# Fast Fourier Asymmetric Context Aggregation Network:
## 4 Experiments
### Evaluation Metrics  
We conduct a comprehensive performance evaluation of the proposed method using five popular evaluation metrics:  
1. **Frechet Inception Distance (FID):** FID [75] is an objective metric widely used to evaluate the quality of images generated by generative models. It measures the distance between the distributions of generated and real images using a pre-trained Inception network, quantifying the perceptual similarity between them. By considering both the global feature distribution and perceptual similarity, FID effectively assesses the overall quality of generated images, aligning closely with human visual perception. We use FID to evaluate the overall diversity and global perceptual quality of the generated images. The calculation of FID is as follows: \[FID=\big{\|}\mu_{g}-\mu_{r}\big{\|}^{2}+\text{Tr}\bigg{(}\Sigma_{g}+\Sigma_{r} -2\big{(}\Sigma_{g}\Sigma_{r}\big{)}^{\frac{1}{2}}\bigg{)},\] (26) where \(\mu_{g}\) and \(\Sigma_{g}\) represent the mean vector and covariance matrix of the generated image features, respectively, while \(\mu_{r}\) and \(\Sigma_{r}\) represent the mean vector and covariance matrix of the real image features, respectively. \(\big{\|}\mu_{g}-\mu_{r}\big{\|}^{2}\) represents the square of the Euclidean norm of the difference between two mean vectors. Tr represents the trace of a matrix. 2. **Structural Similarity (SSIM):** SSIM [76] is an evaluation metric used to measure the similarity of two images. SSIM focuses on the brightness, contrast, and structure of the image. We use SSIM to evaluate the quality of the generated image in terms of local structure and so on. SSIM is calculated as follows: \[\text{SSIM}(x,y)=\frac{\big{(}2\mu_{x}\mu_{y}+C_{1}\big{)}\big{(}2\sigma_{xy} +C_{2}\big{)}}{\Big{(}\mu_{x}^{2}+\mu_{y}^{2}+C_{1}\Big{)}\Big{(}\sigma_{x}^{ 2}+\sigma_{y}^{2}+C_{2}\Big{)}},\] (27) where \(x\) and \(y\) represent the real image and the generated image, respectively. \(\mu\) denotes the mean pixel value, \(\sigma\) represents the standard deviation of grayscale intensity, \(C_{1}\) and \(C_{2}\) are constant coefficients, and \(\sigma_{xy}\) is defined as \[\sigma_{xy}=\frac{1}{N-1}\sum_{i=1}^{N}(x_{i}-\mu_{x})\big{(}y_{i}-\mu_{y}\big{)}.\] (28)
3. **Learned Perceptual Image Patch Similarity (LPIPS):** LPIPS [77] is a metric used to evaluate the perceptual similarity between two images. It assesses image quality by directly extracting features from a pre-trained neural network, making it more aligned with human visual perception. LPIPS places greater emphasis on local perceptual similarity, and we employ it to evaluate the local perceptual quality of generated images. The calculation of LPIPS is as follows: \[\text{LPIPS}(x,y)=\sum_{l}\frac{1}{H_{l}W_{l}}\sum_{h,u}\Big{\|}w_{l}\odot \bigg{(}\hat{\phi}^{l}_{xthr}-\hat{\phi}^{l}_{ythr}\bigg{)}\Big{\|}^{2},\] (29) where \(\hat{\phi}^{l}_{xthr}\) and \(\hat{\phi}^{l}_{ythr}\) represent the normalized corresponding features, and \(w_{l}\) is the scaling weight vector. 4. **Peak Signal-to-Noise Ratio (PSNR):** PSNR is a pixel-level image quality metric that is sensitive to the random noise in the image. We use PSNR to evaluate the pixel-level quality of the generated image. The calculation formula of PSNR is \[PSNR=10\times\log_{10}\bigg{(}\frac{MAX_{l}^{2}}{MSE}\bigg{)},\] (30)where \(MAX_{I}\) represents the maximum pixel value of the image, and \(MSE\) is the average value of the RGB three-channel mean square error of the real image and the generated image. 5. **TOPIQ:** TOPIQ is a deep-learning-based image quality assessment method that utilizes multi-scale features and cross-scale attention mechanisms to evaluate image quality. By simulating the characteristics of the human visual system, TOPIQ leverages high-level semantic information to guide the network's focus on semantically important local distortion regions, thereby assessing image quality. TOPIQ includes both Full-Reference (FR) and No-Reference (NR) forms. In this paper, we use them to evaluate the perceptual quality of the generated images.