Adaptive image data hiding in edges using patched reference table and pair-wise embedding technique

Abstract

Reference table (RT) based embedding method embeds secret digits into pixel pairs under the guidance of a reference table. Most of the existing RT-based methods either require elaborate conversions among different bases, or have limited embedding capacity. In this paper, we use a patched reference table (PRT) as a guide and propose a PRT method to provide a better image quality and extendable embedding capacity. We also exploit the concept of pixel value differencing (PVD) and propose another method PRT–PVD. In the traditional PVD-based methods, the shape of the difference histograms of the stego images is significantly altered and, thus, vulnerable to some steganalyzers. PRT–PVD adopts the PRT method and uses a specially designed embedding sequence to preserve the difference histogram shape. Experimental results reveal that the proposed PRT and PRT–PVD methods not only have better embedding efficiency over the existing methods, but also are robust to detection by modern steganalysis tools.

Introduction

Many media such as texts, images, audios, and videos are digitalized for the purpose of convenient storage and access. Since minor modifications to these digital media are imperceptible to human recipients, some techniques exploit this fact in applications, such as watermarking [5], authentication [19], [36], and data hiding [17], [27], [35]. The purpose of watermarking is for rights of ownership protection, authentication is for data integrity, and data hiding is for secret communication. Recently, the increase for secret communication and the rise of image transmission on the Internet have aroused a tremendous attention on the importance of data hiding in images [8].

The least significant bit (LSB) replacement [27], a widely researched data hiding method, replaces the least significant bits of a cover image by message bits. LSB matching (LSBM) [5] is a similar method that randomly increases or decreases the pixel value by one to match the LSB of stego pixel with the message bit. Although these two methods are simple to implement, the image distortion is relatively large. As a result, it is vulnerable to detection by LSB-based steganalyzers [9], [26]. The optimal pixel adjustment process (OPAP) [2] method greatly improves the image quality obtained by LSB replacement. However, OPAP is equivalent to LSB replacement when a pixel carries one bit. In this case, OPAP not only does not enhance the image quality, but it is also vulnerable to detection by steganalyzers.

Both LSB replacement and OPAP adopt a single pixel as an embedding unit to carry k bits of information. Another type of embedding methods uses a reference table as a guide and employs two pixels as an embedding unit to conceal 2k bits. The embedding methods of this type are referred to as the reference table (RT) based methods. The LSB matching revisited (LSB-MR) [25] and the Exploring Modification Direction (EMD) [38] are two typical RT-based methods. LSB-MR employs two pixels as an embedding unit to conceal two bits by modifying one grayscale value of a pixel at most. EMD extends LSB-MR by embedding a digit in base 5 into two pixels and also modifies the grayscale value of a pixel at most by one. Although the EMD method obtains a very acceptable image quality, the maximum payload is only $\frac{1}{2}{\log }_{2}5\simeq 1.16\mathrm{bpp}$. In 2008, Chang et al. [3] proposed a method (referred to as Sudoku-S in this paper) by using Sudoku solutions as the reference table. In their method, two pixels are used to carry a digit in base 9 and the maximum payload is $\frac{1}{2}{\log }_{2}9\simeq 1.585\mathrm{bpp}$. In the same year, Hong et al. [18] introduced a new method (referred to as Sudoku-SR in this paper) using a new search algorithm to improve Sudoku-S. In their experiments, the stego image quality obtained by Sudoku-SR is 1.8 dB higher than that of Sudoku-S. In 2009, inspired by EMD, Chao et al. [4] proposed a diamond encoding (DE) method. In their method, two pixels are used to carry a digit in base L, where L = 2k² + 2k + 1 and k is an integer larger than 0; therefore, the maximum payload of DE is $\frac{1}{2}{\log }_2(2k^2+2k+1)$ bpp.

For the LSB replacement, OPAP, and the RT-based methods, every pixel carries the same amount of information. We term embedding methods of this type as Type I embedding. Because the perception of the changes in smooth and complex area for human visual system (HVS) is different, another type of embedding methods embeds different amount of information into pixels by considering HVS. We term the embedding methods of this type as Type II embedding. The well-known pixel value differencing (PVD) based methods [20], [24], [31], [34], [37] are of this type. Since HVS is less sensitive to the changes in complex areas, and complex areas often located in two consecutive pixels with larger difference, PVD-based methods embed more information into pixel pairs with larger difference than those with smaller one. The first data hiding method that adopts the idea of pixel value differencing was the PVD method proposed by Wu and Tsai [34] in 2003. However, their method results in a larger distortion, and the corresponding difference histogram significantly deviates from its original shape. Instead of using pixel value differencing, Wang et al. [31] in 2008 proposed a method to embed more information in edges using modulus function (MF-PVD). However, the difference histogram near zero is dramatically increased in their method, and thus, it is likely to be detected by histogram analysis [20].

In 2008, Yang et al. [37] also proposed an adaptive edge method (AE-PVD) and had better performance over prior PVD-based methods. AE-PVD sequentially selects two pixels as an embedding unit, and calculates the absolute difference d of these two pixels. The number of bits to be embedded depends on the value of d. The value of d before and after embedding has to be kept in the same division for correct data extraction. Compared to PVD and MF-PVD, AE-PVD achieves the best image quality under the same payload. However, AE-PVD adopts OPAP method for data embedding and is, thus, vulnerable to the detection by LSB-based steganalyzers when considerable number of pixels carries one bit. Besides, the difference histogram produced by AE-PVD shows abnormal fluctuations and is likely to be detected. In 2010, Joo et al. [20] modified the MF-PVD method so that the shape of the difference histogram is preserved to avoid the steganalysis of histogram detection. However, the image quality of their method is lower than that of AE-PVD method, and is not suitable for application requiring high quality image. In the same year, Luo et al. [22] proposed a data hiding method LC-HVS based on local complexity and HVS. In their method, images are partitioned into blocks of size 4 × 4, and the variance of each block is obtained. Since HVS is less sensitive to the changes in high variance area, they embed more data bits into higher variance blocks than lower ones. However, their method also adopts OPAP technique for data embedding and is, thus, also vulnerable to the detection by the LSB-based steganalyzers.

Recently, some efficient data-hiding methods have been proposed to provide a less detectable mechanism while minimizing additive distortion and offer a performance near the theoretical bounds. These methods are implemented either by embedding the messages into the less detectable part of the cover image, or by embedding more data bits per modification with the smallest embedding impact. The former can be done by using the selection rule to identify individual pixels in the cover image that might be altered during embedding, such as the wet paper code proposed by Fridrich et al. [10], [11]. The latter can be achieved by optimally coding the message using the near-optimal rate-distortion embedding scheme [6], [7]. In these methods, message bits are often carried by a group of pixels and their positions.

Besides, some machine learning techniques [14], [15], [29] also have been investigated in data hiding method. Because the payload and image quality are often contradictory, some recently proposed data hiding methods use machine learning based intelligent approach to achieve an optimal tradeoff between payload and image quality [32]. Amirtharajan and Rayappan [1] used an intelligent chaotic embedding approach to enhance stego-image quality. Wang et al. [33] optimized LSB substitution using cat swarm optimization (CSO) strategy. Lou and Hu [23] proposed an intelligent LSB steganographic method for resisting statistical steganalysis. Hong and Chen [16] used an adaptive pixel pair matching technique to reduce the embedding impact. By employing the machine learning techniques, these methods make a good choice between payload and image quality.

The motivations of this paper are to provide a solution to enhance embedding efficiency and undetectability of the existing RT-based and PVD-based methods. For the existing RT-based methods, including EMD, Sudoku-S, Sudoku-SR, and DE, the base of the embedded digits is not a power of two, and thus an elaborate conversion between bases has to be performed. Moreover, these methods, except DE, have limited payload. For the existing PVD-based method, AE-PVD and LC-HVS are detectable by the LSB-based steganalyzers, while PVD, MF-PVD, and AE-PVD produce abnormal difference histograms.

Two methods are proposed in this paper, including a Type I method PRT using patched reference table, and a Type II method PRT–PVD combining the PRT and PVD embedding techniques. The proposed PRT method uses a specially designed patch to construct a reference table to reduce the embedding impact and to confine the base of the embedded digits to be a power of two. This technique reduces the image distortion and eliminates the elaborate conversion between bases. The proposed PRT–PVD method embeds data using a key-protected embedding sequence with the consideration of HVS, and thus, it provides a good perceptual image quality while disguising the presence of the embedment.

In summary, the proposed methods integrate the patch-based reference table with data hiding approach by considering HVS. The contributions of the proposed methods are listed as follows: (1) The PRT method offers extendable payload, provides a solution to eliminate time-consuming conversion between bases, and achieves a better stego image quality. (2) The PRT–PVD method disguises the embedding sequence and thus, it is robust to the detection of histogram analysis while other PVD-based methods are not. (3) The proposed methods employ two pixels as an embedding unit, which is the most important and the fundamental case when considering n-tuples of pixels as an embedding unit. As a result, the proposed method provides a framework for data embedment, and is applicable to other fields such as image authentication and tamper detection.

The rest of this paper is organized as follows. Section 2 presents the proposed PRT and PRT–PVD methods. Section 3 is the experimental results and Section 4 is the security analysis. Concluding remarks are given in Section 5.