## 1 Introduction
(2013) developed a new approach that produces two differences per pixel, first creating a two-dimensional histogram based on the differences and then reducing this histogram to several single dimensions for data hiding, aiming to achieve high embedding capacity [20]. [PERSON] et al. (2013) proposed a pixel value order-based data hiding method [21]. Their method's aim is to reduce the number of shifted pixels and achieve high image quality. In the method, firstly, 2 \(\times\) 2 blocks are taken from the cover image and the pixel values are ordered in descending. If the two largest values are equal to one, one bit data hiding is performed. If it is greater than one, the difference is increased by one. During data extraction, the difference of one or two indicates that it is hidden data, zero and one, respectively. During the recovery of the cover image, differences greater than one are reduced by one. In interpolation-based methods, new expendable pixels are created by enlarging the size of the cover image. The embedding capacity is increased by the expansion process. Later, without changing the original pixel values, these expendable pixel values are changed and embedded secret data. Since the original pixel values are preserved, the cover image can be easily restored by combining the pixels in the correct positions. In addition, the initial values of intermediate pixels produced by interpolation can be recalculated over the original pixel values. Thanks to this process, the need to associate pixel values with each other in data hiding is eliminated [22; 23; 24; 25; 26; 27; 28; 29]. In addition to these methods, dual image based reversible data hiding techniques are also widely used in the literature in recent years. These techniques create two identical duplicate images from a cover image to increase the overall embedding capacity while hiding secret data. Also, a dual image-based data hiding scheme can ensure higher data embedding capacity, more secure communication, and high visual quality. Because without obtaining two stego images at the same time, it is impossible for third parties to receive all secret messages. [PERSON] et al. (2007 and 2013) combined EMD method with dual image based reversible data hiding technique. Their technique uses a 256 \(\times\) 256 function matrix. It converts bit streams data in the 5-ary notational system data streams ranging from zero to four. Two 5-ary notational system data are embedded into one cover image pixel pair at a time [30; 31]. [PERSON] et al. (2009) developed a dual image based reversible method using a four-way cross pattern. Firstly, the two bits of the four-bit secret data are used to determine the starting position of the pattern, and the other two bits to determine the direction of movement of the pattern. Then, it applies changes to the selected pixels in the pattern to calculate stego pixels [32]. [PERSON] et al. (2015) proposed a new dual image-based data hiding approach using the center folding strategy. Their method firstly decreased the secret data values via a folding strategy technique to obtain high image quality, and then hidden the folded secret data with an averaging method in two stego image pixels [33]. [PERSON] et al. (2018) proposed a new dual image based reversible data hiding method involving the center folding strategy. The method uses a dynamic coding strategy, which utilizes joint neighbor coding, to develop the center folding strategy [34]. [PERSON] et al. (2019) developed a dual image based reversible data hiding scheme using the center folding strategy and the slidable pixel coordinate choosing technique [35]. [PERSON] et al. (2021) developed a center folding based data hiding scheme through the directional pixel value of orders with different block size [36]. [PERSON] et al. (2021) proposed a reversible data hiding scheme for interpolation images featuring a multilayer center folding strategy [37].