# Reducing Safety Risks in Construction Tower Crane Operations: A Dynamic Path Planning Model
## 2 A Dynamic Path Planning Model for Tower Crane Operations
### Path Safety Risk Evaluation Module
Spatial Pyramid Pooling--Fast (SPPF) is a variant of spatial pyramid pooling used to perform pooling operations at different scales and integrate the results to extract multi-scale feature information, thereby enhancing the understanding and processing of targets of varying sizes. 3. Task Head Module: This module is constructed based on the Path Aggregation Network (PAN) framework, which integrates concepts from the Feature Pyramid  
Figure 3: YOLOv8-seg framework. Network (FPN). Up-sampling and contact modules for up-sampling and connection are utilized, which enhances the effective use of multi-scale feature information in instance segmentation tasks, thereby improving detection accuracy and robustness. Images are preprocessed to a standardized resolution of 640 \(\times\) 640 \(\times\) 3 pixels within the input module. The preprocessed images are then fed into the backbone module, where a series of CNN operations extract features. This process involves convolutional operations, with 1 \(\times\) 1 convolutional layers in the C2f component and Bottleneck layers working in concert to process and merge features, thereby extracting semantic information from the input images. The features extracted by the backbone are passed to the task head module for further refinement, specifically for instance segmentation. Up-sampling and contact modules are used to integrate multi-scale feature information, which is critical for accurately detecting and segmenting objects of varying sizes. After feature enhancement in the task head module, the model generates the final output. This output includes the classification of instances into predefined classes, the determination of their shapes, the specification of their bounding box coordinates, and the assignment of confidence scores for each detection. Through instance segmentation, the potential drop zone (the operational hazard radius around the hook) and the protected objects (workers) can be represented in pixel coordinates within the plane projection. This study employs a method to determine the actual coordinates of the objects based on a simple proportional relationship between pixel coordinates and real-world coordinates [14,39,40]. The conversion between pixel coordinates and actual coordinates is described by the following Equation (1) [41]:  
\[(x_{actual},y_{actual})=\frac{L_{a}}{L_{p}}\Big{(}x_{pixel},y_{pixel}\Big{)} \tag{1}\]  
where \((x_{actual},y_{actual})\) represents the real coordinates, \(\Big{(}x_{pixel},y_{pixel}\Big{)}\) represents the pixel coordinates, \(L_{a}\) is the real length of the object, and \(L_{p}\) is the measured length of the object in the image. In this study, the objects are projected onto a horizontal plane, and thus the Z-axis coordinate is not considered. Previous experiments [14] have shown that this method yields a positioning error of approximately 3%. As illustrated in Figure 4, based on the coordinate conversion, the distance between the two closest green grid points that surround the tower crane hook's center blue point is 0.5 m. By real-time monitoring of the potential drop zone and the environment of protected objects, the study identifies the actual distance between the drop zone and the workers during tower crane operations, thereby dynamically perceiving the existing safety risks.