiments are implemented with MATLAB R2017b. Figure 11 shows the twelve stego images obtained by applying the two-layered hiding scheme based on the CMSM.

(**a**) (**b**) (**c**) (**d**)

**Figure 10.** Twelve cover images with size 512 × 512: (**a**) Lena; (**b**) peppers; (**c**) airplane; (**d**) baboon; (**e**) boat; (**f**) Elaine; (**g**) Gledhill; (**h**) sailboat; (**i**) baboon (RGB); (**j**) Lena (RGB); (**k**) peppers (RGB); and (**l**) Tiffany (RGB).

**Figure 11.** Twelve stego images with size 512 × 512: (**a**) Lena; (**b**) peppers; (**c**) airplane; (**d**) baboon; (**e**) boat; (**f**) Elaine; (**g**) Gledhill; (**h**) sailboat; (**i**) baboon (RGB); (**j**) Lena (RGB); (**k**) peppers (RGB); and (**l**) Tiffany (RGB).

The stego images look like the cover images and cannot be distinguished by human eyes. The peak signal-to-noise ratio (PSNR) is used to measure the quality of a stego image. Its calculation is given by Equation (4). In the equation, *P* and *P* represent the cover image and the stego image, respectively, *H* and *W* represent their height and width and (*m*, *n*) represents the coordinate of the pixel.

$$PSNR = 10 \times \log\_{10} \frac{255^2 \times H \times W}{\sum\_{m=1}^{H} \sum\_{n=1}^{W} \left[ P(m,n) - P'(m,n) \right]^2}. \tag{4}$$

In addition, we also use structural similarity index (SSIM) to measure the similarity between a cover image and its corresponding stego image. Let *P* and *P* represent the cover image and the stego image, respectively, the SSIM of the two images can be obtained according to Equation (5), where μ*<sup>P</sup>* is the average of *P*, μ*<sup>P</sup>* is the average of *P* , σ<sup>2</sup> *<sup>P</sup>* is the variance of *<sup>P</sup>*, <sup>σ</sup><sup>2</sup> *<sup>P</sup>* is the variance of *P* and σ*PP* is the covariance of *P* and *P* . In addition, *c*<sup>1</sup> and *c*<sup>2</sup> are constants used to maintain stability and can be obtained by Equations (6) and (7), respectively, where *L* is the dynamic range of pixel values, *k*<sup>1</sup> = 0.01, *k*<sup>2</sup> = 0.03.

$$\text{SSIM}(P, P') = \frac{(2\mu\_P \mu\_{P'} + c\_1)(2\sigma\_{P P'} + c\_2)}{(\mu\_P^2 + \mu\_{P'}^2 + c\_1)(\sigma\_P^2 + \sigma\_{P'}^2 + c\_2)}.\tag{5}$$

$$c\_1 = \left(k\_1 L\right)^2. \tag{6}$$

$$c\_2 = (k\_2 L)^2. \tag{7}$$

Embedding capacity (EC) is another important issue in the image steganography. It is used to measure the maximum amount of secret data that can be embedded in an image by a data-hiding scheme. Since EC is dependent on the image size, we further define the embedding rate (ER) to express the average number of secret bits that each pixel can embed. ER is defined as (8), where ||*S*|| represents the total amount of secret data embedded in the entire stego image.

$$ER = \frac{\|S\|}{M \times N}.\tag{8}$$

Table 1 shows the experimental results of the grayscale images. In our hiding scheme, three cover pixels are applied to embed a secret segment of six digits. Therefore, the ER measure is 6 bits/3 pixels = 2 bits/pixel, the embedding capacity for an applied grayscale cover image is therefore 512 × 512 × 2 = 524,288 bits as shown in the Under full embedding, the proposed scheme achieves a high image quality of PSNR = 46.37 dB and SSIM = 0.9923 in average. The quality of stego image is irrelevant to features of the cover image. For the true color images, each pixel consists of three channels, including red, green and blue. Each of the three channels is represented by one byte. By mapping the three bytes (r, g, b) of a pixel into the CMSM, we can hide a secret segment of six bits by applying the proposed embedding algorithm. Therefore, the embedding capacity of an applied true color image is 512 × 512 × 6 = 1,572,864 bits. The PSNR and SSIM of the true color stego images are very close to the experimental values of grayscale images as shown in Table 2.

**Table 1.** Experimental results for grayscale images.



