Recent developments in laser scanning systems have inspired substantial interest in indoor modeling. Semantically rich indoor models are required in many fields. Despite the rapid development of 3D indoor reconstruction methods for building interiors from point clouds, the indoor reconstruction of multi-room environments with curved walls is still not resolved. This study proposed a novel straight and curved line tracking method followed by a straight line test. Robust parameters are used, and a novel straight line regularization method is achieved using constrained least squares. The method constructs a cell complex with both straight lines and curved lines, and the indoor reconstruction is transformed into a labeling problem that is solved based on a novel Markov Random Field formulation. The optimal labeling is found by minimizing an energy function by applying a minimum graph cut approach. Detailed experiments were conducted, and the results indicate that the proposed method is well suited for 3D indoor modeling in multi-room indoor environments with curved walls. , the reconstruction of curved walls in multi-room environments is still not resolved. Many works have utilized the Manhattan world (MW) assumption [4] , which holds true for many indoor scenes that contain man-made architectural structures. The MW assumption assumes that most man-made structures can be approximated by planar surfaces that are parallel to one of the three principal planes of a common orthogonal coordinate system. Obviously, the MW assumption is not suitable for indoor spaces with curved walls. One direct method for addressing curved walls is to use piecewise straight lines to approximate a curved line [5, 6] , but this method is not always appropriate for the following two reasons. On the one hand, the use of a few piecewise straight lines to approximate a curved line will lead to an unsmooth boundary of rooms [5] . On the other hand, the use of too many piecewise straight lines will lead too many small cells in the cell complex. It is difficult to arrange a label to such small cells. Furthermore, it is not trivial to detect curved surface walls in multi-room indoor environments [7, 8] . Although slices are often used to simplify detection work, detected curved lines are often scattered and broken into pieces and vary in length, which is not suitable for modeling problems. It is also difficult to detect straight and curved lines separately, especially in the case of noisy point clouds. In this work, a novel straight and curved line tracking method with a straight line test was proposed to detect straight and curved walls. Robust parameters are used, and a novel straight line regularization method is achieved by using constrained least squares. Room space decomposition with curved walls is cast as an energy minimization problem that partitions the indoor space into separate semantic entities. A novel Markov Random Field (MRF) formulation is proposed, and the energy function is efficiently minimized using an existing graph cut method. The proposed method is performed without a priori knowledge of viewpoints, and it is not restricted to the strong MW assumption. The assumption of this study is that floor and ceilings are horizontal and walls are orthogonal to the floor. The remainder of this paper is organized as follows. Important related works are introduced in Section 2. The semantic definition of indoor space, structural constraints and the proposed method are described in Section 3. Experiments and the discussion are presented in Section 4. Finally, conclusions are drawn in Section 5. The indoor reconstruction method can be classified as a structural element extraction method and a space decomposition-based method. The former research attempts to classify the point cloud of indoor scenes and extract structural elements. A method for the planar 3D modeling of building interiors from point clouds was proposed in [9] . This method divides indoor points into ceilings, floors, walls, and other small architectural structures according to the normally computed principal component analysis (PCA) algorithm, and random sample consensus (RANSAC) is employed to fit the detected planar primitives. Furthermore, predominantly planar surfaces, such as walls, floors, and ceilings, were modeled [10], despite the presence of significant clutter and occlusion, which occur frequently in natural indoor environments. Shi et al. [11] proposed a semantic geometric modeling method to reconstruct 3D building models with semantic information from the unstructured 3D point cloud. The method enables the accurate detection of wall surfaces. The structural element extraction methods for building structure elements cannot construct complete wall surfaces due to missing data and the existence of occlusion in scanned point clouds. Thus, the space decomposition-based method exploits prior knowledge about building structures to achieve robustness and transform the scene reconstruction into an indoor space decomposition problem. By initializing the domain of the point clouds in the XOY plane, the k-medoids algorithm was applied to cluster subsampled pixels [12] , and room segmentation was then formulated as a clustering problem. Previtali et al. [4] proposed an automatic method for modeling MW indoors from occluded
REF proposed to detect rooms in a cell complex of intersecting lines by an energy minimisation approach.
Automatic Indoor Reconstruction from Point Clouds in Multi-room Environments with Curved Walls
Sensors (Basel, Switzerland)
Sensors (Basel, Switzerland)
Computer Science Medicine Engineering