# Validation of an RF Image System for Real-Time Tracking Neurosurgical Tools
## 4 Discussion
It should be noted that, for magnetic-based tracking systems, mean detection errors of ~0.5 \(\pm\) 0.5 mm have been reported [30], which can raise up to 27 mm due to interference of metallic objects [8]. For optical tracking, mean errors of 0.24 \(\pm\) 1.05 mm have been reported, which can raise up to 1.65 \(\pm\) 5.07 mm when some cameras are occluded [7]. The detection errors reported here are also consistent with the errors reported in other microwave imaging approaches. For example, a similar system was used in [31], also with 16 antennas (operating at 1-4 GHz), to detect intraoperative cranial inner hemorrhages, which reported detection errors between 1 and 5 mm. With the positioning error being dependent on the wavelength of the highest frequency in the system (which is linked to the resolution), the reported results here show consistency with those in [31]. Figure 14 also shows that, after the previous image subtraction, the DAS algorithm does not provide a graphical view of the tool's final-end position in a manner as clear and well-defined as the DMAS algorithm does. Notwithstanding that, in this case, given the simple shape of the tool, the results regarding the position detection after the binarization and centroid computation process are quite similar for both algorithms, as shown in Table 1. That being said, the visual inspection of Figure 14 suggests that the DAS algorithm is more sensible for the luminance threshold (kept constant at 0.8 throughout the whole results analysis). Indeed, lower thresholds would have resulted in a sort of half-moon-shaped white area in the binarized images, instead of the ellipsoid-shaped ones for 0.8, as shown in Figure 15. With the centroids being computed as the mass center of the white area, a lower threshold would lead to a displacement of the finally detected position; thus yielding to a greater error in the detection. Figure 14 confirms that this phenomenon is considerably less noticeable for the DMAS algorithm. The analysis of the detection error as a function of the luminance threshold is shown in Figure 18, which confirms this behavior. These results highlight the dependence of DAS on the luminance threshold and allow us to conclude that DMAS is more robust to DAS to variations in this parameter. Consequently, DMAS is expected to show a more reliable performance when tools with more complex shapes are considered, or when rotations of the tool are involved. Apart from this criterion, no further reasons were detected to claim the outperformance of one algorithm with respect to the other one. It should be noted that the setup considered in this study inherently has a certain instrumental error regarding the reference coordinates obtained from the position of the robot, due to the vibrations of the links of the robot during the movement as well as the oscillations of the tool's final end due to its long shape and the tip-based holding. Therefore, seeing the small differences in the performance of both algorithms (see Tables 1 and 2), both algorithms show acceptable performance for intraoperative tool navigation tracking, and we cannot point to any algorithm being the most advantageous regarding the detection accuracy for the experimental setup considered in this study and a properly selected luminance threshold. As a matter of fact, the raw images (before applying the differential method) for both algorithms (Figure 13) show similar information and even similar shapes for the high-luminance areas, and therefore this above-mentioned higher robustness of DMAS to the luminance threshold seems to come from the differential stage. It should be noted that the DMAS formulation inherently implies noise filtering, which often means detail loss. DMAS differential images (Figure 14) can provide a robust tracking of the tool's final end, but the information related to the tumor position is blurred. DAS raw images (Figure 13), however, allow to see the tumor and even the cranium shape in addition to the tool, which would allow for intraoperative tracking of the tumor.