# Dense-FG: A Fusion GAN Model by Using Densely Connected Blocks to Fuse Infrared and Visible Images
## 4 Experiments and Results
### Experimental Design and Evaluation Metrics
Its definition is as follows:  
\[SD=\sqrt{\frac{1}{MN}\sum_{i=1}^{M}\sum_{j=1}^{N}\left(F(i,j)-\mu\right)^{2}}. \tag{16}\]  
The larger the standard deviation, the more dispersed the gray level distribution of the image, and the greater the contrast of the fused image. \(\mu\) represents the average gray value of the image. (6) Structural similarity (SSIM); this index comprehensively evaluates the degree of similarity between two images by comparing brightness, contrast, and structure information, and is defined as:  
\[SSIM(A,F)=[l(A,F)]^{\alpha}\cdot[c(A,F)]^{\beta}\cdot[s(A,F)]^{\gamma}, \tag{17}\]where \(l(A,F)\), \(c(A,F)\), and \(s(A,F)\) represent brightness distortion, contrast distortion, and structure distortion functions, respectively, and the importance of the three functions in the SSIM factor is defined as follows:  
\[l(A,F)=\frac{2\mu_{A}\mu_{F}+C_{1}}{\mu_{A}^{2}+\mu_{F}^{2}+C_{1}}, \tag{18}\]  
\[c(A,F)=\frac{2\sigma_{A}\sigma_{F}+C_{2}}{\sigma_{A}^{2}+\sigma_{F}^{2}+C_{2}}, \tag{19}\]  
\[s(A,F)=\frac{\sigma_{AF}+C_{3}}{\sigma_{A}\sigma_{F}+C_{3}}, \tag{20}\]  
where \(\mu_{A}\) and \(\mu_{F}\) represent the pixel mean of the source image \(A\) and the fusion image \(F\), respectively; \(\sigma_{A}\) and \(\sigma_{F}\) represent the standard deviations of the source image \(A\) and the fusion image \(F\), respectively; \(\sigma_{AF}\) represent the covariance between the source image \(A\) and the fusion image \(F\); and \(C_{i}(i=1,2,3)\) is to avoid the parameter introduced by the denominator if the above formula is zero. The similarity between infrared image, visible image, and fusion image is expressed as:  
\[SSIM(A,B,F)=\lambda_{A}SSIM(A,F)+\lambda_{B}SSIM(B,F), \tag{21}\]  
where \(\lambda_{A}\) and \(\lambda_{B}\) are the proportional coefficients of the structural similarity between the infrared image and the fused image, and the structural similarity between the visible image and the fused image, respectively. The larger the index value, the higher the similarity between the fused image and the source image. (7) Peak signal-to-noise ratio (PSNR); this metric measures the ratio between the effective information of the image and the noise, and is defined as:  
\[PSNR=10\lg\frac{2^{n}-1}{MSE}. \tag{22}\]  
Among them, \(n\) represents the number of image bits; MSE measures the difference between the source image and the fused image based on pixel error. PSNR can reflect whether the image is distorted to a certain extent. The larger the index value, the better the quality of the fusion image. (8) \(Q_{F}^{A/B}\); this metric is used to measure the amount of edge information transmitted from the source image to the fusion image, and is defined as:  
\[Q_{F}^{A/B}=\frac{\sum\limits_{i=1}^{M}\sum\limits_{j=1}^{N}\left(Q^{AF}(i,j) w^{A}(i,j)+Q^{BF}(i,j)w^{B}(i,j)\right)}{\sum\limits_{i=1}^{M}\sum\limits_{j=1}^{N} \left(w^{A}(i,j)+w^{B}(i,j)\right)}, \tag{23}\]  
where \(Q^{AF}(i,j)\) and \(Q^{BF}(i,j)\) represent the similarity measures between the infrared image, the visible image, and the fusion image; \(w^{A}(i,j)\) and \(w^{B}(i,j)\) are the weight coefficients of the source images \(A\) and \(B\). \[Q^{AF}(i,j)=Q_{g}^{AF}(i,j)Q_{\alpha}^{AF}(i,j). \tag{24}\]  
\(Q_{g}^{AF}(i,j)\) and \(Q_{\alpha}^{AF}(i,j)\) represent the edge strength and orientation value at position \((i,j)\), and are defined as follows:  
\[\left\{ \begin{array}{l}Q_{g}^{AF}(i,j)=\Gamma_{g}\Big{[}1+e^{k_{g}\left(Q^ {AF}(i,j)-\sigma_{g}\right)}\Big{]}^{-1}\\ Q_{\alpha}^{AF}(i,j)=\Gamma_{\alpha}\Big{[}1+e^{k_{a}\left(A^{AF}(i,j)-\sigma _{a}\right)}\Big{]}^{-1}\end{array} \right., \tag{25}\]where \(\Gamma_{g},k_{g},\sigma_{g},\Gamma_{a},k_{a},\sigma_{a}\) are all constants. The Sobel operator is used to calculate the edge strength and orientation value between the source images \(A\), \(B\) and the fused image \(F\), and are defined as follows:  
\[\left\{ \begin{array}{ll}g_{A}(i,j)=\sqrt{S_{A}^{x}(i,j)^{2}+S_{A}^{y}(i,j)^{2 }}\\ \alpha_{A}(i,j)=\tan^{-1}\left[\frac{S_{A}^{y}(i,j)}{S_{A}^{x}(i,j)}\right] \end{array}