## 2 Multi-Feature Detection Method of Image Tampering
The focusing region is the region where the focus is located, which has higher sharpness and can reflect richer details. The defocused region is usually a blurry region. In a stitching tampered image, there are usually multiple focusing regions. Therefore, sharpness detection can effectively detect such stitching tampering. In this paper, a gradient-based image sharpness evaluation function is used to extract the gradient values in the horizontal and vertical directions using the Sobel operator [25]. The larger the average grayscale value of the image processed by the Sobel operator, the clearer the image. The image is divided into 4 \(\times\) 4 non-overlapping blocks, and the sharpness of each image block is calculated by the Sobel operator. If the sharpness of one or more image blocks differs from the rest, this implies that it is very likely that the examined image has been tampered with. Letting the Sobel convolution kernel be \(\mathbf{G}_{x}\) and \(\mathbf{G}_{y}\), one obtains [26]:

\[\mathbf{G}_{x}=\left[ \begin{array}{ccc}-1&0&1\\ -2&0&2\\ -1&0&1\end{array} \right] \tag{6}\]

\[\mathbf{G}_{y}=\left[ \begin{array}{ccc}1&2&1\\ 0&0&0\\ -1&-2&-1\end{array} \right] \tag{7}\]

Then, the gradient of image \(\mathbf{I}\) at point (\(x\),\(y\))is:

\[S(x,y)=\sqrt{\left|\mathbf{G}_{x}*\mathbf{I}(x,y)\right|^{2}+\left|\mathbf{G}_{y}*\mathbf{I}(x,y)\right|^{2}} \tag{8}\]

Thus, the sharpness of the image can be defined as [27]:

\[\text{Ten}=1/k\cdot\sum_{x}\sum_{y}S(x,y)^{2} \tag{9}\]

where \(k\) is the total number of image pixels. ### Salient Region Detection and Natural Scene Statistics

In a tampered image, the tampered area will cause interference in the smoothness, consistency, continuity, regularity, and periodicity of the original image, and change the correlation between image pixels [14], thus causing image distortion. Such distortions can be detected by the NSS model [28; 29]. On the other hand, when acquiring information from the image, the human visual system is more sensitive to the region with high brightness and a complex structure [30]. To reflect the sensitivity of the human vision system, the saliency region detection algorithm usually divides the image into regions of interest (ROI) and regions of no interest (RONI) of the human vision system. In the tampered image, the brightness and structural complexity inside the tampered region are relatively average, and it can only belong to either ROI or RONI, so that the statistical results of NSS of ROI

Figure 2: The results of the CCW chroma detection. (**a.d**) Tampered images; (**b,e**) the images after superpixel segmentation; (**c,f**) chroma detection results. The red box area denotes the tampered area hereinafter. and RONI in the tampered image are significantly different. Therefore, after detecting the salient regions of the image, NSS can be performed on ROI and RONI, respectively, to obtain the texture differences and distortion characteristics. #### 2.3.1 Salient Region Detection Operator of Complementary Color Wavelet

For a color image with a size \(R\times C\), CCW transformation is carried out to obtain 8 directions in 6 levels of sub-band features of black-white, red-cyan, green-magenta, and blue-yellow complementary colors. According to Equation (4), \(\mathbf{O}_{j}^{\mathbf{C},n},\mathbf{O}_{j}^{\mathbf{R},n},\mathbf{O}_{j}^{ \mathbf{G},n},\mathbf{O}_{j}^{\mathbf{B},n}\) can be obtained, where \(j=1,2,\ldots,6\), \(n=k\pi/8\), \(k=1,2,\cdots,8\). The neighborhood in any sub-band is considered, and the coefficient of the coordinate point (\(r\),\(\varepsilon\)) in sub-band \(\mathbf{O}_{j}^{\mathbf{\bullet},n}\) is denoted as \(y_{j}^{\mathbf{\bullet},n}(r,c)\).