## 2 Multi-Feature Detection Method of Image Tampering
The 9 pixel points \(\left\{y_{j}^{\mathbf{\bullet},n}(\widetilde{r},\widetilde{c})\right\}\)\(r-1\leq\widetilde{r}\leq r+1\) in the \(3\times 3\) neighborhood centered on this point, plus \(c-1\leq\widetilde{r}\leq c+1\)

the coefficient \(\left\{y_{j}^{\mathbf{\bullet},n}(r,c)\right\}_{\widetilde{n}=1,\ldots,8, \ \widetilde{n}\
eq n}\) of this point in the other 7 directions in the sub-band, constitute the neighborhood coefficient vector \(\mathbf{\Upsilon}_{j}^{\mathbf{\bullet},n}(r,c)\) of coordinate point (\(r\),\(c\)) in sub-band \(\mathbf{O}_{j}^{\mathbf{\bullet},n}\). The divisive normalization transformation (DNT) factor corresponding to coordinate \((r,c)\) in one of the complementary sub-bands \(\mathbf{O}_{j}^{\mathbf{\bullet},n}\) in the direction \(n\) in level \(j\) can then be written as [31]:

\[z_{j}^{\mathbf{\bullet},n}(r,c)=\sqrt{\left(\mathbf{\Upsilon}_{j}^{\mathbf{ \bullet},n}(r,c)\right)^{\mathsf{T}}(C_{\mathcal{U}})^{-1}\mathbf{\Upsilon}_{ j}^{\mathbf{\bullet},n}(r,c)/N} \tag{10}\]

where \(N=16\), and \(C_{\mathcal{U}}\) is the covariance estimated using all neighborhood vectors in the sub-band. The DNT normalization factor of all coefficients in the whole sub-band of this point in the vector form is denoted as \(\mathbf{Z}_{j}^{\mathbf{\bullet},n}\), which represents the salient feature generated by the complementary color change in the direction \(n\) at level \(j\). Then, the DNT normalization factors obtained from the characteristic coefficients of the four pairs of complementary colors at all levels and in all directions can be fused according to the following formula to obtain the image model of the statistical saliency of the complementary color natural scenes [31]:

\[\mathrm{CCNSSal}=\mathcal{G}\left\{\oplus_{j=4}^{6}\left(\sum_{n=1}^{8}\left( \mathbf{Z}_{j}^{\mathbf{C},n}+\mathbf{Z}_{j}^{\mathbf{R},n}+\mathbf{Z}_{j}^ {\mathbf{G},n}+\mathbf{Z}_{j}^{\mathbf{B},n}\right)\right)\right\} \tag{11}\]

where \(\mathbf{Z}_{j}^{\mathbf{C},n},\mathbf{Z}_{j}^{\mathbf{R},n},\mathbf{Z}_{j}^{ \mathbf{G},n},\mathbf{Z}_{j}^{\mathbf{B},n}\) denote the black-white, red-cyan, green-magenta, and blue-yellow complementary color characteristics of the sub-band DNT normalization factor vector, respectively; \(\sum_{n=1}^{8}\) represents the vector sum in 8 directions, and \(\oplus_{j=4}^{6}(\cdot)\) denotes the operations of the interpolation to size \(R\times C\) and the summation of the corresponding layers. After obtaining the statistical salient map model of the complementary color natural scene, the image of ROI and RONI can be extracted by threshold segmentation, which can be described as:

\[\mathrm{mask}=\left\{ \begin{array}{l}1,\mathrm{CCNSSal}(x,y)\geq T\\ 0,\mathrm{CCNSSal}(x,y)<T\end{array} \right. \tag{12}\]

where the threshold \(T\) is set as the mean value of the saliency map, i.e., \(T=\mathrm{mean}(\mathrm{CCNSSal}(x,y))\); and mask is the template image after binarization of the saliency map, which can be employed to extract the ROI of the image. Figure 3 shows the results of some examples of the segmentation implemented according to (11). The examples in Figure 3 show that the CCW salient region detection operator can effectively divide the region with a complex structure and the region with less texture, and the tampered region will appear in one of the two regions, which provides a basis for the NSS of the two regions, respectively. #### 2.3.2 Extraction of the Statistical Features of Natural Scenes

Most areas of the natural image are relatively smooth, and the adjacent pixels often have high correlation, but the tampered area of the image is not correlated with adjacent pixels, which may lead to texture distortion. The NSS model considers the uniform statistical invariant features of different image scenes and contents, whose changes under such distortions make it possible to judge the changes in these features and thus identify the stitching tampering through the NSS model.