## 5 Results  
In each training scenario described in this paper, the segmentation models were trained with 500 epochs, and approximator models were trained for 1000 epochs with the Adam optimizer [40], whose parameters were set as follows: the learning rate was 0.001, \(\beta_{1}\) was 0.9, and \(\beta_{2}\) was 0.999. Training was completed on an NVIDIA Quadro 6000 RTX GPU (by NVIDIA corporation in Santa Clara, CA, USA) with the tensorflow framework. For a pretrained segmentation model, U-net was trained with the 1404 available images. The mean IoU was the evaluation metric used for the test segmentation results. Usually, the mean IoU is calculated for a set of images, but the same function can be utilized for a single image by setting the number of images per set to one. We tested three inference methods. (1) Segmentation model only--the received distorted image is directly passed to the segmentation model, (2) approximator trained separately--approximator network is trained only according to \(L_{AM}\), and (3) the proposed method--approximator was trained according to both \(L_{AM}\) and \(L_{SM}\) (Figure 6). The obtained IoU values are shown below for each result. All approximations were segmented by using pretrained U-net, and the IoU scores were obtained and are shown below for each segmentation result for the proposed approximator model. Based on the observations, the proposed approximator model which was trained by using the proposed combined learning method presented a low error in approximation and a higher IoU score for semantic segmentation. Since this research field is narrow with limited related works, popular additional segmentation models, Linknet [12] and FPN [29], were tested to prove the modularity of the proposed combined learning method. These methods can be incorporated with many backbones such as Resnet18 [34], SeResnet18 [41], DenseNet121 [42], InceptionV3 [23], MobileNetV2 [43], and EfficientNetB0 [44]. The proposed approximator model was trained separately and combined with Linknet and FPN. The results are shown in Figures 8-10 for five testing images and their corresponding segmentation labels (the obtained IoU score is shown below each result). Table 1 summarizes the effects of the proposed combined learning method in terms of the mean IoU score. The obvious fact is that the segmentation models themselves could not have a higher segmentation score for distorted images. We have reached a point where we are closer to the related literature, which is worked out as  
Figure 7: Samples of testing images (**top**), their corresponding segmentation labels (**middle**), and the received images (**bottom**) for results comparison. Images are named 1 to 5 for cross referencing them respectively between other figures. the approximator trained separately, and it presented an improvement of 5.52% for Unet, 10.0% for Linknet, and a 0.6% reduction in FPN. However, by using the proposed combined method, we have achieved 65.83% improvement for Unet, 75.36% for Linknet, and 53.6% for FPN. Table 2 shows a summary of the results for different backbones. Even without the proposed method, some backbones presented a relatively higher IoU score than that which was obtained with the separately trained approximator as they are much more tolerant of images with distortions. In this case, backbones such as DenseNet121 produced a slightly lower IoU score with a separately trained approximator. However, with the proposed method, the same backbone presented a higher IoU score. Figure 8: Results (IoU score) obtained from the proposed approximator network and U-net. Images are named 1 to 5 for cross referencing them respectively between other figures. Figure 9: Results (IoU score) obtained from the proposed approximator network and Linknet. Images are named 1 to 5 for cross referencing them respectively between other figures. To compare different backbones quantitatively, Table 3 summarizes parameter counts and computational complexity.