**5. Experimental Results**

The experimental results are shown in this section. Six grayscale images of size 512- by-512, including Lena, Baboon, Boat, Peppers, Airplane (F-16), and House, are used in our experiments. The cover images and the stego-images which are embedded 10,000 bits of secret data are shown in Figure 6 . In addition, the variations in image quality under different embedding capacities are compared (as shown in Figure 7) . The most common strategy to measure the image quality is the calculation of Peak Signal to Noise Ratio (PSNR) function which is defined as

$$\begin{array}{rcl} \text{PSNR} &=& 10 \cdot \log\_{10} \left( \frac{255 \cdot 255}{\text{MSE}} \right) \text{'} \\ \text{MSE} &=& \frac{1}{\text{MN}} \cdot \sum\_{i=1}^{M} \sum\_{j=1}^{N} (\mathbf{x}\_{i,j} - \mathbf{x}\_{i,j}')^2 . \end{array}$$

The results of the testing image (Lena) is presented in Figure 7. In addition, from the line chart can be observed that when the embedding capacity is less than 60,000 bits, the PSNR will decrease steadily. However, when the embedding capacity is more than 60,000 bits, PSNR will begin to decline relatively quickly.

**Figure 6.** The cover images and the stego-images (embed 10,000 bits).

**Figure 7.** PSNR (dB) and embedding capacity (bits) of the proposed scheme, for image Lena.

#### *5.1. Performance Comparison between the Proposed Method and Baseline Approaches*

In this subsection, the proposed method is compared with the previously mentioned schemes. The compared results divide into two parts: maximum embedding capacity and embedding capability in different embedding capacities. The comparison results show that the proposed method has better embedding capacity, and the image qualities are still maintained well.

5.1.1. Maximum Embedding Capacity

We compared the embedding capacity and the image quality when the cover image was embedded once from beginning to end. The comparison is between the proposed method and the methods of Ni et al. [46], Lee et al. [47], Li et al. [21], and Cai et al. [5]. Shown in Table 9 is the comparison of maximum embedding capacity for six test images between the proposed method and the other schemes . In addition, the Table 10 is the comparison of PSNR for maximum embedding capacity between the proposed method and the other schemes.

**Table 9.** Comparison of maximum embedding capacity (bits) for six test images between the proposed method and the methods of Ni et al. [46], Lee et al. [47], Li et al. [21], and Cai et al. [5].


From the results in Table 9, whether in a smooth image (like image Lena) or in a complex image (like image Baboon), the proposed method has a better embedding capacity.

According to Table 10, the average PSNR of the stego-image among the previous schemes [5,21,46,47] and the proposed method are 53.04 dB, 51.75 dB, 51.61 dB, 63.72 dB, and 48.55 dB, respectively. Clearly, the larger the embedding capacity is, the lower the quality of the image we get. Although the PSNR of the proposed method is lower than other methods, the embedding capacity of it is much more than other methods. According to the above results, when the cover image is only embedded once, our proposed method can have the maximum embedding capacity and maintain good image quality.

**Table 10.** Comparison of PSNR (dB) between the proposed method and the methods of Ni et al. [46], Lee et al. [47], Li et al. [21], and Cai et al. [5] for maximum embedding capacity.


5.1.2. Embedding Capability in Different Embedding Capacities

In this section, the variations in image quality under different embedding capacities between the proposed method and the methods of Ni et al. [46], Lee et al. [47], Li et al. [21], and Cai et al. [5] are compared. The image quality comparison for six test images in different embedding capacities between the proposed method and the other schemes are shown in Tables 11–13 . In addition, the performance comparisons between the proposed method and other related researches are shown in Figure 8 as line graphs.

**Figure 8.** Performance comparisons among the proposed method and other approaches on different images.

**Table 11.** Comparison of PSNR (dB) between the proposed method and the methods of Ni et al. [46], Lee et al. [47], Li et al. [21], and Cai et al. [5] for a capacity of 1000 bits.



**Table 12.** Comparison of PSNR (dB) between the proposed method and the methods of Ni et al. [46], Lee et al. [47], Li et al. [21], and Cai et al. [5] for a capacity of 5,000 bits.

**Table 13.** Comparison of PSNR (dB) between the proposed method and the methods of Ni et al. [46], Lee et al. [47], Li et al. [21], and Cai et al. [5] for a capacity of 10,000 bits.


*5.2. Comparison between the Proposed Method and the Different Embedding Methods with Different Octant Embed Number*

In this subsection, the variations in image quality under different embedding capacities between the proposed method and the different embedding methods are compared. The different embedding methods are generated by reducing the octant embed number of the 3D-PEH in the proposed method. The comparison results are shown in Figure 9.

(**a**) Embedding capacity range: 10 to 100

 capacity range: 5000 to 50,000

(**b**) Embedding capacity range: 1000 to 10,000

According to the above results, when the bits of embedded secret data are few, the distortion of the image can be slightly reduced by embedding the secret in fewer octants. Thus, the reducing effect is limited. Conversely, when the bits of embedded secret data is larger, the better quality of the image can be kept by embedding secret in more octants of the 3D-PEH. It can be expected that the more bits of embedded secret data, the larger gap between different embedding methods occurs. Therefore, we consider embedding secret data in eight octants in the proposed method.
