# Validation of an RF Image System for Real-Time Tracking Neurosurgical Tools
## 3 Experimental Validation and Results
### Data Extraction and Results  
The images in Figure 14 show a clear evolution of the tool's final-end position throughout the trajectory. These images are, therefore, suitable for providing a targeted navigation track. To provide navigation assistance and accurate guidance capabilities, the exact coordinates of the tool's position must be detected. To that end, each image in Figure 14 was binarized with a 0.8 threshold, which means that a new binary black-and-white associated image was created in which the pixels with luminance lower than 0.8 in the original image were set to black, otherwise to white. An example of this process for \"p5-p4\" images for both algorithms is shown in Figure 15. As it can be seen, the resulting images are  
Figure 14: Differential navigation images for a selection of the positions obtained with DAS and DMAS algorithms. The position and shape of the cranium (white) and tumor (pink) are depicted in the last image for reference. Figure 13: Navigation images for a selection of the positions obtained with DAS and DMAS algorithms. The position and shape of the cranium (white) and tumor (pink)are depicted in the last image for reference. more convenient for processing and detection of properties. Each binarized image was then analyzed and the coordinates of the centroid of the remaining white region were computed. As seen in Figure 14, the high-luminance regions correspond to the tool's final-end positions, and therefore these centroids' coordinates were associated to the real tool's final-end coordinates. The binarized images had 1300 \(\times\) 1301 dimensions. The computed centroids were defined within an image-based coordinate system, having the origin in the top-left corner. In order to be able to compare with the reference coordinates of the tool's final end, which were obtained through the robotic arm positions, considering the common coordinate system centered in the antenna system (and in the cranium as well), the equivalence of pixels to physical distance was required. These data were obtained thanks to the real cranium dimensions and its pixel-based dimensions computed from the initial cranium images (see Figure 12 top). The equivalence was thereby found to be 1 column pixel = 0.1922 mm; 1 row pixel = 0.2255 mm. With these data, the microwave image-based detected tool's final-end coordinates were obtained. A scheme of the coordinate detection process is depicted in Figure 16.  
The results for the detection of the tool's final-end coordinates are shown in Table 1, which gathers the detected coordinates both with DAS and DMAS algorithms when the differential images (Figure 14) are considered and compares them to the reference coordinates obtained from the robotic arm at each position. Position p1 is not considered since there was no prior position to perform the image subtraction and the tool was considerably far from the antenna system. The evolution of the detected coordinates with both algorithms, as well as the reference coordinates from the robot, show the approaching trajectory of the tool to the tumor, from p2 to p8. Specifically, the detected coordinates in p8 for DAS and DMAS algorithms show a difference of (12.5886, \(-\)15.1963) mm and (12.3963, \(-\)15.7374)  
Figure 16: Scheme of the coordinate detection process. Figure 15: Example of the binarization process for “p5–p4” images. mm, respectively, with respect to the corresponding detected coordinates of the tumor's center (first row), which are coherent with the visual observation (see Figure 17). This is also confirmed by the small error in p8 for DAS and DMAS with respect to the reference coordinates from the robot: \(\Delta(\text{p8})=(-0.8544,\,-0.5576)\) mm for DAS and \(\Delta(\text{p8})=(-1.3925,\,-0.1743)\) mm for DMAS. Considering the reference coordinates from the robot, Table 2 shows an error analysis for the performance of DAS and DMAS. Position p2 was excluded because the tool was still too far from the antenna system region.