# Data Hiding Method for Color AMBTC Compressed Images Using Color Difference
## 1 Introduction  
Recently, many people participated in the production and distribution of various media contents with smartphones. Therefore, interest in digital content ownership is increasing more than ever. On the other hand, advanced image processing tools and experienced designers can make the authenticity of digital images difficult [1]. Therefore, \"to see is to believe\" has become meaningless. Nevertheless, data hiding (DH) [2] is emerging as a potential solution. DH is used for intellectual property protection, content authentication, annotation, watermarking technology, etc., and supports confidential communication. The difference between DH and watermarking technology is that watermarking technology reveals that digital contents are applied with watermarking technology, but DH technology protects digital contents by hiding the existence of secret information. DH uses mostly the spatial domain. Thus, data can be efficiently embedded by flipping the redundant bits of the Least Significant Bit (LSB) [3] of the pixels. The merit of spatial domain-based DH [4] is that it is possible to keep a marked high-quality image and to embed enough data. The weakness is that if the LSBs change due to simple image processing, the hidden data in the LSBs can be destroyed. While, although the merit of frequency domain-based DH [5] is that it is strong against image processing attacks, it has the demerit that the Embedding Capacity (EC) is low and the quality of a marked image is relatively not high. Frequency domain compression methods include Discrete Cosine Transform (DCT) [6, 7], Discrete Wavelet Transform (DWT) [8], and Singular Value Decomposition (SVD) [9]. Also, BTC (Block Truncation Coding) [10] is being actively researched as a cover media for DH. BTC is a compression coding with fast compression calculation speed and moderate bit rate. Absolute Moment BTC (AMBTC) [11], proposed by [PERSON] and [PERSON], is the most used BTC method. AMBTC quantizes pixels in blocks. As a result of quantization, two pixels and a bitmap representing each block are obtained. This is denoted by \((a,b,BM)\) called trio. First, the bitmap is directly replaced with the secret bits [12], where a secret bit is a one-to-one relationship with a pixel. This method may be applied if the difference between the two quantization levels of blocks is less than \(T\) (threshold value) (\(b-a\leq T\)). Here, DH performance may vary depending on the texture of the cover image. Second, there is a lossless DH [13] using the order of two quantization levels (OTQL). For example, to embed the '1' bit, the order of \(a\) and \(b\) is reversed as follows: \(trio(b,a,BM)\). Since this method does not change the coefficients of the two quantization levels, the original cover image can be completely restored. Third, [PERSON] & [PERSON] [14] introduces a method that combines DBR (Directly the Bitmap Replacement) and OTQL. Moreover, they introduced an optimization equation that reduces errors generated when bit-planes are changed. Fourth, [PERSON] et al. [15] introduced a method embedding as much as \(log_{2}^{T}\) bits by using difference expansion of two quantization levels. The merit of this method does not depend on the type of blocks. Fifth, [PERSON] et al. [16] proposed an effective DH method for two quantization levels of each block of AMBTC using Hamming code. In order to solve the image distortion error problem, they introduced a method of optimizing the codeword and reducing pixel distortion by using a lookup table. Meanwhile, since a color image consists of R, G, and B layers, it is compressed into six quantization levels and three bitmaps per block and can be represented as 96 (=\(6\times 8+16\times 3\)) bits per block (e.g., the \(4\times 4\) sized block). On the other hand, our proposed color AMBTC is represented with 9 quantization levels and a common bit-plane per block.