# Filtering Organized 3D Point Clouds for Bin Picking Applications
## 6 Results
To show the consequences of running the new method with different values than the nominal values of the parameter \(\rho_{thr}\), the ratios \(\theta_{n,Lo}\) and \(\theta_{n,Hi}\) defined in (5) are plotted in Figure 13.0 The two other parameters were set to their nominal values (\(d^{*}_{max}\), \(\Delta d^{*}\)) and the ratio \(\theta_{n,Lo}\) in Figure 18a corresponds to the reduced \(\rho_{thr}=0.5\,\rho^{*}_{thr}\), while \(\theta_{n,Hi}\) in Figure 18b corresponds to the larger \(\rho_{thr}=1.5\,\rho^{*}_{thr}\). To visualize the impact of using non-default values of \(\rho_{thr}\) in the new method, a binary 2D map with the locations of outliers is shown in Figure 19a. White pixels are outliers identified by running the new method with the nominal parameter \(\rho^{*}_{thr}\), while pixels displayed in yellow mark outliers missed when the smaller, more restrictive threshold \(\rho_{thr}=0.5\,\rho^{*}_{thr}\) is used. In Figure 19b, the unfiltered 3D point cloud \(\widetilde{\mathbf{P}}_{n}\) is plotted in black and the missed outliers shown in Figure 19a are plotted in yellow. The plotted results obtained from the dataset with parts are shown in Figure 8b. Figure 13.1 Comparison of the SOR (n = 1) with the new method (n = 2) run with the nominal values of the parameters \(\left(\rho^{*}_{thr}\), \(\Delta d^{*}\right)\) and two different thresholds \(d_{max}\): (**a**) \(\omega_{n,Lo}\) ratio for the reduced \(d_{max}=0.5\,d^{*}_{max}\); (**b**) \(\omega_{n,Hi}\) ratio for the increased \(d_{max}=1.5\,d^{*}_{max}\). Figure 13.2 Comparison of filtering efficiency provided by SOR and the new method run with the nominal values of the parameters \(\left(\rho^{*}_{thr},\,d^{*}_{max},\,\Delta d^{*}\right)\): (**a**) \(\alpha\) ratio; (**b**) \(\beta_{n}\) ratio where n = 1 is for SOR and n = 2 is for the new method. Figure 13.3 Outcomes of the new method run with the nominal values \(\left(\rho_{thr}^{*},\ \Delta d^{*}\right)\) and two different values of \(d_{max}\): (**a**) \(d_{max}=0.5\ d_{max}^{*}\); (**b**) \(d_{max}=1.5\ d_{max}^{*}\). Yellow points indicate identified outliers, black points are the remaining points from the dataset, and a grey colored plane is added at \(z=z_{thr}\). For better visualization, a scale on the z-axis is stretched by 1.5. Finally, to visualize the impact of a reduced value of the step \(\Delta d\) on a performance of the new method, the 2D binary map is shown in Figure 13.4 The proposed method was run twice, with the default values of the parameters \(\left(\rho_{thr}^{*},\;a_{max}^{*}\right)\) and two values of \(\Delta d\): the nominal \(\Delta d^{*}\) and the reduced \(0.1\;\Delta d^{*}\). The white pixels are the locations of outliers found with the nominal step value, while the yellow pixels show extra identified outliers when the reduced value of the step was used. Presented in Figure 20, a map obtained for the dataset with parts is shown in Figure 8b; the maps obtained for other datasets reveal a similar pattern, i.e., an increased number of outliers for reduced step \(\Delta d\). A majority of  
Figure 13.5 Effect of running the new algorithm with two different values of the parameter \(\rho_{thr}\): nominal and reduced. In the binary map shown in (**a**), the white pixels are locations of outliers when the nominal value was used, while yellow pixels mark outliers missed when reduced, more restrictive threshold was applied. In (**b**), the whole unfiltered 3D point cloud is plotted with black points, yellow points are missed outliers displayed in (**a**). the yellow pixels are false negatives, i.e., they are 3D points which, after visual inspection, should be in the inliers category.