# A Linkage Representation of the Human Hand Skeletal System Using CT Hand Scan Images
## 4 Discussion  
The present study proposed a novel method for estimating hand joint centers from 3D hand skeleton motions reconstructed from CT scans and building participant-specific linkages from the derived hand joint centers. The novelty of our method lies in (1) the use of 3D hand skeleton motions reconstructed from CT scans, (2) the use of the same bone \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Finger**} & \multicolumn{3}{c}{**Segment 1**} & \multicolumn{3}{c}{**Segment 2**} & \multicolumn{3}{c}{**Segment 3**} & \multicolumn{3}{c}{**Segment 4**} \\ \cline{2-11}  & **Actual** & **Estimated** & **Difference** & **Actual** & **Estimated** & **Difference** & **Actual** & **Estimated** & **Difference** \\ \hline Thumb & 35.8 & 35.9 & 0.1 & 47.9 & 44.0 & \(-\)3.9 & 35.0 & 33.8 & \(-\)1.2 & 26.0 & 25.9 & \(-\)0.1 \\ Index & 91.9 & 90.0 & \(-\)1.9 & 41.3 & 43.7 & 2.4 & 23.8 & 24.2 & 0.4 & 21.1 & 20.6 & \(-\)0.5 \\ Middle & 86.1 & 86.6 & 0.5 & 47.6 & 48.8 & 1.2 & 27.2 & 28.5 & 1.3 & 22.5 & 21.9 & \(-\)0.6 \\ Ring & 81.4 & 81.8 & 0.4 & 44.0 & 45.5 & 1.5 & 24.9 & 27.4 & 2.5 & 23.3 & 22.3 & \(-\)1.0 \\ Little & 77.8 & 80.3 & 2.5 & 33.8 & 36.3 & 2.5 & 18.7 & 18.9 & 0.2 & 20.5 & 19.8 & \(-\)0.7 \\ \hline \hline \end{tabular} Note: For the thumb, Segment 1 is the carpal segment, 2 the metacarpal, 3 the proximal phalangeal, and 4 the distal phalangeal. For the four fingers, Segment 1 is the carpometacarpal segment, 2 the proximal phalangeal, 3 the middle phalangeal, and 4 the distal phalangeal.  
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Table 4: Differences between the internal hand link lengths estimated from the proposed regression models and the actual internal hand link lengths (unit: mm). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Coordinate** & **Thumb** & **Index** & **Middle** & **Ring** & **Little** \\ \hline \multirow{2}{*}{\(x\)} & \(-\)0.261 \(\pm\) 0.008 (0.966, & \(-\)0.264 \(\pm\) 0.003 (0.998, & 0.000 \({}^{1}\) & 0.208 \(\pm\) 0.003 (0.997, & 0.403 \(\pm\) 0.005 (0.998, \\  & \(-\)6.9–6.0, [-0.28, -0.244]) & \(-\)2.1-1.4, [-0.270, -0.258]) & (\(\cdot\)) & \(-\)2.1-1.7, [0.202, 0.214]) & \(-\)3.8-3.4, [0.392, 0.414]) \\ \multirow{2}{*}{\(y\)} & 0.110 \(\pm\) 0.003 (0.990, & 0.461 \(\pm\) 0.005 (0.998, & 0.458 \(\pm\) 0.004 (0.999, & 0.421 \(\pm\) 0.004 (0.999, & 0.380 \(\pm\) 0.004 (0.999, \\  & \(-\)3.5–4.5 (0.104, 0.116]) & \(-\)6.9–5.4, [0.450, 0.472]) & \(-\)4.8-5.8, [0.449, 0.467]) & \(-\)5.4–4.0, [0.412, 0.430]) & \(-\)5.9-4.0, [0.371, 0.389]) \\ \multirow{2}{*}{\(z\)} & \(-\)0.225 \(\pm\) 0.005 (0.993, & 0.000 \({}^{1}\) & 0.000 \({}^{-}\) & \(-\)0.028 \(\pm\) 0.003 (0.883, & \(-\)0.054 \(\pm\) 0.005 (0.889, \\  & \(-\)2.8–3.1, [-0.236, -0.214]) & (\(\cdot\)) & (\(\cdot\)) & \(-\)5.0–2.8, [\(-\)0.034, -0.022]) & \(-\)8.7-3.4, [\(-\)0.065, -0.043]) \\ \hline \hline \end{tabular}
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Table 3: Coefficients for estimating the carpometacarpal (CMC) joint center of the thumb and the metacarpophalangeal (MCP) joint centers of the four fingers (B, where \(x\) = B \(\times\) hand breadth; C, where \(y\) = C \(\times\) hand length; D, where \(z\) = D \(\times\) hand breadth for the thumb and \(z\) = D \(\times\) hand length for the ring and little fingers) based on 15 male hands (mean \(\pm\) standard error, \(R^{2}\), maximum residual range, and 95% confidence interval).