## 3 Space Matching Process Using Multi-Resolution Cube Grid
### Pre-Processing for Data Optimization  
Converting the point cloud data into grid system is essential for space analysis. However, point cloud data collected through laser scanning is large in volume and requires considerable processing time for converting. As such, this study proposed a pre-processing method based on sub-sampling which can optimize the point cloud data prior to space analysis and verified the applicability thereof by comparing the accuracy.  
As an actual space for optimizing spatial analysis data, a room size of 2.5 m \(\times\) 9.4 m \(\times\) 2.6 m was selected and an as-built model reflecting the shape of space was created through laser scanning. Through the Leica C5 laser scanner, the shape information of the room was obtained in the form of a point cloud, and the final output was generated in the pts format through matching work and format conversion (Leica Cyclone Software: Cyclone).  
Sub-sampling of point cloud data was performed first for data optimization. Sub-sampling refers to a function that sets the user's desired space within the space consisting of points and reduces several points in the set space to a single point. It is used to reduce the load for handling and loading of massive point cloud data and to reduce the data volume. The data collected through laser scanning resolution set at Mid, has the capacity of 259 MB and consists of total 14,317,597 points. Increasing the resolution in the laser scanning step increases the capacity and number of points. Figure 6 below shows the example of sub-sampling.  
Sub-sampling was performed using open software \"Cloud Compare,\" and the space interval was set to 10 cm, which was lower than the grid box size provided by the space analysis system. Sub-sampling output capacity was reduced to 27.4 MB and the total number of points was reduced to 705,478. By comparing the processing time of space analysis system for the original data and  
Figure 5: Space analysis software.  
Figure 6: Point cloud data for sub-sampling.  
the sub-sampling data respectively, the applicability of the optimized data (light weight) through sub-sampling was verified.  
Table 4 below summarizes the comparison results of processing time using the original data and the sub-sampled data and the resulting values respectively. The original data and the sub-sampled data were tested for the grid box sized 1 m \(\times\) 0.7 m \(\times\) 0.5 m in the space analysis system, respectively.  
In case of the original data, it took 168 s to load the data. When the space analysis was performed, it took 66 s for the grid box size 1 m, 114 s for box size 0.7 m, and 416 s for box size 0.5 of the respective set values. For the sub-sampled data, it took 7 s for data loading (\(-\)161 s compared to the original data), and it took 8 s for grid box size 1 m of the set value (\(-\)78 s compared to the original data), 15 s for box size 0.7 m (\(-\)99 s compared to the original data), and 27 s for box size 0.5 m (\(-\)389 s compared to the original data) of the respective set values. When the space analysis results were compared, both original data and sub-sampled data showed the same resulting values with 20 each for box size 1 m, 74 each for box size 0.7 m, 103 each for box size 0.5 m respectively. In the space analysis system,  
\begin{table}
\begin{tabular}{c c c c} \hline \hline - & \multicolumn{2}{c}{**Original Point Cloud**} & \multicolumn{2}{c}{**Sub-Sampled Point Cloud**} \\  & **(14,317,597–259 MB)** & **(705,478–27.4 MB)** \\ \hline - & time & Result & time & Result \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparison of original data and sub-sampled data for data processing.  
the sub-sampling technique was used to optimize and minimize the amount of input data, and as a result, the same resulting values as the original data were acquired within the shortened processing time, verifying its suitability.