# PEE: Prior-Enhanced and Resolution-Extended Object Detection for Industrial Laminated Panel Scenes
## 3 Materials and Methods
### General Overview  
The detection of laminated panels can be framed as a multi-task learning problem, where both classification and bounding-box regression are optimized together. This approach helps to accurately identify and locate objects, as commonly performed in many high-performing single-stage detectors. Specifically, for an input image with input \(H\times W\times C\), the single-stage detector is trained and reasoned to obtain a classification score of dimension \(N\times 1\), a confidence score of \(N\times 1\), and position coordinates of \(N\times 2\), where \(N\) denotes the total number of prediction frames. As shown in Figure 2, the whole detection pipeline consists of five parts: a backbone network with Adown and RepNCSPELAN4 modules for efficient processing and extraction of features; a feature-processing module with MRPE; YOLONeck for further processing of features; a bottleneck with a resolution-extended network (REN) for extracted features for high-resolution enhancement, stitching, etc. ; and a detection head with six independent branches to output the final results. The feature maps at all scales share the same detection head to increase the efficiency of the additive measurements. The shared detection head has two components: regression and classification branches. Like other popular single-level detectors, YOLOv9's loss consists of three components: bounding-box regression loss, confidence loss, and category classification loss. Assuming that the loss function of YOLOv9 is \(L\), we can express it as a weighted sum of the three main components:  
\[\mathrm{L}=\lambda_{\mathrm{bbox}}\cdot L_{\mathrm{bbox}}+\lambda_{\mathrm{ conf}}\cdot L_{\mathrm{conf}}+\lambda_{\mathrm{cls}}\cdot L_{\mathrm{cls}} \tag{1}\]  
where \(L_{\mathrm{bbox}}\) is the bounding-box regression loss, and in our example, the IoU loss is used. \(L_{\mathrm{conf}}\) is the confidence loss, and the binary cross-entropy loss is applied. \(L_{\mathrm{cls}}\) is the category classification loss. Specifically, \(bbox\) represents the bounding box of the target. In object detection, the model needs to predict the position information of each target, usually represented by a rectangular box. This bounding box is usually represented by fourcoordinates, which are the positioning information of the target area. The model predicts these values through regression tasks. Conf is the confidence score, which represents the confidence that the predicted bounding box contains the target. It reflects the confidence level of the model as to whether the current prediction box contains a certain target. This value is usually between 0 and 1, where 1 indicates that the model is very certain that there is a target within the box, and 0 indicates that the model is almost certain that there is no target within the box. Usually, conf is calculated based on the probability of the target's existence, and CIs is the class score, which represents the probability that each predicted box belongs to a different category. For multi-class object detection tasks, the model outputs a category score vector for each bounding box, representing the probability that the box belongs to each category. Since there are eight categories of objects to be distinguished, the multivariate cross-entropy loss is then utilized. The bounding-box regression loss (BBox loss), confidence loss (Conf loss), and category classification loss (Cls loss) are the three main components of the total loss function in an object detection model. The BBox loss is used to measure how accurately the model predicts the location and size of the object by comparing the predicted bounding box coordinates with the ground truth. Conf loss refers to the model's ability to correctly predict the presence of an object within the bounding box. It is measured using binary cross-entropy, where the model learns to classify whether a given region contains an object or not. CIs loss is used to evaluate how well the model assigns the correct object category to each detected object.