# C3 VFC: A Method for Tracing and Quantification of Microglia in 3D Temporal Images
## 4 Results
### Performance Evaluation
Manually tracing an object is indeed subject to intra-user and inter-user variability, especially in 3D, but such manual measurements represent the best existing choice for a baseline of quality. We use five different distance measures to measure the error between the baseline and reconstruction results. We evaluate the performance of the reconstructions by measuring the average Euclidean distance between the reconstruction result and ground truth. We input the SWC format reconstructions into Vaa3d to measure the entire structure average from 1 to 2 (\(ESA_{12}\)), ESA from 2 to 1 (\(ESA_{21}\)), average bidirectional-ESA (ABESA), difference structure average (DSA), and percentage of  
Figure 6: Visual comparison of the multi-cellular reconstruction results using C3 VFC (our method), APP2, FMST, and MST. Separated cells are distinguished by color for the result of every method. different structure (PDS), which were introduced and defined in [47]. \(ESA_{12}\) is a measure of the distance of a voxel from the ground truth to the closest voxel on the reconstruction result. \(ESA_{21}\) is a measure of the distance of a voxel from the reconstruction result to the closest voxel on the ground truth. \(ABESA\) refers to the smallest spatial distance of a voxel between the reconstruction result to the closest voxel on the ground truth. \(DSA\) refers to the average spatial distance for the voxels that are different between the reconstruction result and the ground truth result. \(PDS\) is the percentage of the voxels that are different between the reconstruction result and the ground truth result. We use the default value of \"2 voxels\" in spatial distance to account for human error, because the authors in [47] experimentally proved that this default value gives sufficient visual difference to distinguish different results. Table 1 shows the average and standard deviation of these distances compared with the manual baseline result. A lower value for each of these distances signify a higher accuracy measure to the ground truth. From Table 1, C3 VFC has a lower error in all of the measures compared to APP2, FMST, and MST. APP2 achieved the second-closest distance for four of the five measures: \(ESA_{21}\), \(ABESA\), \(DSA\), and \(PSA\). FMST and MST have a low \(ESA_{12}\) but higher \(ESA_{21}\) values signifying that their reconstruction contained a larger amount of false positive branches. FMST and MST also had the largest PDS values which tells that these reconstructions were the most different to the baseline reconstruction. The visual testimonial can be seen in Figure 7 where FMST and MST capture erroneous branches and noise that do not belong to the cell of interest. APP2 showed the most competitive results for all scores but it seemed to have missed the shorter processes and may over-prune its segmentation results. It must be noted that APP2 did not perform well when the entire multicellu  
Figure 7: Reconstruction results of 3D microglia images. The first column on the left is the original image with the region of interest boxed out on the left. The following columns show the 3D reconstruction in the SWC format. the algorithm, as shown in Figure 6. FMST and MST seemed to be an over-segmentation, which was posed as an advantage of their algorithms, but the pruning was insufficient for glial images. From Table 1, if we consider the mean distance measure with the standard deviation, C3 VFC achieves the best performance in four of the five accuracy measures: \(ESA_{21}\), \(ABESA\), \(DSA\), and \(PSA\). The mean distance measure with the standard deviation requires adding and subtracting the standard deviation from the mean to find the range of distance measures. C3 VFC found up to a 53% improvement compared to APP2, FMST, and MST using the five accuracy measures (\(ESA_{12},ESA_{21}\), \(ABESA\), \(DSA\), and \(PSA\)).