# Intelligent Recognition of Road Internal Void Using Ground-Penetrating Radar
## 2 Materials and Methods
### Image Quality Evaluation Metrics  
In this study, four metrics--_PSNR_, _SSIM_, _LPIPS_, and _NIQE_--were employed to evaluate the quality of enhanced images. These metrics are commonly used in various fields such as medical imaging, security surveillance, and remote sensing for assessing image compression and denoising effects, as well as evaluating image processing quality [39; 40].  
(1) _PSNR_ is a measure used to assess the quality of reconstructed images. A higher _PSNR_ indicates a better quality of image reconstruction, suggesting closer approximation to the original image.  
_PSNR_ is calculated as shown in Equation (1).  
\[PSNR=10\times\log_{10}\left(\frac{MAX_{I}^{2}}{MSE}\right) \tag{1}\]  
where \(MAX_{I}\) denotes the highest pixel value. \(MSE\) is the mean square error.  
(2) _SSIM_ is utilized to assess the visual resemblance between two images and is suitable for evaluating the effects of image quality enhancement. \(SSIM\) takes into account the structural information of images, reflecting the perceptual differences in image quality as seen by the human eye. The calculation method for \(SSIM\) is shown in Equation (2).  
\[SSIM(x,y)=\frac{\left(2\mu_{x}\mu_{y}+c_{1}\right)\left(2\sigma_{xy}+c_{2} \right)}{\left(\mu_{x}^{2}+\mu_{y}^{2}+c_{1}\right)\left(\sigma_{x}^{2}+\sigma _{y}^{2}+c_{2}\right)} \tag{2}\]  
where \(x\) and \(y\) are the window regions of the two images; \(\mu_{x}\) and \(\mu_{y}\) are the mean values; \(\sigma_{x}^{2}\) and \(\sigma_{y}^{2}\) are the variances; \(\sigma_{xy}\) is the covariance; \(c_{1}\) and \(c_{2}\) are constants used to maintain stability.  
(3) _LPIPS_ is a metric for assessing image similarity that considers the characteristics of human visual perception, using deep learning models to evaluate visual differences between two images. The lower the _LPIPS_ value, the smaller the perceptual differences between the two images, indicating that the corresponding algorithm maintains higher visual quality and similarity.  
Unlike metrics based on simple pixel comparison, _LPIPS_ utilizes the advanced features of images in calculating differences between them, providing better performance and robustness when dealing with complex features. The calculation method is detailed in Equation (3).  
\[LPIPS(x,y)=\sum_{k=1}^{N}\left(\frac{1}{H_{n}W_{n}}\sum_{i=1}^{H_{n}}\sum_{j=1 }^{W_{n}}\left\|\omega_{n}\odot\left(F^{n}(x)-F^{n}(y)\right)\right\|_{2}\right) \tag{3}\]  
where \(LPIPS(x,y)\) represents the perceptual similarity measurement between images x and y; \(N\) represents the count of layers; \(F\) is the pretrained network; \(H_{n}\) and \(W_{n}\) are the height and width of the feature map; \(F^{n}(x)\) and \(F^{n}(y)\) are the feature representations; \(\omega_{n}\) is the weight parameter at layer \(n\); \(\odot\) denotes element-wise multiplication; \(\left\|\cdot\right\|_{2}\) is the L2 norm.  
_NIQE_ is a no-reference image quality evaluation technique that operates without the need for an original or an ideal reference image. Based on a natural scene statistics model, _NIQE_ learns statistical characteristics from high-quality natural images and constructs a probabilistic model describing these statistical features. _NIQE_ assesses image quality by comparing its features with those of the learned model, determining deviations from this norm. A lower _NIQE_ value indicates that the image quality is closer to that of high-quality natural images. The computational method for _NIQE_ is shown in Equation (4).  
\[NIQE=\sqrt{\left(x-\mu\right)^{T}\Sigma^{-1}(x-\mu)} \tag{4}\]  
In the equation, \(x\) represents the feature vector; \(\mu\) and \(\sum\) are the mean and covariance of the pretrained model. \(\left(x-\mu\right)^{T}\Sigma^{-1}(x-\mu)\) represents the Mahalanobis distance, which quantifies the degree of deviation between the image features and the model features.