# Image Dehazing and Enhancement Using Principal Component Analysis and Modified Haze Features
## 4 Experimental Results
### Objective Assessments  
Figures 9-11 compare the performance of the haze removal using the existing and proposed methods. The objective assessments were performed using [PERSON]'s method and a set of test images, which were presented in [PERSON]', [PERSON]', [PERSON]'s, and [PERSON]'s works, as shown in Figure 8[1, 4, 5, 16]. \(\Sigma\) and \(\overline{r}\) respectively represent the ratios of brightest and darkest pixels and the ratio of gradient norms between the input and haze-removed images [21]. The small value of \(\Sigma\) means that the resulting image has a lower brightness saturation while preserving the dark region. On the other hand, if \(\overline{r}\) is close to 1, the gradient of the resulting image does not change without over-dehazing [22]. The objective assessments are summarized in Table 2.  
As shown in Figures 9b-11b, [PERSON]'s method provided an enhanced result in the sense that it preserved the details in the dark and bright regions with the best score of \(\Sigma\)[1]. Although [PERSON]'s method provided improved results using \(l_{1}\)-norm minimization, it could not avoid saturation in the bright region, as shown in Figures 9c-11c[9]. Since [PERSON]'s method reduced the haze component based on the haze-line, it was able to preserve the color information, as shown in Figures 9d-11d[8]. Figure 8: The test images used for the objective assessment of haze removal [1,4,5,16]: (**a–j**) are the real haze images to evaluate the performance of haze removal. Reproduced with permission from [1], IEEE, 2011, reproduced with permission from [4], IEEE, 2014, reproduced with permission from [5], IEEE, 2016, reproduced with permission from [16], IEEE, 1969. Figure 9: Experimental results of haze removal using the proposed and existing methods: (**a**) an input haze image [1], reproduced with permission from [1], IEEE, 2011, (**b**) [PERSON]’s method [1], (**c**) [PERSON]’s method [9], reproduced with permission from [9], IEEE, 2013, (**d**) [PERSON]’s method [8], reproduced with permission from [8], IEEE, 2016, (**e**) [PERSON]’s method [2], (**f**) [PERSON]’s method [6], and (**g**) the proposed method. However, it is difficult to choose an appropriate parameter to obtain the optimal result and the resulting images include brightness saturation. Figures 9e-11e show the resulting images fromusing [PERSON]'s method with the halo effect near the edges [2]. Although [PERSON]'s method estimated the transmission using the convolutional neural network, the resulting images show color distortion because of the inaccurately estimated atmospheric light [6]. On the other hand, the proposed method provided better results than most existing methods with improved contrast and lower brightness saturation. Since [PERSON] et al. used the random forest of 200 decision trees with multiscaled haze features to solve the regression problem [4], their algorithm took about 193.9253 and 99.9524 s for feature extraction and the learning of random forest, respectively, for an input image of size 3873 \(\times\) 2516, as shown in Figure 12a. On the other hand, since the proposed method divides the input image into 5 \(\times\) 5 non-overlapping patches to extract the haze features, it took only about 9.7474 and 25.6829 s with and without parallel processing for feature extraction, respectively. The estimation of transmission using the trained random forest took about 17.0358 s with 100 decision trees. In addition, the proposed  
Figure 11: Experimental results of haze removal using the proposed and existing methods: (**a**) an input haze image [16], reproduced with permission from [16], IEEE, 1969, (**b**) [PERSON]’s method [1], (**c**) [PERSON]’s method [9], (**d**) [PERSON]’s method [8], (**e**) [PERSON]’s method [2], (**f**) [PERSON]’s method [6], and (**g**) the proposed method.