# Indoor Building Reconstruction from Occluded Point Clouds Using Graph-Cut and Ray-Tracing
## 4 Applications and Accuracy Evaluation
### Results
The parameter \(\tau_{R}\) governs the fusion of similar plans extracted by RANSAC and thus it is indeed designed to mitigate for over-segmentation problems. Indeed, an over-segmented point cloud is likely to be more prone to classification errors. In the presented example, \(\tau_{R}=2\varepsilon\) was selected for the plans distance and \(\tau_{R}=\alpha\) for normal distances. The parameter \(\lambda\) weights the data term and the smoothness term in Equation (6). To test the contribution of these two terms in the final model, different values of \(\lambda\) were tested. For lower values of \(\lambda\), the smoothness term increased in favor of a smoother solution and consequently some details were filtered out (Figure 12). In the presented case, a value of \(\lambda\) ranging between 0.5 and 0.8 provided the best reconstructed model. Figure 12: ‘Cell complex’ reconstruction for the adopted data set: (**a**) detected primitives; (**b**) induced ‘cell complex’ with ‘pending walls’ (red); (**c**) initial labeling of the ‘cell complex’; (**d**) final labelling (\(\lambda=0.8\)); and a detail of the complex with different values of \(\lambda\) (**e**). To evaluate the quality of the generated model the standard deviation of the unsigned distances between the original point cloud and the reconstructed objects (walls, floor, and ceiling) was used. Figure 13a,b presents point clouds colored with the absolute distance associated to the walls and ceiling, respectively. For the data set considered the RMS of the unsigned distance is slightly lower than 3.0 cm. This means that on average, the walls are reconstructed with a precision of about 3.0 cm (which can be considered comparable to the accuracy of the original point cloud). Figure 14a shows the histogram of residuals between the reconstructed model and point cloud for the walls, showing that more than 65% of the points has a distance from the reconstructed model smaller than 3.0 cm. The visualization of absolute distances (Figure 13a) thanks to a color-bar allows those walls or portions of walls having a larger discrepancy to the point cloud to be displayed rapidly. For example, a small portion of walls feature a standard deviation of 20 cm which is likely to mean that the reconstruction has been wrong or that the object is not really a portion of wall (e.g., it could be a piece of furniture). Indeed, assuming that there is no significant noise in the data, the factors that might influence the standard deviation of the models are the number of planes composing it and the amount of points which emerge from the wall (objects leaning against walls). Concerning the ceiling, a similar consideration can be adopted. However, the distribution of absolute distances follows an unusual path (Figure 14b). This is probably due to the fact that in the current implementation the case of a suspended ceiling (i.e., a ceiling with different heights in the same room) has not been considered. However, in the data set this situation occurred causing larger discrepancies in those areas, as in the yellow areas in Figure 13b. Figure 13: Point clouds colored with points-to-model unsigned distances for walls (**a**) and ceiling (**b**). A second test was performed on an extended area, including the central corridor, of the same dataset. The aim of this second test was to verify the robustness of the presented method in the case of a large amount of clutter. Indeed, due to the presence of moving people during the data acquisition phase the scene was characterized by significant clutter (Figure 15a). Also in this case results in terms of data completeness and data quality confirm the ones previously obtained. In particular, more than 81% of points has a discrepancy from the reconstructed model which is smaller than 4.0 cm. Figure 14: Histogram of residuals between the reconstructed model and point cloud for walls (**a**) and ceiling (**b**).