## 6 Evaluations
The column at the center (Figure 14b,e,h,k) shows the geometrical components found on the corresponding scene. Finally, the last column (Figure 14c,f,i,l) shows the generated graphs classified correctly. As our approach is probabilistic, it can deal with the noise from the sensor; as well as partially occluded views, at this time, with occlusions no greater than 50% of the main horizontal plane, as this plane is the key factor in the graph. While types of furniture can have the same graph structure, values in their components are particular for a given instance. Therefore, it is not possible to recognize with the same graph different instances of a type of furniture. In other words, a particular graph for a bed cannot be used for beds with different sizes; however, the graph structure could be the same. Additionally, to test the approach on more examples, we have tested on selected images from the dataset SUNRGB-D [23]. Figure 17 shows the results of the geometrical components' extraction and the graph generation for the selected images. The color images corresponding to house environments similar to the test environments scenes are presented at the top of the figure; the corresponding geometrical component extraction is shown at the center of the figure; and the corresponding graphs are presented at the bottom of the figure. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Main Node** & **Main Node Sim.** & **Adjacent Nodes** & **Adjacent Node Sim.** & **Graph Similarity** \\ \hline \multirow{3}{*}{H00} & Table & V02 & Table leg & 0.0.6670 \\  & 0.8743 & & 0.7015 & \\ \cline{1-1}  & Chest of Drawers & V02 & No Match & X \\ \cline{1-1}  & 0.8014 & & & \\ \hline \multirow{3}{*}{H01} & Chair & V01 & Backrest & 0.5740 \\  & 0.9891 & & 0.8878 & \\ \cline{1-1}  & Center Table & V01 & No match & X \\ \cline{1-1}  & 0.8895 & & & \\ \cline{1-1}  & Couch & V01 & Backrest & 0.3204 \\ \cline{1-1}  & 0.7277 & & 0.7150 & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Example for graph classification. Figure 14: Results obtained for the furniture detection; each row shows the results for one scene. In (**a**,**d**,**g**,**j**), the original point clouds from the scenes. In (**b**,**e**,**h**,**k**) are shown the geometrical components found in the scene; the vertical planes are in green color, the horizontals in yellow and the legs in red. The bounding boxes in (**c**,**f**,**i**,**l**) show the graphs generated that were correctly identified as a piece of furniture. It is important to note that to detect the geometrical components over these scenes, the point cloud from each selected scene was treated using the intrinsic and extrinsic parameters provided in the dataset. Consequently, a similar footprint reference frame is obtained such as the frame provided by the robots in this work. This manual adjustment was necessary to simulate the translation needed to align the coordinate frame of the image with the environment, as described in Section 4.1. Since the proposed approach requires a complete model for each piece of furniture, which were not provided by the dataset, it was not possible to match the graphs generated to a given piece of furniture. However, the approach has worked as expected (Figure 17). Figure 16: Graph comparison: in (**a**), one of the graphs generated from the scene in Figure 14b, and in (**b–d**), partial graphs selected for matching corresponding to the chair, the center table and the couch. Figure 17: Tests over images from the dataset SUNRGB-D [23]: at the top, the RGB images, in the middle, the corresponding extracted geometrical components, and at the bottom, the corresponding graphs. Figure 15: Graph comparison: in (**a**), one of the graphs generated from the scene in Figure 14b; in (**b**,**c**), partial graphs selected for matching with the graph in (**a**), corresponding to the table and the chest of drawers.