# A Point Cloud Registration Algorithm Based on Weighting Strategy for 3D Indoor Spaces
## 2 Weighting Strategy of Targets in Semantic Segmentation
### Definition of Alternatives and Criteria  
In the classic CRITIC method, objects of different categories are defined as alternatives and performance metrics of different aspects of objects are defined as criteria [31]. This paper proposes a novel definition of alternatives and criteria, considering the practical significance of labels in semantic segmentation. The individual segmentation performance of each label influences the overall segmentation performance, and these influences positively correlate. A better local segmentation performance contributes to the improvement in overall segmentation quality. On the other hand, the labels have relative independence, allowing them to serve as different criteria for the same performance metric. Therefore, in the following sections of this paper, different performance metrics in semantic segmentation will be defined as alternatives, and different labels will be defined as criteria.  
Based on the format of point cloud data in semantic segmentation, we define each point cloud as a vector,  
\[\overrightarrow{p_{i}}=\{x_{i},y_{i},z_{i},R_{i},G_{i},B_{i},L_{i}\},0\leq i\leq n \tag{1}\]  
where \(x\), \(y\), and z are the 3D coordinates of point cloud, \(R\), \(G\), and \(B\) are the color information of each point cloud. \(L\) represents the label of each point cloud, indicating which class of target it belongs to, and \(n\) is the number of all the point clouds in the space.  
We can divide the labels of point clouds used in this paper into the following categories based on the Stanford Large-Scale 3D Indoor Spaces Dataset (S3 DIS) classification [32], as shown in Table 1.  
All the labels refer to common furniture found in indoor rooms, with the exception of the last one, \"clutter\", which is added to categorize point clouds that cannot be reliably classified into a specific class.  
We assume three performance metrics as alternatives for the weighting strategy, which include the importance (IM) of labels, the intersection-over-union (IoU) of labels, and the Class-Pixel-Accuracy (CPA) of labels [33; 34]. We subjectively assign and quantitatively express the importance of labels in the following ways, as shown in Table 2:  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline
**Class** & **Ceiling** & **Floor** & **Wall** & **Beam** & **Column** & **Window** & **Door** & **Table** & **Chair** & **Sofa** & **Case** & **Board** & **Clutter** \\ \hline No. & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The labels of point clouds in 3D indoor spaces.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline
**Class** & **Ceiling** & **Floor** & **Wall** & **Beam** & **Column** & **Window** & **Door** & **Table** & **Chair** & **Sofa** & **Case** & **Board** & **Clutter** \\ \hline IM & 0.2 & 0.2 & 0.2 & 0.2 & 0.6 & 0.6 & 0.4 & 1 & 1 & 0.8 & 0.6 & 0.6 & 0.1 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The importance of labels in 3D indoor spaces.  
We set the maximum score of importance at 1. We assign a lower importance to objects such as ceilings, floors, and walls that serve as backgrounds. We assign a higher importance to furniture like tables, sofas, and chairs, which are numerous and highly utilized. Other types of furniture, with relatively infrequent use, fall between the two in terms of importance. We set the importance of clutter objects to only 0.1 in order to exclude them from the radar detection range.  
We define the IoU and CPA based on a confusion matrix, a specific matrix that visualizes algorithm performance, where each column represents predicted values, and each row represents the actual categories [35]. In the semantic segmentation results of point clouds, we evaluate the segmentation performance for each class using a binary confusion matrix.