# Infrared and Visible Image Fusion: Methods, Datasets, Applications, and Prospects
## 3 Performance Evaluation of Infrared and Visible Image Fusion
### Qualitative Evaluation (Objective Evaluation Method)  
According to a certain algorithm, objective assessment methods provide quantitative evaluation value and can quantitatively assess the efficacy of fused pictures [70]. The objective evaluation approach has the benefits of being simple, highly effective, highly certain, inexpensive, and highly operable. It has the ability to overcome the limitations of subjective evaluation techniques that are easily influenced by a variety of elements, such as the surroundings. The basic foundations of objective evaluation techniques include information theory, structural similarity, image gradient, statistics, and the human visual system. We will briefly go over a few performance metrics used to gauge the quality of fused images below [71]. Table 3 displays the findings of the examination of the performance metrics for image fusion. * Peak signal-to-noise ratio (PSNR) The peak signal-to-noise ratio [72] primarily evaluates the ratio between the image's effective information and noise, which might indicate image distortion and reflect the quality of the fused image. PSNR is defined as follows: \[PSNR=10\log\frac{X^{2}}{MSE}\] (13)In Equation (13), X represents the difference between the maximum and minimum values of the gray scale of the ideal image, which is usually taken as 255. The higher the value of PSNR, the better the quality of the fused image. * Entropy (EN) Entropy [73] is mainly an objective evaluation index to evaluate the amount of information contained in an image. If the entropy increases after fusion, it indicates that the fusion information increases and the fusion performance improves. EN is defined as: \[EN=-\sum\limits_{i=0}^{n}{{{X_{i}}{{\log}_{2}}{{X_{i}}}}}\] (14) In Equation (14), n stands for the grayscale level, \(X=\{X_{1},X_{2},...,X_{n}\}\) for the picture's grayscale distribution, and \(X_{i}\) for the normalized histogram of the corresponding grayscale level in the combined image. The more information in the fused image, the larger the EN, and the better the performance of the fusion method is proven. However, noise has an impact on EN, and the more noise, the greater the EN. * Mean square error (MSE) The mean square error [74] reflects the difference between the fused image and the reference image and is an objective evaluation index of image quality based on pixel error. MSE is defined as: \[MSE=\frac{1}{{{mn}}}\sum\limits_{i=1}^{m}{{{\sum\limits_{j=1}^{n}{{{\left({{A_{ ij}}-{B_{ij}}}\right)}^{2}}}}}}\] (15) In Formula (15), \(A_{ij}\) and \(B_{ij}\) are the gray values of pixels of the fused image and the reference image located in row \(i\) and column \(j\). The smaller the MSE, the smaller the difference between the images, and the better the fusion quality. * Root mean square error (RMSE) Root mean square error [75] is an evaluation index reflecting spatial details. RMSE is defined as: \[RMSE=\sqrt{\frac{1}{{{mn}}}\sum\limits_{i=1}^{m}{{{\sum\limits_{j=1}^{n}{{{ \left({{A_{ij}}-{B_{ij}}}\right)}^{2}}}}}}}\] (16)
* Nonlinear correlation coefficient (NCC) The nonlinear correlation coefficient [76] represents the nonlinear correlation between the fused image and the source image. NCC is defined as: \[NCC=\frac{{\sum\limits_{i=2}^{m}{\sum\limits_{j=1}^{n}{{{\left({{A_{ij}}*{B_{ ij}}}\right)}}}}}}{{{{\left({{A_{ij}}}\right)}^{2}}}}\] (17)
* Structural Similarity Index Measure (SSIM) The structural similarity index [74] is an index used to evaluate the similarity of images A and B, mainly studying the relationship between the change in image structure information and image perception distortion. SSIM is defined as: \[SSIM(A,B)=\frac{{{{\left({{2{\mu_{A}}{\mu_{B}}+{C_{1}}}\right)}{{\left({{2{ \delta_{AB}}+{C_{2}}}}\right)}}}}}}{{{{\left({{\mu_{A}^{2}}+{\mu_{B}^{2}}+{C_ {1}}}\right)}{{\left({{\delta_{A}^{2}}+{\delta_{B}^{2}}+{C_{2}}}\right)}}}}}\] (18) In Equation (18), \(\mu_{A}\) and \(\mu_{B}\) are the average intensity of images A and B, respectively, and \(\sigma_{A}\) and \(\sigma_{B}\) are the standard deviation of images A and B, respectively.