## 3 Results  
### Detection Rate and Accuracy Test  
The detection rate and accuracy of the system are tested with real hitting. First, the half-table is divided into six equal areas, with a size of approximately 45 cm \(\times\) 75 cm, and labeled areas 1-6 (Figure 5a) in line with standard table tennis training practices. This six-zone division is not arbitrary but is commonly used in foundational training programs to assess players' ability to place the ball effectively across different areas of the table. Such division reflects conventional coaching strategies aimed at skill categorization and stroke accuracy improvement. Then, the test player starts hitting the ball to the different areas randomly with different ball heights and speeds. The landing point is recorded by the system and a human observer. A total of 10 sets of tests are conducted, with each test consisting of 20 balls being hit. For each ball, the event of ball landing and the landing point are recorded both by the system and the human observer. The detector rate is defined as the number of landings of the ball recognized by the system/the number of landings of the ball confirmed by the human eye. The accuracy of the system is defined as the consistency of the landing point recognized by the system with that recognized by the human eye. If the landing point recorded by the system is the same as that recorded by the human eye, the accuracy is defined as 100%. Also, the evaluation of the ball detection rate and landing point accuracy is conducted using camera-based ground truth. While human observation remains a widely accepted standard in practical table tennis training scenarios--where coaches visually assess ball landing positions and player performance--we recognize the need for an objective quantitative measurement to enhance the scientific rigor of our approach. To achieve this, we implement a precise ground truth calibration process prior to system operation. The four corners of the table are carefully calibrated using a stereo camera setup, ensuring accurate spatial positioning. The coordinate system of the table, with its center defined as the origin, is aligned with the ball's trajectory tracking coordinate system in airspace. This alignment allows for the direct mapping of the ball's detected trajectory onto the physical table surface with high spatial consistency. The system is capable of reliably identifying the ball's landing, even at the table edges and corners, due to this accurate calibration, ensuring robustness in real-world scenarios.  
The test results are shown in the boxplot in Figure 5b. The raw data are shown in Table S1. The y-axis stands presents the rate, and the x-axis presents the detection and accuracy rates. The raw test data are attached in the Supplementary Materials. Interestingly, with the YOLOv5 algorithm and TensorRT, the system is able to achieve an average ball detection rate of 100% while maintaining a high accuracy rate of 98.1 \(\pm\) 2.5%, indicating the effectiveness of the system in detecting fast-moving objects with the YOLOv5 algorithm, which is better than some of the other algorithms, such as ViBe (94.1%) or the dynamic color gamut method (93.2%) [17].