# Automatic 3D MRI-Ultrasound Registration for Image Guided Arthroscopy
## 4 Results and Discussion
Figure 8: Random study registration results with 100 randomly initialized transformations for 11 subject cases along with the percentage of converged optimizations. Figure 6: A sagittal slice is extracted from a 3D US volume and output at four different stages of the method is shown along with the ground truth. Algorithm’s output is shown in red, and the ground truth slice is shown in blue. From top-left: (**a**) initial orientation; (**b**) output after pre-initialization; (**c**) output after applying distance transforms; (**d**) final output after implementing LC\({}^{2}\) registration. Figure 7: Final registration output of Subject 5: US aligned on respective MRI. To assess the reproducibility of the manual registrations here used as ground truths, a second experienced orthopaedic surgeon (Y.T.5) performed the manual registrations for a subset of the MRI-US pairs (8 out of 11). The second surgeon utilized the MRI alignment provided by the first expert and then performed the registration between the MRI-US pairs independently from the first surgeon, following the same procedure. Since for each MRI-US pair registered by both surgeons, the MRI volume is fixed in a common position, the difference between the US volume translation/rotation values selected by the two surgeons is utilized to quantify the inter-observer variability as shown in [27]. The inter-observer reproducibility study results reported in Table 3 show that the mean difference between the manual registrations performed by the two surgeons is 4.41 mm \(\pm\) 1.88 mm for translation and 7.77\({}^{\circ}\)\(\pm\) 2.80\({}^{\circ}\) for rotation. The difference in these registrations could be because the rigid match itself might be insufficient for alignment between the knee US and MRI volumes. This is possibly a result of minor leg movements from the reference position during the MRI acquisition. Moreover, during the US acquisition, it is also possible to have small shifts of the patella due to the pressure exerted by the probe that could have possibly affected the overlap of this bone in the two modalities. This effect might have introduced a degree of subjectivity in finding the best compromise to align the bone-like surfaces in the two modalities resulting in a possible mismatch among the operators. In both our achieved results (Table 2) and inter-operator study (Table 3), it can be observed that the registration error increases as the angle of flexion increases. It can be highlighted from comparing these tables that the registration error of the proposed automated algorithm for almost all tested cases is either smaller or comparable to the inter-observer registration difference (\(p\)-value \(<\) 0.002) and thus our registration method can be considered comparable to clinical standards. Figure 9 shows the registration output of subject 6 in frontal, axial and lateral planes for all the four flexion angles. It can clearly be seen from the overlapping images that the registration error (in particular the rotation) keeps increasing as the flexion angle is increased. A possible explanation for this could be, as the flexion angle increases, the lateral and medial femoral cartilage, which are the basis of our algorithm, shift posteriorly and go behind the patella and hence cannot clearly be distinguished in the US volume. In addition, as the knee flexion increases, the area of femoral cartilage in the knee gap decreases, thereby hindering the accuracy of initialization.