# Full-Reference Image Quality Assessment Based on Multi-Channel Visual Information Fusion
## 2 Proposed Method  
### Construction of Multi-Channel LoG Filtering  
During image quality assessment, image features that are consistent with human visual perception are generally introduced, such as image structure and texture. The literature [30] mentions that the difference of Gaussian (DoG) can be used to simulate the visual characteristics of cats. However, when constructing the DoG method, different standard deviations and scale differences are usually tuned to obtain the ideal feature differences, making the fusion of methods at different scales very complex. When adjusting the scale, the DoG operators can be approximated by the second-order derivative of Gaussian, which corresponds to the LoG operator [15]. This operator can simulate the neural mechanism of human vision. Therefore, to simplify the calculation, LoG is used here to calculate the image difference values, with:  
\[L\partial G=\frac{1}{\sqrt{2\pi\sigma^{2}}}\frac{m^{2}+n^{2}-2\sigma^{2}}{ \sigma^{4}}\mathrm{e}^{-(m^{2}+n^{2})/(2\sigma^{2})} \tag{1}\]  
where \(\sigma\) is the standard deviation of \(L\partial G\), and \(m\) and \(n\) represent the positions of each pixel (for ease of writing, \(x\) is used here to represent the pixel position, i.e., \(x=(m,\,n)\)). Before constructing a multi-channel LoG filter, the image needs to be preprocessed, that is, the RGB image is mapped to the opposite uniform color space. At present, there are many methods for color space conversion, such as CIELab [31], LMN [32], YIQ [33], and YUV [34]. To reduce the errors generated during color space conversion, the evaluation standard values of the color space in four public databases are calculated first, and the ideal uniform color space is determined through their values. The top-ranked evaluation standard values are highlighted in bold, as shown in Table 1.  
From the data in Table 1, it can be seen that _LMN_ has the best overall performance among the four uniform color spaces. Therefore, the _RGB_ image is transformed into the _LMN_ uniform color space in the proposed method. The transformation formulation is as shown in Equation (2):  
\[\left[ \begin{array}{c}L\\ M\\ N\end{array} \right]=\left[ \begin{array}{ccc}0.06&0.63&0.27\\ 0.30&0.04&-0.35\\ 0.34&-0.6&0.17\end{array} \right]\left[ \begin{array}{c}R\\ G\\ B\end{array} \right] \tag{2}\]  
where \(L^{\star}\) represents luminance component; \(M^{\star}\) and \(N^{\star}\) represent chromaticity components. Traditional calculation methods generally convolve the operator \(L\partial G\) with the image luminance component, ignoring the importance of color components. In this paper, the operator \(L\partial G\) is convolved with the three color components in the uniform color space, as implemented by Equation (3):  
\[ \begin{array}{l}LLoG_{i}(x)=L_{i}(x)*L\partial G(x)\\ MLoG_{i}(x)=M_{i}(x)*L\partial G(x)\\ NLoG_{i}(x)=N_{i}(x)*L\partial G(x)\end{array}  \tag{3}\]  
where \(i\) represents the image type (i.e., original image \(f_{1}\) and distorted image \(f_{2}\)) and \({}^{\star}\) represents convolution calculation. Next, after convolution, the three components are fused, and this process is defined as:  
\[LMNLoG_{i}(x)=\left(LLoG_{i}{}^{2}(x)+MLoG_{i}{}^{2}(x)+NLoG_{i}{}^{2}(x) \right)^{\frac{1}{2}} \tag{4}\]  
the MLG similarity can be represented as:  
\[SIM_{LoG}(x)=\frac{2\cdot LMNLoG_{1}(x)\cdot LMNLoG_{2}(x)+T_{1}}{LMNLoG_{1} {}^{2}(x)+LMNLoG_{2}{}^{2}(x)+T_{1}} \tag{5}\]  
where \(T_{1}\) is a constant for increasing formula stability. To verify the performance of MLG, two groups of original and distorted images with the same specifications are selected from the TID2008 database [35], and the image