# Infrared and Visible Image Fusion: Methods, Datasets, Applications, and Prospects
## 3 Performance Evaluation of Infrared and Visible Image Fusion
### Qualitative Evaluation (Objective Evaluation Method)
\(\sigma_{AB}\) is the covariance of A and B, and \(C_{1}\) and \(C_{2}\) are the constants of images A and B, respectively. The higher the SSIM value, the more similar the two images are. The performance of image fusion can be evaluated by the total amount of similarity between the following fused images F and the source images A and B: \[M_{F}(A,B)=SSIM(F,A)+SSIM(F,B)\] (19)
* Mutual information (MI) Mutual information [77] is an index to measure the similarity of gray distribution between images A and B, and the probability of gray distribution can be obtained from the image histogram. MI is defined as: \[I(A,B)=\sum_{a,b}P_{AB}(a,b)\log\frac{P_{AB}(a,b)}{P_{A}(a)P_{B}(b)}\] (20) In Equation (20), \(P_{AB}(a,b)\) represents the joint distribution probability, and \(P_{A}(a)\) and \(P_{B}(b)\) are the distribution probabilities of a and b, respectively. * Visual information fidelity (VIF) An index that is unified in the human visual system and used to assess the efficacy of picture fusion is the fidelity of visual information. [PERSON] [78] et al. (2013) used the VIF model to extract the visual data from the source photos, eliminate the distorted data, and eventually accomplish successful visual information fusion. A VIF created specifically for fusion evaluation emerges from the study's integration of all the visual data. Building a model to estimate the distortion between the fused image and the source image is the goal of VIF. There are four steps to this process. The fused image and the source image are first filtered and separated into various blocks. Second, look for distortions in each block's visual data. Third, the fidelity of the visual information in each block is calculated. Fourth, calculate the overall index based on VIF. \begin{table}
\begin{tabular}{c c c c} \hline
**Evaluation Index** & **Desired Value** & **Evaluation Effect** & **Reference** \\ \hline PSNR & Higher value & The higher the proximity, the better the fusion quality & [72] \\ EN & Higher value & The richer the information, the better the fusion quality & [73] \\ MSE & Lower value & The smaller the differences, the better the fusion quality & [74] \\ RMSE & Lower value & The smaller the differences, the better the fusion quality & [75] \\ NCC & Between 0 and 1, ideal value & The better the quality \\  & for perfect match is 1 & of fusion \\ SSIM & Between 0 and 1, ideal value & The higher the similarity, \\  & for perfect match is 1 & the better the fusion quality \\  & & The more source image \\ MI & Higher value & information is retained, \\  & & the better the fusion quality \\ SD & Higher value & The higher the contrast, \\  & & the better the fusion quality \\ AG & Higher value & The richer the information, \\  & & the better the fusion quality \\ \hline \end{tabular}
\end{table} 
Table 3: Evaluation effect of image fusion performance index. * Standard deviation (SD) Standard deviation [79] is based on a statistical concept that reflects the distribution and contrast of a fused image and is used to measure the change in pixel intensity in a fused image. SD is defined as: \[SD=\sqrt{\sum_{i=1}^{M}\sum_{j=1}^{N}\left(F(i,j)-\mu\right)^{2}}\] (21) The average value of the fused image is represented by the variable \(\mu\) in Equation (21). Because the human visual system is more sensitive to contrast, high-contrast areas are typically easier to spot, and fusion images will also provide stronger visual effects. High-contrast images typically have bigger SD standard deviations. * Average gradient (AG) The average gradient [80] is used to represent the expressiveness of the texture and detail of the fused image and is usually used to evaluate the sharpness of the image. AG is defined as: \[AG=\frac{1}{M*N}\sum_{i=1}^{M}\sum_{j=1}^{N}\sqrt{\frac{1}{2}(\left(F(i,j)-F( i+1,j)\right)^{2}+\left(F(i,j)-F(i,j+1)\right)^{2})}\] (22) In Formula (22), the size of the fused image is \(M*N\), and \(F(i,j)\) represents the gray pixel of the image at pixel level \((i,j)\).