Extraction of Indoor Objects Based on Exponential Function Density Clustering Model

Objective Indoor point clouds include walls, ceilings, floors, and many objects in a room. The extraction of a room' s walls, ceilings, floor, and many objects is critical for many applications, including object identification for indoor navigation, facility management, and reconstruction of construction. Given this, this study proposes using an exponential function to construct a density clustering model according to the local density within a cutoff distance. First, the distance between the boundary and an indoor point cloud is used to construct the constraint condition of wall density clustering. Then, a room's ceiling and floor are extracted according to the exponential function of the z value and local density model. Next, the local density model of different objects is constructed, and the constraint distance is determined according to the size of the local density. Simultaneously, cluster centers are recognized as points for which the product value of the local density and constraint distance is abnormally large. Finally, the cluster of each point is determined by the distance between the point and cluster center. Then, indoor object extraction is achieved by judging the distance between neighboring clusters. We conduct the extraction of indoor point clouds of different scenes and compare our method with the CFDP and DPC algorithms. Comparison results show that the DPC method is inferior to the proposed method but superior to the CFDP method. In addition, the extraction accuracy, recall, and F1-measure of different types of indoor point clouds are calculated in terms of the matching rate, true positive, false positive, and false negative. This study's findings show that the performance of the proposed method is affected by the degree of closeness between objects. Methods For an indoor point cloud, the exponential function is used to construct the density cluster model of walls, ceilings, floors, and objects in a room. We can extract them based on their density clusters. Before the determination of the density cluster, the cutoff distance and local density within the cutoff distance are determined according to the relationship between angular resolutions and the scan distance. Concerning wall extraction, the comprehensive density function for wall extraction is obtained according to the local density within the cutoff distance and distance constraints. A wall's point cloud can be extracted according to the inflection point of the wall density. Concerning floor and ceil extraction, the exponential function is used to construct the density function of the z value, and then, the distributions of the density functions of ceilings and floors are obtained. According to the inflection point of ceiling and floor density, the ceiling and floor's point clouds are extracted. Concerning indoor object extraction, the prerequisite of indoor point cloud clustering is the determination of the cluster center. The cluster center can be determined by the constraint distance and local density. First, the constraint distance is determined according to the magnitude of the local density within the cutoff distance. Second, the clustering center is determined according to the product of the local density and constraint distance. Third, point cloud clustering is performed according to the distance between each point and clustering centers. Finally, we perform the extraction of indoor objects according to the aggregation of adjacent point cloud clusters. Results and Discussions Table 1 shows that the extraction ratios of point clouds on the wall, ceiling, and ground are similar to 95%. For the apartment, the number of wall, ceiling, and ground points is less than the actual number, indicating that there is an omission extraction phenomenon. For the bedroom, the ceiling and ground points extracted are less than the actual points, indicating that there is an omission extraction phenomenon. However, points extracted from the wall are larger than the actual points, so there is an over-extraction phenomenon. The main reason for this phenomenon is that parts of the point clouds from the ceiling and ground are considered point clouds from the wall. As presented in Table 3, for the first type of room, the proposed method accurately extracts 22 objects, and the extraction ratio is 78.6 %. Similarly, the extraction ratios in the second and third types of rooms are 74.3 % and 40 %, respectively. Therefore, most of the objects in the first and second types of rooms are extracted, and no more than half of the objects in the third type of room are accurately extracted using the proposed method. The reason for this result is that almost all objects in the first and second types of rooms are not close to each other, but most of the objects in the third type of room are close to each other. Table 5 shows that the precision of the first type of room is slightly higher than that of the second type of room, but they are all significantly higher than that of the third type of room. The recall of the first type of room is slightly less than that of the second type of room but greater than that of the third type of room. The F1-score of the first type of room is almost the same as that of the second, and they are greater than that of the third type of room. The extraction quality of the first and second types of rooms is superior to that of the third type of room. Conclusions This study presents a clustering model of indoor point cloud density based on an exponential function. First, the cutoff distance function model is developed according to the distance and angular resolution of point clouds. Second, the local density model based on the exponential function is constructed by analyzing the number of points and distance mean and standard deviation. Third, according to the distance between the point cloud and boundary, the constraint distance density of judging a wall is obtained. Similarly, the density function of the z value is constructed according to the amplitude distribution and the exponential function of the z value. Combined with the local density, the density clustering model of walls, ceilings, and floors is obtained. For indoor objects, the constraint distance is determined according to the local density within the cutoff distance. In addition, the clustering center can be determined according to the product of the constraint distance and local density. Finally, indoor targets are clustered according to the clustering attribute of each point. Based on the density clustering model, walls, ceilings, floors, and objects in the room can be extracted. The proposed method is compared with other clustering algorithms in different indoor scenarios, and the results show that the number of objects extracted using the proposed method is greater than that extracted using the CFDP and DPC methods. In addition, when there are a few noise points between adjacent targets, the extraction effect of the proposed method is better than that of the CFDP and DPC methods. Furthermore, accuracy, recall, and F1-score are used to evaluate the object extraction performance of the proposed method, which varies with types of rooms. The results show that the proposed method is more suitable for rooms with non-adjacent objects, and its performance is related to the closeness of adjacent objects. Given the shortcomings of the proposed method, future research work will focus on the extraction of objects close to each other. In addition, a future clustering algorithm can accurately extract some small items on other objects, such as books or cups on a table.