## 3 Full Description of the Approach
### Segmentation into Structural Elements
#### 3.2.1 Segmentation into Sub-Spaces  
First, a floor segmentation is performed for scans resampled at 1 cm. For each scan, an histogram describing the distribution of points along \(z\) axis is created and analysed in order to determine the ground and ceiling altitudes. Thanks to ground altitudes, scans are grouped into several clusters representing the different floors. The floor segmentation result obtained for indoor point clouds presented in Figure 2b is shown in Figure 3.  
Figure 1: Overview of the developed approach.  
Figure 2: Dataset used to illustrate the approach: (**a**) Photograph of the acquired building. (**b**) Indoor colourized point clouds (\(\sim\)1.7 billion points before resampling).  
Then for each floor, a room segmentation is performed. At this stage, a binary image is generated based on the projection onto an horizontal plane of a slice of point clouds at ceiling levels. The advantage of considering the ceilings is that at this location the point clouds of different rooms are not linked together. A slice of 30 cm was chosen. The distances between the ceilings and interior contours of doors are generally higher than this value. One should note that if the distances are smaller than the defined value, the link between rooms can be removed by considering the standard deviation of points along \(z\) axis (explanation below).  
The generated binary image for the first floor of INSA building is presented Figure 4a. A pixel is coloured in white if it contains at least one point and in black otherwise. A pixel size of three times the spatial resampling namely 3 cm is chosen. The choice of the image pixel size is induced on one hand by the thinnest wall that can be encountered. A higher pixel size can cause the disappearance of thin walls and can consequently create links between rooms. On the other hand, by considering a spatial resampling of 1 cm the binary image does not contain \"holes\". During the creation of the binary image, the standard deviation of points along \(z\) axis is also calculated for each pixel. The pixels corresponding to walls have a higher standard deviation and are temporarily coloured in black in the room segmentation process to ensure that there are no links between rooms.  
A region growing is then applied in the image to identify 2D regions representing rooms. During this process, 2D regions are removed if their surfaces are lesser than a threshold (\(s_{min}=1\) square metre). The result of the region growing applied to the image Figure 4a is presented in Figure 4b. It is superimposed with an existing floor map. The result is satisfying since the rooms are correctly detected.  
Finally, to move from 2D to 3D regions representing the rooms, 2D regions are considered from ground height to ceiling height of the floor. A filter is also considered to eliminate 3D regions which are too small or which do not describe rooms. For this purpose, a minimum height \(h_{min}\) of 1.8 m was chosen. This choice was induced by the fact that regarding to the French \"Carrez\" law, parts of an enclosed area with a ceiling height of less than 1.8 m are excluded from the calculation of the effective usable surface area of an accommodation. Moreover, by considering that a room measures at least one square metre of surface, a minimal volume \(v_{min}\) of 1.8 cubic metres (1 m\({}^{2}\times 1.8\) m) was fixed. At the end of room segmentation, points which are not assigned to a region are kept aside for a further use.  
Figure 3: Floor segmentation result—3 floors of the INSA building (one colour per floor).