## 3 Methodology
### HRNet-Based Joint Extraction  
The specific bounding boxes obtained from object detection are used for human pose estimation. Given the importance of real-time computation and its impact on subsequent action recognition, both the accuracy of human pose estimation and the need for minimal computational time are crucial factors. The extraction of human joints involves a maximum likelihood estimation process, which identifies the pixels in an image most likely to correspond to joints. The joint detection process employs an architecture similar to U-Net, generating a series of heat maps for human joints. The coordinates of all joints and their corresponding confidence levels are determined by identifying the points with the strongest response in each heat map. Accurate key point estimation is crucial for precise human pose estimation. In this paper, we use the HRNet algorithm [28] as the backbone for human body key point extraction. The detailed structure of HRNet is shown in Figure 3. The input image is first downsampled through two convolutional layers, reducing its dimensions to 64, followed by bottleneck layers that adjust the number of channels without altering the width and height. The top-level high-resolution branch is maintained throughout, while new low-resolution, high-channel branches are generated using the transition module. In the stage module, these branches are unified in terms of width, height, and the number of channels through upsampling and downsampling, enabling data exchange and feature fusion. The deeply fused multi-scale features are iteratively passed forward, and finally, merged into the high-resolution branch, with the output heat map generated by a convolutional layer. This output has a shape of \((64,48,17)\), representing 17 heat maps of \(64\times 48\), corresponding to the 17 joint points defined by the COCO standard. The pixel with the highest score in each heat map indicates the position of the corresponding joint point. Considering that the proposed methods may be applied on edge devices in the future, which demand real-time analysis, we introduce a regression-based approach and loss function optimization to replace the heat map method. Instead of outputting single joint point coordinates, the regression method outputs two one-dimensional vectors for the horizontal and vertical axes, denoted as \((W,1)\) and \((H,1)\). This results in a final output shape of \((W+H,17)\) for the 17 joint points, significantly reducing computational overhead. The modified overall architecture is shown in Figure 4. The encoder is responsible for encoding the image, with HRNet still serving as the backbone to extract features and produce encoding vectors for the 17 joint points (K1 to K17), with a shape of \((17,H,W)\). The horizontal and vertical coordinates are then calculated through 34 one-dimensional vectors (ux1 to ux17 and uy1 to uy17) generated by the coordinate mapper, and finally, decoded to determine the positions of the 17 joint points. The residual log-likelihood estimation (RLE) regression method optimizes the loss function in regression-based approaches, addressing the issue of low accuracy by refining the loss function. By applying standardized flow and maximum likelihood estimation techniques, RLE allows simple regression models to learn Gaussian or other true data distributions, similar to the heat map method. This significantly enhances accuracy while retaining the low computational and memory overhead benefits of regression methods. To ensure that the regression method and the flow model are trained jointly, the logarithm of the target distribution is decomposed into three components, as shown in Equation (7). Here, \(\mathcal{Q}(x)\) represents a simple Gaussian distribution, the second term, denoted as \(\mathcal{G}_{\phi}(x)\), is the distribution that the standardized flow aims to learn, referred to as the log-likelihood estimation term, and \(s\) is a constant.