## 3 Proposed Algorithm
The flowchart of pixel value prediction for prediction image generation using the APDLS technique was constructed as follows: In Figure 6, the parts related to V\({}_{\text{3V}}\), V\({}_{\text{3C}}\), V\({}_{\text{4S}}\), V\({}_{\text{4N}}\), and V\({}_{\text{4W}}\) should be removed. If dev1 is greater than or equal to \(\beta\), the pixel value of the cover image becomes the predicted pixel value. If dev1 is less than \(\beta\), it is determined whether it is a simple inclined surface or flat surface. If it is a simple inclined surface or flat surface in the X-axis direction, the rounded value of V\({}_{2}\) is used as the predicted pixel value. Otherwise, the rounded value of V\({}_{1}\) is used as the predicted pixel value. By changing Figure 6 as described above, the flow chart of pixel value prediction using APDLS can be obtained. The prediction image generated by applying the APDLS technique to the sample cover image in Figure 7a is shown in Figure 7f. As shown in Figure 7f, the APDLS technique used only the predicted values V\({}_{1}\) and V\({}_{2}\). The predicted pixel values at locations 2 and 3 were 156 and 156, which were the rounded values of V\({}_{1}\). Since locations 7 and 8 had simple inclined surface characteristics, the predicted pixel values at locations 2 and 8 were 157 and 158, respectively, which were the rounded values of V\({}_{2}\). Therefore, when the APDLS technique was applied, the prediction image was generated as shown in Figure 7f. After constructing the difference sequence using the cover image and the prediction image, and generating the histogram of the difference sequence, we could see that PP\({}_{1}\) = 0, h (PP\({}_{1}\)) = 11, PP\({}_{2}\) = 1, and h (PP\({}_{2}\)) = 7. Therefore, the maximum number of data bits that could be embedded in the cover image using the APDLS technique was h(PP\({}_{1}\)) + h(PP\({}_{2}\)) = 18 bits. In the APDLS technique, if \(\beta\) is set to 15, and a prediction image is generated for the sample image as shown in Figure 7a, 20 bits can be embedded in the cover image. In the ARDHA technique, if \(\beta\) is set to 15, and a prediction image is generated for the sample image, 24 bits can be embedded in the cover image. If \(\beta\) is set to 20, and the APDLS and the ARDHA techniques are used to generate the prediction image for the sample image, the APDLS and ARDHA techniques can embed 22 and 25 bits in their cover images, respectively. These results occurred because the number of predictions increased as \(\beta\) increased, the frequencies at the highest and second-highest peak points in the histogram of the difference sequence increased, and the number of data bits that could be embedded increased. As the APD technique does not use the prediction image, the embedded bits were always equal to 15 bits, regardless of \(\beta\). As shown in Figures 11 and 12, if the ARDHA technique was used to embed confidential data in the cover image, it could embed 8 and 5 more confidential data bits than the APD and APDLS techniques, respectively. In addition, the original confidential data could be extracted without data loss from the stego-image, and the original cover image could be restored without distortion from the stego-image. Therefore, the proposed ARDHA technique could be effectively used in digital watermarking, military, and medical applications.