# Image Forensics Using Non-Reducing Convolutional Neural Network for Consecutive Dual Operators
## 4 Experimental Results
### Detection of Dual Operators Sequence for Similar Specification  
In this section, the robustness of the proposed technique is discussed on two operator sequences under multiple parameters of operators. The specification is the same as used in CNN model training. The detection accuracy of the two operator sequences is given for the possible five classes as discussed in Section 2.1. \(\Omega\Omega\) class denotes the pristine image, \(\Omega\Omega\) class denotes images operated by operator \(\alpha\), \(\Omega\Omega\) class denotes images operated by operator \(\beta\), \(\Omega\Omega\) class denotes images first operated by operator \(\beta\) than operator \(\alpha\). There are 15,000 images of the five classes in the testing set. It can be noticed from the Confusion matrix of operators, Gaussian blurring with standard deviation 1.0 (GAU_1.0) sequence, and median filtering of filter size 3 \(\times\) 3 (MF3) as shown in Figure 10, where the proposed CNN network can classify two operator sequence images with good accuracy. The experimental results show that 991 GAU_1.0 operated images out of 15,000 GAU_1.0 operated images are misclassified in class \(\Omega\Omega\), which is first operated by MF3 and then operated by GAU_1.0. Figure 9: Filtered images of layer 6 and 15 kernels. The detailed results of the detection accuracy for different operator pairs are shown in Table 1. Gaussian blurring with standard deviation 0.7 (GAU_0.7), 1.0 (GAU_1.0), median filtering of filter size 3 \(\times\) 3 (MF3), 5 \(\times\) 5 (MF5), un-sharp masking sharpening with radius 2.0 (SH_2.0), 3.0 (SH_3.0), up-sampling with factor 1.2 (UP_1.2) and 1.5 (UP_1.5) operators are considered, where pairs of operators are represented in Table 1 for \(\alpha\) and \(\beta\). The average detection accuracy of five classes is more than 92% in all of the cases. The operator sequence with operator SH_2.0 or SH_3.0 is more challenging when compared with other operators, as shown in Table 1. The internal statistical information of an image is highly affected after applying un-sharp masking than other operators, as can be seen in Figure 4.  
As shown in Figure 11, the behavior of operators can also be visualized in the plot of mini-batch loss. The curve of \(\alpha\) = GAU_0.7 & \(\beta\) = UP_1.2 becomes stable shortly with fewer peaks and valleys in the curve if compared with \(\alpha\) = GAU_0.7 and \(\beta\) = SH_2.0. Similar attributes of stability are also followed by UP_1.5. \begin{table}
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The JPEG format is widely used when the visual quality remains good even after the compression in a real scenario as the default format. Therefore, three steps are considered in the detection of operator sequences in compressed images. In the first, the image is JPEG compressed with quality factor Q1. The operator sequence is applied to compressed images in step 2. In step 3, JPEG compression is applied with quality factor Q2. Detailed discussion regarding JPEG compression is given in Section 2.2. The confusion matrix of five class classifications on compressed images with Q1 = 75 and Q2 = 85 is shown in Figure 12. Two operators, Gaussian blurring with standard deviation 1.0 (GAU_1.0) and up-sampling with factor 1.5 (UP_1.5) are considered. The performance of the proposed CNN can degrade on compressed images in comparison to the uncompressed images. However, while considering the small image size (64 \(\times\) 64) and low compression quality factors, the performance is satisfactory. In Table 2, the results are shown for compressed images. The number of images for training, validation, and testing is similar to be considered in uncompressed images. Multiple compression quality factors are considered to visualize in the real scenario for Q1 = Q2, Q1 \(<\) Q2, and Q1 \(>\) Q2. The difference between quality factors Q1 and Q2 are also varied from 5 to 20. Compression omits the artifacts of the operator. Still, the average detection accuracy is nearly 90% in most of the cases.