# Image Shadow Removal Using End-To-End Deep Convolutional Neural Networks
## 4 Experiment
### Performance Comparison Analysis  
In order to evaluate the performance of the RSnet network, this paper chose to use the structural similarity SSIM (structural similarity) and the peak signal-to-noise ratio (PSNR) as evaluation indicators to assess the model. On this basis, the RSnet algorithm proposed in this paper was compared with several popular algorithms in recent years. SSIM is an index to measure the similarity between two images. It is widely used to evaluate the quality of image processing algorithms. The larger the SSIM value of two images, the higher the similarity between them and the better the corresponding shadow removal effect in the model is. Conversely, the smaller the value of SSIM, the lower the similarity between the two, and the worse the removal effect of the corresponding algorithm is. PSNR is the most common and widely used objective measurement method for evaluating image quality. It is similar to SSIM. When the PSNR value of two images is larger, it indicates that the corresponding shadow removal model is better. Otherwise, the smaller the PSNR value, the worse the removal effect of the corresponding algorithm is. (Notably, the PSNR score is not exactly the same as the visual quality seen by the human eye. It is possible that a higher PSNR seems to be worse than a lower PSNR. It is because the sensitivity of the human eye to the error is not absolute, and the perceived result is affected by many factors.) The definitions of SSIM and PSNR are as follows:  
\[SSIM(x,y)=\frac{(2\mu_{x}\mu_{y}+c_{1})(2\sigma_{xy}+c_{2})}{(\mu_{x}^{2}+\mu_ {y}^{2}+c_{1})(\sigma_{x}^{2}+\sigma_{y}^{2}+c_{2})}, \tag{8}\]  
\[PSNR=10\times\lg(\frac{L\times L}{MSE})\text{ here }MSE=\frac{1}{n}\sum_{i=1}^{n }{(x_{i}-y_{i})^{2}}. \tag{9}\]  
It is worth noting that in order to better reflect the removal effect of the shadow image, we chose shadow/output and target/output as the quality measurement properties of the algorithm, where shadow/output represented the corresponding evaluation index value between the original shadow image and the shadow removal obtained by the algorithm. target/output represented the actual ground shadow-free image (target) and the evaluation index value corresponding to the shadow removal image obtained by the algorithm. In order to evaluate the performance of the algorithm more fairly, we only showed the shadow/output values of the UCF database in different algorithms, and the target/output value is not given since the UCF database did not provide a true ground-free shadow (target). It can be clearly seen from Table 2 that the SSIM index values obtained in the RSnet model were superior to the SSIM values of other algorithms, regardless of shadow/output or target/output. In particular, as can be seen from the last line of Table 2, in the newly created RSDB database, when the SSIM values of other algorithms were compared with the SSIM values obtained by the RSnet model of the algorithm, the SSIM value of the former was lower, the shadow removal effect of the image was poorer, and the value of the RSnet model was much higher than other algorithms. Particularly, in the evaluation of the real ground shadow-free image and the shadow removal image obtained by the algorithm, it can be seen from Table 2 that it was 1.09 times the SSIM value obtained by the shadow removal algorithm proposed by [PERSON] [21], and 1.47 times the SSIM value obtained by the model proposed by [PERSON] [28]. Of course, the comparison on the database proposed in this paper was not standardized. Therefore, Table 2 also shows the SSIM values on other shaded databases such as LRSS. By analyzing the SSIM values on other databases in Table 2, it can be found that RSnet exhibited better robustness and better image shadow removal. The processing effect was much better, especially in the third line UIUC database, which demonstrated a desired shadow removal effect. The SSIM value between the original shadow image and the algorithm-derived shadow removal image was larger than the value under the LRSS database.