## 3 Results
The means (SDs) of the tiboferomal FE speeds for trials with different rotation speeds were quantified as 42.6 (16.4)\({}^{\circ}\)/s, 65.7 (32.0)\({}^{\circ}\)/s, 86.7 (40.7)\({}^{\circ}\)/s, 121.0 (54.7)\({}^{\circ}\)/s, and 154.5 (68.6)\({}^{\circ}\)/s for the isolated femoral FE tasks; 51.6 (24.3)\({}^{\circ}\)/s, 74.2 (34.7)\({}^{\circ}\)/s, 96.9 (44.3)\({}^{\circ}\)/s, 122.5 (50.1)\({}^{\circ}\)/s, and 158.5 (68.6)\({}^{\circ}\)/s for the isolated tibial FE tasks, and 84.6 (41.2)\({}^{\circ}\)/s, 101.4 (34.3)\({}^{\circ}\)/s, 121.5 (62.8)\({}^{\circ}\)/s, and 145.0 (80.7)\({}^{\circ}\)/s for the tiboferomal FE tasks. The influence of rotation speeds on the pose errors is shown in Figure 6, in which the maximum differences of the moving averaged absolute errors across all tested speeds were 0.16, 0.23, and 0.22 mm for the three translational components and 0.26, 0.22, and 0.26\({}^{\circ}\) for the rotational components. The moving averaged absolute errors were below 0.36 mm in translation and 0.44\({}^{\circ}\) in rotation (Figure 6). When comparing the mTRE obtained from the proposed method with and without incorporating template registration, a substantial difference was found (Figure 7). With template registration, the MIBFT-determined pose parameters yielded final mTRE values of generally less than 2 mm (Figure 7A). When template registration was not utilized, a proportion of registrations unsuccessfully localized the bone in 3D space, as indicated by instances with final mTRE values larger than 6 mm (Figure 7A). It also led to gradually increased averaged final mTRE values with respect to initial mTRE values, as shown in Figure 7B. Figure 6: The scatter plot of the absolute errors for the six degrees-of-freedom of both the femur and tibia against the rotation speeds of the tiboferomal flexion and extension. The different colors represent data obtained from different trials with different prescribed motion speeds. The black solid lines indicate the moving average of the absolute errors across various speed intervals. The agreement of the MIBFT-determined tibiofemoral 6-dof kinematics with those of the standard reference values is shown in Figure 8. The MIBFT reproduced tibiofemoral kinematics that were in good agreement with the standard reference kinematics. The Bland-Altman plot gave mean differences for all translation components ranging from \(-0.17\) to \(0.22\) mm and an LoA in the range of \(-0.67\) to \(0.88\) mm. For flexion/extension, abduction/adduction, and internal/external rotation, the mean differences ranged from \(-0.04\) to \(0.38^{\circ}\), and the LoAs were in the range of \(-0.85\) to \(1.6^{\circ}\). Based on the same experimental dataset, the MIBFT appeared to outperform typical model-based tracking using a single-plane image [24] and the previously reported MCPI method [40] in terms of the Rms errors of skeletal poses (Figure 9). As indicated by the boxplot, the median, 25 and 75%  
Figure 8: Bland–Altman (BA) plots show the agreement of the six degrees-of-freedom tibiofemoral kinematics obtained from MIBFT and the marker-based MoCap (standard reference). The blue solid lines indicate the mean differences and the dashed yellow lines show the limits of agreement (LoA) of the differences. Figure 7: (**A**) Scatter plot of the final mean target registration errors (mTREs) against the initial mTREs obtained from MIBFT with (blue dots) and without template registration (red dots). (**B**) The mTREs were also averaged over fixed intervals of initial mTRE to observe the general trends in the errors.