## 3 Proposed Algorithm  
In general, local similarity, curved surface characteristics, and edge characteristics exist in images. That is, adjacent pixel values of an image are very similar, and various curved surface characteristics such as flat surface, simple inclined surface, simple convex surface, and simple concave surface exist in particular locations of the image. Various edges also exist in specific portions of the image. In the proposed algorithm (ARDHA), the locations where local similarity is expected to be high were selected by using neighboring pixels. Next, it was examined whether a flat surface or a simple inclined surface or a simple convex surface or a simple concave surface exist at each location. At each location where local similarity was not expected to be high, it was examined whether a strong edge or a normal edge or a weak edge exist. Thereafter, the pixel values at each location were accurately predicted according to the investigated characteristics. A prediction image was generated using the precisely predicted pixel values, and a difference sequence was generated using the cover and prediction images. If the prediction image was generated very close to the cover image, the frequencies at the highest and second-highest peak points in the histogram of the difference sequence increased. Thus, the number of confidential data bits that could be embedded in the cover image could be increased. The more accurate the pixel value prediction, the higher the frequencies at the highest and second-highest peak points in the histogram of the difference sequence, and the greater the number of confidential data bits that could be embedded in the cover image. The flowchart for obtaining the predicted pixel values to generate the prediction image is shown in Figure 6. Figure 7a shows a sample cover image, and Figure 7b shows the prediction order of the pixel values in a predictable region (the region inside double line marked as Region1. 1 to 16). Figure 6: Flowchart of pixel value prediction to generate the prediction image. Pixels values are unpredictable in the region outside the double line (two rows on the top and two columns from the left and right sides) as shown in Figure 7b. Figure 7c,d show the neighboring pixels used to predict pixel values at locations 1, 5, 6, and 10 using a flat surface, simple inclined surface, simple convex surface, and simple concave surface characteristics. Figure 7e shows the neighboring pixels used to predict pixel values at locations 6 and 10 using strong edge, normal edge, and weak edge characteristics. As shown in Figure 7e, at 6, 21 pixels in three rows above the location and 3 pixels in the three columns to the right were used to predict the pixel value using the edge characteristics. At 10, 21 pixels in three rows above and 3 pixels in the three columns to the left were used to predict the pixel value using the edge characteristics. Therefore, the region where pixel values were predictable using edge characteristics was the remaining portion except three rows on the top and three columns on the left and right sides (the region inside the bold black square marked as Region1(E). 6, 7, 10, 11, 14, and 15). The neighboring pixels used for prediction were the pixels of the cover image that had already been scanned in inverse s-order. The prediction images generated by applying the APDLS and the proposed ARDHA techniques to the sample image are shown in Figure 7f,g, respectively. As shown in Figure 6, to predict the pixel value, it was necessary to determine whether each location in the inverse s-order was within the region where pixel values were predictable. If the current location is not within Region1, the pixel value of the cover image becomes the predicted pixel value. If the current location is within Region1 where pixel values are predictable, the predicted pixel value is calculated according to the procedure of the proposed technique.