Steganography is a means of covert communication in which secret information is embedded into some form of digital media, such as an image, video or text file . In multimedia security, steganography forms a critical research topic . In general, images are considered as the embedding medium due to minute changes in an image being imperceptible to the human eye . The capacity for a steganographic algorithm represents the amount of data that can be embedded in an image before there is a noticeable visual change in the image . Steganalysis is the process of detecting if a given image has information hidden in it or not . In this regard, we can convert this problem into that of a simple classification problem. To detect if an image is embedded with information we propose the use of an ensemble color space model. Recently, it was seen an ensemble colorspace model  obtained excellent results on large scale image classification datasets such as imagenet . Based on  we propose a novel steganalysis approach.
We use a colorspace approach to determine if an image is hiding information or not. We use ColorNet  and take the final activation map from each colorspace. We use weighted averaging to obtain a single feature map from all the individual feature maps that are generated by each colorspace. It was seen  that each color space had features explicit to themselves and this would help us detect minute changes in the image. We then use a levy-flight grey wolf optimization method (meta-heuristic approach) to select a smaller subset of features. Using these features, we classify the given image into one of two classes: containing concealed information or not.
Ii Related Work
Steganography algorithms can be classified broadly into four categories: 1) cover image size 2) embedding domain-based algorithms 3) nature of retrieval based algorithms 4) adaptive steganographic algorithms. In the case of 2-D images, the information is embedded onto the 2-D plane of the cover image. This embedding can be done over transform domain coefficients (such as discrete cosine transforms, Fourier transforms, etc.) or on the spatial domain (an example is LSB). The 3-D approaches essentially follow the same general procedure. However, the procedure is repeated on multiple planes (for instance RGB in a color image has 3 planes that can embed information). Image steganography on 3-D images can be made in either geometrical domain , representation domain  or topological domain . Some of the transform-based steganographic algorithms include discrete Fourier transform (DFT) , discrete cosine transform (DCT), discrete wavelet transform , complex wavelet transform  among others. Here, frequency coefficients obtained after applying transforms are used to hide secret bits. Along with the security being improved, these algorithms are robust to image compression, cropping, scaling, etc. Off late, machine learning approaches have been proposed such as SVM (Support Vector Machine), genetic algorithm approaches , neural network-based steganography . Though these approaches are black-box approaches, they have shown good results.
Steganalysis is the method of trying to either determine a stego image (image where information is hidden) or extract the secret information. Our method deals with the former. We treat the problem at hand to be a classification problem, wherein, each image either contains some hidden information or not. There are two basic approaches to steganalysis: signature steganalysis and statistical steganalysis. Signature steganalysis is the method wherein patterns, or signatures relevant to various steganographic algorithms are searched for. The statistical approach searches for mathematical results to determine if the information is being hidden.
Signature steganalysis is further classified into specific embedding  and universal blind steganalysis . Specific embedding approaches are impractical because we need to know what steganography approach has been used to embed information. Hence, universal blind steganalysis [8,17] is preferred. These approaches help in the extraction of high dimensional features. However, the curse of dimensionality occurs. Hence, a need to reduce feature size occurs. Some commonly used algorithms to do the same include wrappers, filters, etc. Filters are less complex; however, they perform poorly. Wrapper methods evaluate feature subset using predictive models . However, wrappers are complex and time-consuming.
To overcome this, meta-heuristic approaches have been deployed. These approaches solve optimization problems by utilizing natural phenomena [19-20]. It was seen that Grey Wolf Optimization (GWO) performed better than other metaheuristic approaches for solving non-linear problems in a multi-dimensional space . However, it has a slow convergence rate and gets trapped in local optima at times. It has been seen that GWO can be optimized by modifying it’s parameter A to obtain a quick convergence rate, better convergence precision and higher agility for global searching.
Iii Proposed Approach
Iii-a Overall architecture and effect of using color spaces
We consider steganalysis as a 2 class classification problem. The overall architecture is described in figure 1. The experimental analysis along with details regarding training set etc are explained in the next section. Recently, the effect of color spaces on image classification has been explored . It was seen that individual color spaces inherited classification features explicitly to themselves. This helped us ponder about the ability to extract information in an image where there is secret information being embedded. Colornet  being an ensemble model, that could extract features specific to each colorspace, was an excellent choice to utilize to help us in determining if an image could have information hidden in it. The output of Colornet is a high-dimensional vector, which causes a computationally intensive execution. To reduce the number of features selected we have to use an optimization approach for feature selection. Figure 1 shows the architecture of the model.
Iii-B Optimization process for feature selection
Iii-B1 Feature selection using LF-Grey Wolf optimization
In GWO, the head of the pack is the . The next level of the hierarchy is , and finally followed by . GWO models the social hierarchy and mathematically illustrates the hunting procedure as an optimization problem. If X(t) and X(t) represent the position of prey and wolf at iteration ’t’, we can mathematically model the encircling process  with two coefficients A and C as shown in (1). A and C are calculated by (2).
Here, r and r are random vectors in [0,1], a is a parameter that decreases linearly from 2 to 0 over iterations and also helps to control step size D of a grey wolf. Implementation of the end of the hunting process is done by decreasing the value of A which in turn depends on a. Once a turns zero, it means that the wolves have stopped moving. The linear decrease in A helps to exploit search space with minimal exploration. Hence, this traps a local optimum.
The size of the aggregated feature map creates an issue in terms of the complexity of the algorithm and the overall time needed for execution. To deal with this, we propose the use of levy flight-based grey wolf optimization (LF-GWO) for feature selection based on Levy probability function in (3). Here, represents position parameter, represents scale parameter and represents the collection of samples in the distribution. The above equation holds good for all positive values of and 0 otherwise.
The parameter A is modified by the Levy flight function as A = L(S)*r1. This makes A take up values in a non-linear decrease. S is the position of the wolf and r1 is a random vector.
Iii-B2 Choice of optimization function
The reason for selection of LF-GWO is based in the statistical results obtained in . It was seen that for 15 defined benchmark functions, the wilcoxon rank sum test of LF-GWO outperforms existing optimization approaches in terms of mean fitness values.
Figure 2 represents a comparison of the LF-GWO with Grey Wolf Optimization (GWO), Gravitational search algorithm (GSA), particle swarm optimization (PSO) and fast evolutionary programing (FEP) using a boxplot and a graph showing how quickly the convergence of the best fitness value is obtained with respect to the number of iterations. The box plot represents the benchmark function defined in equation 4 and the convergence map that of the function defined in equation 5.
Iv Experimental Analysis
Iv-a Datasets and training
Most commonly used steganalysis datasets are the Bossbase  and BOWS2 . Each contains 10000 grayscale images. However, the approach proposed is dependent on color, and as such, we use a dataset with color images. Hence, starting with the 10000 images of Bossbase  dataset, we generate a dataset by following the process done in . We downsampled the full-resolution images to a size of 512x512. We then followed the process in , so that the training and testing scenarios were conducted in a similar environment. In , two datasets were created by using two demosaicing algorithms: Patterned pixel grouping (PPG) and Adaptive Homogeneity-Directed (AHD) and named BOSS-PPG-LAN and BOSS-AHD-LAN correspondingly. Further, by removing the down-sampling method, we can obtain two more datasets: BOSS-PPG-CRP and BOSS-AHD-CRP. By pairing a demosaicing algorithm with bilinear or bicubic kernels, we obtain four more datasets: BOSS-PPG-BIL, BOSS-AHD-BIL, BOSS-AHD-BIL, and BOSS-AHD-BIC.
We train our model by utilizing mini-batch stochastic gradient descent with the following parameters: learning rate : 0.0001, weight decay : 0.0005, step size : 5000, momentum: 0.75, gamma : 0.75, batch size: 32, maximum iterations: 40 x 104. Testing of the trained model was done for every 5000 iterations and accuracy in 40 x 104 iterations. HILL, SUNIWARD, CMD-C-SUNIWARD and CMD-C-HILL: 4 state of the art color steganography algorithms, were used as attacking targets for experimental analysis. The embedding payload was set to 0.2 bpc (bits per channel/band pixel) and 0.4 bpc. In order to select the most challenging scenarios and also follow similar conditions for result comparison, we followed the process executed in WISERNet .
Iv-B Results comparison
To compare our results, we considered three deep learning approaches for color steganalyzers, that are widely considered state of the art approaches: WISERNet , Deep Hierarchical Representations (DHR)  and Deep-CNN . Experiments were conducted on the same datasets and using similar resources for a fair comparison. Popular steganography methods such as SUNIWARD , MiPOD , HILL  adopt an additive embedding distortion approach for minimizing framework . Recently, CMD-C was proposed  by improvising the CMD approach for color images. We denote the CMD-C method using SUNIWARD and HILL as CMD-C-SUNIWARD and CMD-C-HILL respectively. Although DHR  and D-CNN  can be executed in channel-wise convolution, normal convolution and input concatenation as seen in , we show results only for the normal convolution as WiserNet  outperforms DHR and D-CNN in all cases. We also compare results with the Pixel Vector Cost (PVC)  and channel gradient correlation (CGC) .
The parameters used in terms of batch size and iterations were the same for all the comparisons. The other parameters were used as described in the original paper. Each experiment constituted 75 percent training images, i.e., 7500 images and 2500 images were used for testing. All experiments were performed 10 times and the average accuracy of testing was used. Table 1 compares the results of our approach with WISERNet (W-Net) , DHR , D-CNN , on BOSS-PPG-LAN (B-P-L), BOSS-PPG-BIC (B-P-Bc), BOSS-PPG-BIL (B-P-Bl), BOSS-AHD-BIC (B-A-Bc) and BOSS-AHD-BIL (B-A-Bl) with 0.2 bpc and table 2 with 0.4 bpc. As can be seen, the proposed method outperforms other state of the art methods for all but one case and also the percentage increase in detection is significant when patterned pixel grouping is performed on the datasets.
Further experimental analysis is done by mixing datasets as shown in . Table 3 shows how the datasets were mixed. We further label the datasets in roman numerals for simplicity to display in the comparison of steganalyzers in table 4 and 5. BPL, BPBc, BPBl, BABc, BABl, BAL are further abbreviations of BOSS-PPG-LAN, BOSS-PPG-BIC, BOSS-PPG-BIL, BOSS-AHD-BIC, BOSS-AHD-BIL and BOSS-AHD-LAN.
Similarly to tables 1 and 2, table 4 compares results on the above-mentioned mixture of datasets with 0.2 bpc. Table 5 compares the results with 0.4 bpc. As can be seen, the proposed method outperforms recent state of the art approaches, by a significant margin.
With recent developments of color based steganography algorithms, the need for a powerful steganalyzer is needed. We saw recently, that an ensemble model of colorspaces has a significant impact on classification results. We propose StegColNet as a powerful color image steganalyzer. We employ an ensemble colorspace strategy to determine if an image is protecting information or not. We use ColorNet and take the final activation map from each colorspace. We use weighted averaging to obtain a single feature map from all the feature maps that are generated by each colorspace. We then use a levy-flight grey wolf optimization method to select a smaller subset of features. Using these features, we classify the given image into one of two classes: containing concealed information or not.
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