## 3 Results and Discussion
### Detecting Small Objects  
Although more smaller objects were detected, the results were still not satisfactory and the issue persisted. Therefore, additional modifications were made to the training process:  
* Weights were added to the error function. This way, the error for all negative pixels decreases and for all positive pixels increases, resulting in an increased number of false positives, but also more true positives.
* Training data number in TFRecord increased to 50. This ensures that the model is not overfit.
* Cropping augmentation was modified so that images would be normally distributed.  
Figure 7: Results of two-step identification algorithm for the EnglishLP database: (**a**) precision scores; (**b**) recall scores; (**c**) F1 scores; (**d**) Pt1 point error scores; (**e**) Pt2 point error scores.  
Before the changes, the most suitable option was \"2 Point_wing,\" and after the changes, it became \"2 Point_wing_2.\" As shown in Figure 7, the modifications increased both false positives and true positives. Additionally, the number of correctly identified smaller objects also increased. Since the aim was to improve the accuracy of the proposed system without changing the model structure, it was decided to add an additional detection step using the same structure as described previously:  
1. The coordinates obtained from a predicted object are used to crop a potential license plate. Since there may be cases where the preliminary detection is biased, the coordinates are scaled twice before cropping.
2. Cropped images are processed by the network so that it returns nine values for each image: coordinates of four corners (x, y) and whether a license plate is present.  
The cropped images are relatively small, so it was possible to further minimize the structure of the network by reducing the input to 128 \(\times\) 128 \(\times\) 3 and removing parts of the network that use the \"Up-sampling2D\" layer, as shown in Figure 8.  
Once the model was trained, it was combined with the predicted number detection algorithm. The results are shown in Figure 9 for the AOLP database and labeled as \"combined\". The biggest improvement is observed with the UFPR_ALPR database, which contains many small objects. The precision of object point detection was doubled.  
Figure 8: Improved CNN network structure for precise license plate identification.  
There was also a significant decrease in the number of incorrectly detected false positive objects at the lower limit. However, there was also a decrease in the number of correctly detected objects, which occurred because the verification model returned a sufficiently low result for positive objects. Therefore, the number of positively detected objects decreased significantly at the higher limit. To solve this problem, it was decided to combine the results of the preliminary detection and verification models using Formula (8):  
\[score=1 stageScore\times 0.5+2 stageScore\times 0.5 \tag{8}\]  
The proposed modification suggests that using a threshold of 0.5 would achieve the highest possible result for these combinations. The results of this modification are shown in Figure 9, labeled as \"combined_mergedScores\". Moreover, an additional advantage of the proposed verification model is that it provides the object coordinates of all corners, which can be utilized to perform perspective transformations, enabling the restoration of an image to its normal position, irrespective of whether it was rotated or bent.