## 4 Discussion  
The present study proposed to use the same bone surfaces among different hand postures for the estimation of finite joint CoRs by registration of each bone segment of the template posture to the corresponding bone segment of the other postures. Reconstructed hand skeletons from different CT scans at different hand postures could have different bone surfaces even with the same segmentation parameters due to the differences in intensity values among different CT scans. Different centerlines of the same distal bone segment at different postures could be identified if different bone surfaces were used, which could cause errors during the estimation of finite joint CoRs. Obvious errors observed in [PERSON] et al. 's study could be caused by the usage of different bone surfaces in their study. In the present study, the identified centerlines of the same distal bone segment at different postures were exactly the same after using the same bone surfaces among those postures. Unlike [PERSON] et al. 's study, no apparent errors were observed in the present study. Figure 12: The average of mean distances of an estimated finite joint CoR to other estimated finite joint CoRs at each rotation angle group for (**a**) the metacarpophalangeal joint, (**b**) the proximal interphalangeal joint, and (**c**) the distal interphalangeal joint. The proposed method was found superior to [PERSON]'s method in terms of variation of estimated finite joint CoRs among different postures at most finger joints. The proposed method improved variation in estimated finite hand joint CoRs by 16.0% to 67.0% at different joints compared to [PERSON]'s method. [PERSON]'s method showed a much higher variation than the proposed method when the rotation angle was smaller than five degrees, as shown in Figure 12. Especially for the MCP joint, the variation in [PERSON]'s method reached 9.4 mm, which is quite large as the sizes of the hand joints are small, whereas the variation in the proposed method achieved 2.7 mm. In [PERSON] study, it was concluded that [PERSON]'s method could not perform well when the rotation angle was less than five degrees (mean error > 11 mm), which could explain why [PERSON]'s method showed a large variation when the rotation angle was smaller than five degrees in the present study. The proposed method showed a slightly higher variation than [PERSON]'s method (difference = 0.05 mm) at the PIP joint of the ring finger, which was caused by a larger variation at the PIP joint of the ring finger for the proposed method (2.6 mm) than [PERSON]'s method (1.2 mm). In the present study, the variation of estimated finite joint CoRs decreased as the rotation angle increased, which is in agreement with previous studies [15; 22; 23]. The accuracy of [PERSON]'s method is dependent on the distribution of landmarks, whereas the proposed method does not need any landmarks. Furthermore, [PERSON]'s method was found more sensitive to rotation angle than the proposed method. The differences in variation of estimated finite joint CoRs between the rotation angle group from 0 to 5 degrees to the remaining groups for [PERSON]'s method and the proposed method for the MCP, PIP, and DIP joints were 6.1 mm, 1.1 mm, and 1.9 mm, respectively. Therefore, the proposed method outperformed [PERSON]'s method, especially in the small rotation angle range (0-5 degrees). Besides, the fluctuations were found in variation among different rotation angle groups in [PERSON]'s method but not in the proposed method, indicating that our method is more stable than [PERSON]'s method. The proposed method is similar to [PERSON] et al. 's method. Both the methods estimate a finite finger joint CoR as the intersection point of the centerlines of the distal bone segments of a joint between two hand postures that are reconstructed from CT scans. The difference between the methods is that the proposed method includes an extra registration procedure to register each bone segment in the template posture to that in each of the nine remaining postures.