## 2 Related Work and Comparisons between the Methods  
[PERSON] et al. [6] reviewed the recent advances on RDH in the past two decades, including various RDH schemes in image spatial domain, RDH for compressed images, robust RDH which aims at recovering hidden message from the lossily compressed image, RDH for encrypted images and RDH for video and audio. The RDH in image spatial domain is the most investigated subject and strongly related to this paper. We summarize progresses on this subject as below.  
1. Lossless compression-based methods. Most early RDH was implemented based on lossless compression [35; 36; 37; 38; 39; 40; 41; 42]. Partial space is released by lossless compressing a feature set of the original image, and the data is embedded using the released space to achieve RDH. The performance of this method depends on the lossless compression algorithm used and the selection of compressed feature sets. The experimental results suggest that the algorithm based on lossless compression will result in greater distortion and poorer embedding effect than the subsequent RDH method.
2. Integer-transform-based methods. Integer-transform-based methods can be seen in [36; 39; 41]. In this type of method, the original image is initially divided, so that multiple adjacent pixels can form an embedding unit. Subsequently, the secret information is embedded into each unit using integer transform. However, this type of method usually uses the average value of a pixel block to predict each pixel in the block, so that the image redundancy cannot be well utilized. Moreover, its algorithm cannot control the maximum modification range of each pixel so that the embedded distortion cannot be controlled effectively. Due to two defects mentioned above, the embedding performance of the integer transform-based methods is limited. The performance of this type of method has been significantly improved compared to the lossless compression-based methods; however, it still cannot achieve good embedding performance.
3. Two-phase embedding with location maps. There are RDH schemes proceeds with two-phases (e.g., [43; 44; 45]) using location maps which map each pixel to a certain value and also ensure the reversibility of the cover image. In [44], [PERSON] et al. considered even-valued and odd-valued pixels separately and embed the secret data bit for each pixel of the cover image by changing its value by at most 1. Their work improves previous complementary embedding strategy by [PERSON] and [PERSON] [43] which uses vertical embedding and horizontal embedding separately in two phases. [PERSON] et al. considered even-valued and odd-valued pixels with location maps as well while the cover image is divided into non-overlapping 2-by-2 blocks of pixels and the secret bits are converted into 2-bit segments and embedded into the blocks by increasing or decreasing the pixel value of the corresponding block by at most 1. Since the second phase embedding has the affect as complement of the first phase embedding, this kind of approach persist the stego-image's quality while doubling the EC.
4. Histogram modification-based methods. In this type of method, the original image is mapped to space with a lower dimension at the beginning by using the redundancy of the image. Then generate a histogram by counting the distribution of the low-dimensional space. Finally, the reversible embedding is realized by modifying the histogram. The earliest method having a great impact is proposed by [PERSON] et al. in 2006 [46]. In this method, the secret data is embedded into the pixels with the highest frequency in the image histogram by expanding the histogram. The stego-image with this method maintains high image quality, but the embedding rate is low. Therefore, [PERSON] et al. [47] improved the method of [46], which uses the image difference histogram that the shape rule is similar to Laplace distribution. The histogram of the method experiences a very high peak and rapidly dropping; therefore, it can have a better embedding capacity while maintaining image quality.