# Improved U-Net++ with Patch Split for Micro-Defect Inspection in Silk Screen Printing
## 4 Performance Analysis  
The methods and algorithms used in the proposed architecture were evaluated and validated for their effectiveness on various tasks, models, and datasets. Table 1 summarizes the specifications of the proposed system. We performed performance analysis using Dice scores. The dice score and Jaccard index have become some of the most popular performance metrics in medical image segmentation. [PERSON] et al. were among the first to suggest the dice score for medical image analysis by evaluating the quality of automated white matter lesion segmentations [27]. In scenarios with large class imbalances with an excessive number of (correctly classified) background voxels, they showed that the dice score is a special case of the kappa index, a chance-corrected measure of agreement. They further noted that the dice score reflected both the size and localization agreement, more in line with the perceptual quality compared to pixel-wise accuracy. The range of the dice score is between 0 and 1, and this is a probability value that collects how much the actual value and the predicted value overlap. It is 1 if the labeled area and the predicted area are the same; otherwise, it is 0. The dice score is the harmonic average of precision and recall and is expressed as follows. In binary image segmentation, \(y\) can be thought of as a set of pixels labeled as the foreground. It is, therefore, well-defined to consider set theoretic notions such as \(y\cap\bar{y}\) for two different segmentations. This motivates the use of multiple set theoretic similarity measures between two segmentations named \(y\) and \(\bar{y}\). The equation for the dice score is as follows:  
\[D(y,\bar{y})\ :=\ \frac{2|y\ \cap\ \bar{y}|}{|y|+|\bar{y}|}. \tag{1}\]  
Mainly, three hypotheses were considered for the Dice score with respect to data preprocessing, the model, and correlation between the loss function and model performance. The hypotheses were as follows:  
1. The original image input, that is, the input to which the patch-split method is applied, increases the Dice score. The Dice score is often used to quantify the performance of image-segmentation methods. 2. Compared to the feature pyramid network (FPN) [33] and DeepLabV3, the U-net++ architecture increases the Dice score. 3. The Dice score can be increased by learning multiple loss functions and summing their values. Because transfer learning is known to be efficient and effective in many deep learning computer vision studies, experiments were conducted with transfer learning using a pretrained network as a classification task [34]. The architecture of the backbone network was EfficientNet-b0. The reason for using EfficientNet-b0 was because the production cycle time of the site may increase during lengthy inspections; therefore, a fast reference time is required and a backbone network such as EfficientNet-b0 can ensure compliance. The learning rate was 0.0001 in float form, and the AdamW Optimizer was adopted [35]. \begin{table}
\begin{tabular}{c c} \hline \hline
**Hardware Environment** & **Software Environment** \\ \hline CPU: Intel Core i9-10900 Processor & Ubuntu 20.04 \\ GPU: Nvidia GeForce RTX 3080 & Python 3.7 \\ RAM: Samsup Electronics DDR4 32 GB & CUDA 11.2 \\ SSD: Samsup Electronics 970 EVO & \\ series 1 TB M.2 NVMe & \\ HDD: Western Digital BLUE HDD 4 TB & \\ Vision Camera: Lucid TRI1225-MC 12 MP & \\ Customized mechanical part & \\ for quality inspection & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: System specifications. For learning, an epoch consisted of 30 batch sizes of 2. The learning rate scheduler of the experiment utilized the cosine annealing learning rate, and as a scheduler is frequently used for various tasks, partial restarts are also gaining popularity in gradient-based optimization to improve the rate of convergence in accelerated gradient schemes to deal with ill-conditioned functions Therefore, the scheduler can solve overfitting by solving the local minima problem and as such, is suitable for the class imbalance problem.