**4. Discussion**

When using mathematical methods, the macro differences between the motion data of novice students and the teacher were higher than the distances between the motion data of senior students and the teacher on eight motions of Baduanjin. Because the motion data of the experimental analysis are the rotation data of specific skeleton points measured by the IMU, if the teacher's motions were taken as the standard, the results show that the motions of senior students were closer to the standard motions. Therefore, IMU can effectively distinguish the differences in motion accuracy in Baduanjin between novice and senior students.

When using the original frames to evaluate the differences at 17 skeleton points in eight motions between novice and senior students, the results show the differences in motion accuracy between the two groups on skeleton points varied for the different motions. For Motion 1, the differences between the two groups were mainly concentrated on the head-spine segmen<sup>t</sup> and upper limbs, especially the right upper limb. The differences mean that the motion errors of novice students relative to senior students were mainly concentrated on these joints. The results are consistent with the common motion errors described in the official book: "When holding the palms up, the head is not raised enough, or the arms are not raised enough" [30]. However, for Motion 4, the common motion errors are described in the official book as: "Rotating head and arm are insufficient" [30]. The description shows that the main errors occur in the head-spine and bilateral upper limbs. However, significant differences of skeleton points were at bilateral upper limbs but not head-spine. This difference may be related to the small number of participates in this study.

In this study, we also used two methods to extract key-frames. The raw data can be effectively compressed to decrease the data storage space using extracting key-frames [40,41]. The repetitiveness of action exercises in the teaching process will generate an extremely large amount of raw data. From the results, both key-frames extraction methods can effectively compress the raw data. We also found that the data processing speed could be accelerated on key-frames. However, the compression rates of key-frames on different motions when using key-frames on inter-frame pitch were different. We found that the differences in skeleton points on the key-frames on inter-frame pitch were not consistent with the results on the original frames. However, there was high consistency between the results on the key-frames on clustering and the results on the original frames, especially when the compression rate was 15%. Therefore, we can use key-frames to replace the original frames to evaluate motion accuracy of Baduanjin in order to decrease data storage space and processing time.

However, the small number of participants in our study limits the application of the results. As the participants were from a university in China, the results might only be suitable for university students in China because different populations have variations in anatomical characteristics, physiological characteristics, and athletic ability.

Based on our results, IMU can e ffectively distinguish the di fference in the motion accuracy of Baduanjin between novice and senior students. Therefore, in the following work, we can develop a system using IMU to evaluate the motion quality of students and provide feedback to teachers and students. Thus, it would be able to assist teachers in correcting errors in the motions of students immediately.
