# Semantic Component Association within Object Classes Based on Convex Polyhedrons
## 7 Experimental Evaluation
### Results  
A few sample results are shown in Figure 5. True positives, i.e., points that were correctly associated with the target component, are depicted by the green color, while false positives, i.e., points that were falsely associated with the target component, are depicted in red color. The false negatives, representing the target component points, which were not associated with the target component by the proposed algorithm, are depicted in blue color. The quantitative results obtained by the described experimental procedure are presented in Table 2. Each of the three component association methods were tested with and without using the neighborhood similarity, i.e., with weight \(w_{N}\) equal to one and zero, respectively. The number of representative objects was the greatest integer \(\leq\) 10% of all models in the model database of each object class. The presented IoU values represented the average over all objects of a particular class excluding the representative objects. Figure 5: Sample results. In order to compare the proposed method with the state-of-the-art approaches, the following experiment was executed. For each of the five classes: mugs, knives, bags, caps, and laptops, Steps 1-10 were performed on the training subset, which included the selection and annotation of representatives. Note that only a small representative subset of the training dataset was annotated. The number of annotated representatives was the greatest integer \(\leq\)10% of all models in the training subset of each object class. Then, the database was extended (Steps 1-8) by the test dataset; the labels were assigned to the models from this subset; and the accuracy analysis was performed (Steps 11-12). The results of the accuracy analysis performed on the test subset measured by per-class IoU are given in Table 3. At the bottom of the table, the accuracies achieved by the three methods (DSA, OCA, and MST) proposed in this paper are given. Since this paper investigated component association with a small set of representatives, it was not expected to outperform the existing methods extensively trained using large annotated datasets. Let us assume a database with the total number of objects as stated in Table 4. The running times of the automatic component annotation with the included neighborhood similarity (\(w_{N}=1\)) in \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{1}{c}{**Class**} & **Mug** & **Knife** & **Bag** & **Lamp** & **Cap** & **Laptop** \\ \hline \multicolumn{1}{c}{total No. of objects} & 184 & 391 & 68 & 210 & 53 & 451 \\ \hline \multicolumn{1}{c}{No. of representatives} & 18 & 39 & 6 & 21 & 5 & 45 \\ \hline \multirow{4}{*}{IoU} & \(w_{N}=0\) & 78.50 & 75.40 & 44.10 & 43.10 & 82.50 & 75.30 \\  & \(w_{N}=1\) & 77.40 & 73.30 & 50.30 & 57.20 & 84.80 & 77.20 \\ \cline{2-7}  & OCA & \(w_{N}=0\) & 73.90 & 58.00 & 48.00 & 53.60 & 82.40 & 58.90 \\  & \(w_{N}=1\) & 75.10 & 62.40 & 43.60 & 65.40 & 82.40 & 59.30 \\ \cline{2-7}  & MST & \(w_{N}=0\) & 77.90 & 75.90 & 42.60 & 36.80 & 82.70 & 76.70 \\  & \(w_{N}=1\) & 76.30 & 73.20 & 60.90 & 53.00 & 75.90 & 76.10 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Accuracy of the automatic component annotation. DSA, direct segment association; OCA, object-constrained association; MST, minimum spanning tree.