# Filtering Organized 3D Point Clouds for Bin Picking Applications
## 7 Discussion  
The performance of the proposed filtering method, gauged by the ratios \(\alpha\) and \(\beta_{2}\), clearly outperforms the general use SOR procedure when applied to the shiny parts shown in Figure 8a-c.f. As explained in Section 5.3, both ratios play complementary roles, and their small values mean that the majority of outliers is identified exclusively by the new method. Results shown in Figure 15 confirm this conclusion for datasets (a, b, c, f). The binary 2D maps shown in Figure 14 provide graphic evidence aligned with the conclusion based on the ratios \(\alpha\) and \(\beta_{2}\). In addition, closer inspection of the 2D maps reveals a difference in the characteristics of the outliers filtered by both methods. A majority of the outliers identified by the new method are grouped in large clusters of connected pixels, as shown in Figure 14a. Contrary to this, the outliers filtered by SOR are mostly single, isolated pixels dispersed across the 2D map, as displayed in Figure 14b. That difference between both maps originates from fundamentally different filtering mechanisms: in SOR, filtering is based on the thresholding of mean local distances. Such an approach cannot identify large blobs of 3D points, as their local distances to the nearest neighbors fall below the threshold. The new method can find even large clusters on 2D maps that correspond to large groups of 3D points if their z components are separated by a distance \(\Delta d\) from the surrounding points in the organized point cloud.  
However, the ratios \(\alpha\) and \(\beta_{2}\) for nonglossy parts, such as those displayed in Figure 8d,e, clearly contradict the conclusions based on the analysis of results for shiny parts: both ratios are large for datasets (d, e), as shown in Figure 15. Relatively large values of \(\beta_{2}\) cause the ratios \(\beta_{1}\) to be small, which means that a substantial fraction of outliers is found only by SOR (i.e., they are missed by the new procedure). As the ground truth for outliers is not available, the observed underperformance of the new method for datasets (d, e) should be  
Figure 20: 2D binary map illustrating the impact of the reduced parameter \(\Delta d\) on the performance of the new method. White pixels are locations of outliers when the procedure is run with the default value of \(\Delta d\), yellow pixels are extra outliers identified when the reduced parameter was applied.  
attributed to the characteristics of both datasets and properties of the ratios \(\alpha\) and \(\beta_{2}\). If the outliers identified only by SOR contain many false positives, this will incorrectly boost the total number \(N_{1}\) of outliers found by SOR only and will cause a disproportional increase in the ratios \(\alpha\) and \(\beta_{2}\), as follows from (3). Compared to shiny parts, the datasets (d, e) for nonglossy parts are very clean and they contain a small number of visually detectable outliers, as demonstrated in Figure 12. This causes the standard deviation \(\gamma\) of mean distances to the nearest points to be small. This, in turn, affects the thresholding utilized by SOR. As a consequence, the small threshold causes the misclassification of many 3D points as outliers, in contradiction to the visual inspection. An example of such a case is shown in Figure 21. Outliers found by SOR are plotted in yellow but many of these points are located close to 3D points, correctly representing the scanned surfaces of screws. Thus, many of the yellow points are false positives, i.e., inliers misclassified as outliers.  
For the same dataset (d), the new method identifies a smaller number of outliers, which agrees with the visual inspection. Thus, the overestimated number of outliers identified by SOR, paired with a smaller number of the outliers found by the new method, leads to misleading, large values of the ratios \(\alpha\) and \(\beta_{2}\), as shown in Figure 15 for datasets (d, e).