## 4 Result and Discussion  
This section presents the performance analysis of the proposed hand detection and tracking framework. The evaluation primarily focuses on the performance of the SSD hand detection model on the EgoHands dataset, specifically the testing dataset portion. The evaluation utilizes COCO's detection evaluation metrics, including mean Average Precision (mAP) at different Intersection over Union (IoU) thresholds, average recall (AR), and detection speed, to assess the model's ability to detect hand objects from input images. The evaluation results are then compared with a benchmark model, the Faster R-CNN algorithm, which is widely recognized as one of the most popular and accurate object-detection models. In the latter part of the experiments, the evaluations focused on the performance analysis of the proposed hand tracking algorithm, as well as the integration of the SSD model with the KCF tracker. The evaluation was performed by running the model inference on sequences of video containing hand movements forming trajectory-based hand gestures and some free hand motions without describing any specific gesture meaning. All videos were recorded using Microsoft LifeCam NX-3000 (Microsoft, China), and the relative distance from the camera to the subject (the hand object) was about 0.5 m. For the trajectory-based hand gestures, there were ten trajectories used to simulate the tracking of hand motion, which described gesture numbers zero to nine. For the free hand motion, there were seven video sequences used to simulate different scenes such as slow movement, fast movement, occlusion behind objects, outdoor lighting conditions, less background contrast, and deformable hand shapes. The tracking rate and accuracy of estimating hand position were evaluated using the TRDR (tracking detection rate) and OTE (object detection error) measures [33]. To observe any improvements in tracking performance, the proposed algorithm was compared to the original KCF tracker. All experiments were conducted on a local computer equipped with an Intel Core i5 CPU 2.50 GHz processor, 8.00 GB RAM, and running the Windows 10 operating system. Table 1 presents the performance of the SSD and Faster R-CNN hand detection models on the testing data of the EgoHands dataset. The computed metrics reveal that the overall detection accuracy of the SSD model is slightly lower than that of the Faster R-CNN model. However, in terms of detection speed, the Faster R-CNN model performs significantly slower, taking approximately 15 times longer for inference compared to the SSD model. The slower computation speed of the Faster R-CNN model can be attributed to the heavy workload of the selective search method utilized in the model. This method requires computing four similarity measures, including color similarity, texture similarity, size similarity, and shape similarity, for every detecting frame. Additionally, the Faster R-CNN model necessitates two shots of the image--one for region proposal generation and another for object detection--further contributing to slower real-time computation speed. Considering the trade-off between speed and accuracy, this evaluation justifies the selection of the SSD model for implementation in a real-time hand tracking system. In the following experiments, the performance of the hand tracking framework is evaluated using image frames from the webcam feed. The SSD detection model is configured with an IoU threshold of 0.5 to suppress false positives during the inference process. Table 2 presents the results of the proposed tracking-by-detection algorithm on video sequences captured from the webcam feed, specifically for ten trajectory-based gestures ranging from '0' to '9'. The comparison with the original KCF tracker and the improvement achieved by the proposed algorithm are also provided. It can be observed that the integration of the SSD algorithm (i.e., the proposed algorithm) has significantly enhanced the overall accuracy and tracking rate of the KCF tracker.