During the last decade laser scanners have gained popularity in architecture, engineering, construction and facility management (AEC/FM). Other measurement methods such as total stations, measuring tapes and based-stereo-camera prototypes are too time-consuming or inaccurate compared to scanners, particularly in large-scale environments. Moreover the high density provided by a single scan (which could be over several million points) makes this technology very suitable for use in the 3D modeling of facilities.

Most of the time, the dense raw data provided from scanners are manipulated by a designer or processed by an engineer in order to create a simplified model of the scenario. This well known reverse engineering process is applied to 3D model creation. Thus, a simplified model provides a high-level representation of the scenario that ranges from a single CAD model, in which a wall is represented as a set of independent planar surfaces, to a Building Information Model (BIM), in which a wall is thought as a volumetric object composed by multiple surfaces with several relevant properties like color, material, cost, etc. Much of the emphasis in previous works has been on creating visually realistic non-parametric models rather than accurate parametric ones. Some examples in this category include methods by El-Hakim et al.[1], which is focused on indoor environments and Früh et al.[2] and Remondino et al.[3], which are focused on outdoor environments. In these cases, a great part of the modeling process is supervised by the modeler so that it cannot be said that models are obtained in an automatic manner.

In this paper we introduce a method that automatically yields Boundary Representation Models (B-rep) for indoors after processing dense point clouds collected by laser scanners from key locations through an existing facility. The 3D model then represents the current state of the building, what is named as the “as-is condition”. This model does not necessarily have to be coincident with either the designed (“as-designer condition”) or the built model (“as-built condition”). In fact, the facility could have lightly been modified or restored from its initial design. In other occasions, we cannot access to the design drawings or they merely do not exist. Thus, the automatic creation of “as-is models” of inhabited scenarios is a challenging research field which is gaining attention from different applications including architecture, engineering, robotics, etc.[4].

Although there are not many publications dealing with the automatic creation of 3D models, in the last years several interesting works related with some of the stages of this process can be found in the literature. A review for automatic reconstruction of as-built building information models can be found in [4]. The process of creating a single-semantic model can vary depending on the input and expected output. Generally, the automatic modeling process can be divided into three steps: data acquisition, data processing and data modeling, and most of the published papers concentrate on the second stage: data processing.

In this framework, 3D data processing means processing millions of unstructured 3D data in order to obtain higher level data structures. Several approaches that convert 3D data into high-level representations in buildings context can be found over the last years. We can here distinguish between proposals to detect and model single objects or particular parts of large scenarios and those than completely model indoors and outdoors.

As regards the first sort of proposals, one of the earlier works that obtain 3D models from laser scanner in a local space context is the one of Kwon et al.[5]. They introduce a set of algorithms for fitting sparse point clouds to a set of single volumetric primitives (cuboids, cylinders and spheres) which can be extended to groups of primitives belonging to the same object. An automated recognition/retrieval approach for 3D CAD objects in the construction context is presented in [6]. In [7] a semiautomatic method to match 3D existing models to data of industrial building steel structures is proposed. The author develops a variant of the ICP algorithm for data registration in order to recognize CAD models objects in large site laser scans. The method is semiautomatic because a coarse registration needs to be performed manually. The same author presents in [8] a plane based registration system for coarse registration of laser scanners data with 3D models in the context of AEC/FM industry. The approach is based on finding planes from the point cloud and matching them with the ones extracted from the 3D models. Nevertheless, the matching process is performed by hand. Other authors [9] propose the combination of point clouds, acquired by means of laser scanners, and photogrammetry in order to generate 3D models of a building under construction. The work of Rusu et al.[10] correctly recognizes and localizes relevant kitchen objects including cupboards, kitchen appliances, and tables. They interpret the improved point clouds in terms of rectangular planes and 3D geometric shapes. One of the innovations consists of including a novel multi-dimensional tuple representation for point clouds and robust, efficient and accurate techniques for computing these representations, which facilitate the creation of hierarchical object models.

Detailed models of part of the walls and building façades are obtained in [2,11–13]. In [11,12] the data processing goes from detecting windows through low data density regions to discover other data patterns in the façade. In [13] important façade elements such as walls and roofs are distinguished as features. Then, the knowledge about the features’ sizes, positions, orientations, and topology is introduced to recognize these features in a segmented laser point cloud. Früh et al.[2] develop a set of data processing algorithms for generating textured façade meshes of cities from a series of scans, corresponding to vertical 2D surfaces, obtained by a laser scanner. Thrun et al. developed a plane extraction method based on the expectation-maximization algorithm [14]. Other researchers have proposed plane sweep approaches to find planar regions [15,16]. Valero et al.[17] focus on the modeling of those linear moldings that typically surround doorways, windows, and divide ceilings from walls and walls from floors.

With respect to the automatic creation of complete indoor models, geometric surfaces or volumetric primitives can be fitted to a 3D point cloud to model walls, doors, ceilings, columns, beams, and other structures of interest. In its most simple format, the modeled primitives are annotated with labels (e.g., “wall”). In a higher modeling degree, spatial and functional relationships between nearby structures and spaces are established. Interesting developments can be seen in [18] and [19]. In these works, Adan et al. identify and model the main structural components of an indoor environment (walls, floors, ceilings, windows, and doorways) despite the presence of significant clutter and occlusion, which occur frequently in natural indoor environments, but they deal with rectangular rooms. Furthermore, in the present work we present an approach to identify walls in rooms with more complicated geometries. Okorn et al.[20] present an automated method for creating accurate 2D floor plan models of building interiors. They project the points onto a 2D ground plane and create a histogram of points density, from which line segments corresponding to walls are extracted using a Hough Transform. The first steps of our proposal seem to be inspired in the same strategy since we also project the points to extract the approximate 2D wall’s location. Nevertheless, this is only used to later retrieve the corresponding 3D data and delimitate with precision the points belonging to the walls.

This work aims to make progress in the creation of automatic 3D models from point clouds provided by scanners [21]. The contributions of this work lie in three points: accuracy of the model, coherent representation and evaluation of the method. First, we propose a voxelization (discretization) of the space with which to accurately define the planes fitted to the points belonging to the ceiling, floor and walls of the facility. Second, we generate a complete boundary representation model of the indoor in which faces, edges and vertices are coherently connected. Third, once the method is designed and implemented, we make a performance evaluation by measuring the geometric modeling accuracy, the recognition accuracy and the relationship modeling accuracy. The following sections explain the main stages to achieve a complete B-rep model of interiors and present the results obtained.

The segmentation stage provides the set of points belonging to each wall (including floor and ceiling) of the indoor scene. The following step consists of converting this raw information into high level surface representation. Within the 3D representation models universe we have chosen the boundary representation (B-rep) model [22]. In B-rep, a shape is described by a set of surface elements along with the connectivity information which describe the topological relationship between the elements.

The process to achieve a B-rep of an interior space starts calculating the planes which best fit every set of the segments associated to the walls. To do this, we have used the Singular Value Decomposition (SVD) technique [23]. Through SVD, the closeness between the plane and the segmented points is easily calculated. The steps to calculate the plane equation that best fits a generic set of points are shown below.

Each point cloud P = (p₁,p₂,…,p_n), corresponding to a wall, can be fit to a plane defined by the equation: (4) Π : A   x + B   y + C   z + D = 0

The best fit plane is that which minimizes the sum of the distances between every point p_i and the plane Π. Therefore, we can calculate each fit plane by minimizing the expression: (5) ∑ i = 1 n | A x i + B y i + C z i + D | 2 A 2 + B 2 + C 2

Setting the partial derivative with respect to D equal to zero, we obtain: (6) D = − ( A x 0 + B y 0 + C z 0 )in which p₀= (x₀, y_0,z₀) is the centroid of P. Replacing (6) in (5): (7) ∑ i = 1 n | A ( x i − x 0 ) + B ( y i − y 0 ) + C ( z i − z 0 ) | 2 A 2 + B 2 + C 2

Let us introduce the matrix M = [p₁ − p₀ p₂ − p_{0 …} p_n − p₀]^T, in which p_i= (x_i, y_i, z_i) and p₀= (x₀, y₀, z₀), and the vector v = [A  B  C]^T. We can show the problem over a matrix representation: (8) ( v T M T ) ( M v ) v T v

This expression is called a Rayleigh Quotient and is minimized by the eigenvector of M^TM that corresponds to its smallest eigenvalue. Next, we use the singular decomposition of M = USV^T, in which the columns of V are the singular vectors of M and the eigenvectors of M^TM. Therefore, the solution of Equation (5), provide us the normal of the plane Π, n Π → = [ A B C ]. The parameter D is calculated from Equation (6).

The last stage consists of calculating the intersections between connected planes. Note that the topological relationship between the walls is established as the edges and corners are extracted in figure I. So, we know which planes have to be themselves intersected and, therefore, we can find the 3D edges and corners of the room. For instance, the ceiling and floor’s planes pairwise intersect with each wall’s plane and define the edges at the top and down of the room; and vertices are extracted after intersecting three planes.

Figure 5 illustrates an example with the results of our approach. Part (a) represents the planes fitted to the walls and part (b) shows the set of labeled vertices of the room. Figure 4(c) contains the relationship graph in which adjacent faces in the diagram share one edge.

Our approach was tested on panoramic range data appertaining to inhabited interiors. Note that we are dealing with very complex scenarios, in which furniture and other objects contribute to clutter and occlusions. They contain a wide variety of objects that occlude not only the walls, but also the ceiling and floor. Three to six laser scans were taken per room. A FARO Photon laser scanner provided 38 million points per room. Figures 7 and 8 show the resulting 3D B-rep models for two rooms.

In this section we present the results obtained for two different inhabited indoors. These interiors do not have rectangular but arbitrary plans. The first room corresponds to the Virtual Reality Lab at the Escuela Técnica Superior de Ingenieros Industriales (UCLM). The second one is the living room of a private flat.

After defining the B-rep model we aim to investigate the accuracy of the obtained models. Firstly, we determine the error committed when we represent the walls of the rooms by means of planes. We thus measure the quadratic distance of every point of the walls to the corresponding plane. Distances between the sensed points and the planes are represented in colormaps in Figure 6(a) for different walls of the lab and (b) for two walls belonging to the living room. It can be seen different regions where an important variation of color is produced. These areas can be owing to typical objects hanging on the wall (pictures, posters, and so on), moldings and doorframes. Of course, some of the errors come from the fact that the walls, ceiling and floor are not totally flat. The corresponding error means, for both inhabited interiors, are presented in Table 1, in which d̄ represents the mean value for the distances between each 3D point and its corresponding plane.

The mean error of the fitted planes ranged between 0.59 and 4.64 cm for the lab and between 0.19 and 6.5 cm for the room. In any case, for the majority of the walls the mean error is around below 2 centimeters, despite being severely occluded by tables and chairs. On the other hand, the wall which fitted worse was number 2 of the lab. In this case, there was a big projection panel which largely occluded the wall. Most points sensed in this part of the room corresponded to the panel, so that the calculated plane fitted the panel instead of fitting the wall.

We focused most of our analysis on understanding the performance of our modeling results, since this aspect of the algorithm is considerably less studied than planar wall modeling. We considered two aspects of the performance: first, how reliably the walls can be detected, and second, how accurately they are modeled. To answer the first question, we compared the detected walls with walls of the ground truth model. No fails were reported in this aspect and all existing walls were correctly detected. Failed detections mainly might occur in severe occlusion circumstances.

The second question was tackled first generating the geometrical ground truth of the scenes. We constructed by hand the ground truth models of the rooms with the help of a Leica DISTOTM A6 laser tape measure, which provides 1 millimeter accuracy. In order to assess the error committed, the ground truth models were then compared with our 3D models (see Figures 7 and 8). The results are summarized in Table 2.

We first compared the lengths of the vertical and horizontal edges of each face of the ground truth models with ours and the difference between are denoted as d_v and d_h in Table 2. The value of d_v was similar for all pairs of walls; around 0.87 cm for the lab and 0.80 cm for the living room. The smallest value of d_h in the living room was for number 3. In this case, the mean value was less than 2 cm in both rooms.

In order to compare the accuracy of the orientation of the faces, we calculated the difference between the respective normal vectors (α in Table 2). The smallest faces yielded a high rate in α, which distorted the average value. Thus, although the mean value of α were 1.59° and 1.85° for the lab and the living room respectively, in the majority of the faces α was less than this value.

Once we have presented the results for these two inhabited interiors, we can establish some difference between them. The living room has more and smaller walls than the laboratory, what might lead the reader to believe that the segmentation process is particularly complicated in this case. However, if we compare the mean values for the different parameters in Tables 1 and 2, the deviations with the ground truth are lower in the living room’s case. This result can be due to the fact that a multitude of pieces of furniture occlude the walls of the room and, consequently, the segmentation process may yield more imprecise segments.

Automatic creation of “as-is models” of inhabited scenarios is a challenge research field which is gaining attention from different applications in AEC/FM contexts. In this paper an approach for automatically creating Boundary Representation Models (B-rep) from dense point clouds collected by laser scanners is presented.

The method here proposed is based on segmenting the data by optimizing the discretization of the space. We make a 2D projection of the data in the voxel space and coarsely determine the segments in which the points lie. The voxels’ size is adjusted to the walls, taking into account the flatness tolerances in construction, improving the approach of previous works [18,19] in which predefined voxels’ sizes were used. Then the boundary representation model is generated by intersecting the planes that contains the 3D segments, calculating the faces, edges and vertices, and establishing the relationship between components. This idea has been tested in arbitrary shape plans providing excellent results.

The results lead us to state that the majority of the wall’s points were correctly segmented. We have also evaluated the performance and accuracy of our method comparing the ground truth and the query B-rep models. Overall modeling accuracy for the AEC domain typically needs to be at least within 2.5 cm of the ground truth, so that the precision of our model is clearly above the standard (between 0.8 cm and 1.88 cm for vertical and horizontal edges).

This research is a part of a larger project which aims to obtain automated reverse engineering of buildings including more complex semantic models. Future improvements to the method will be addressed in two lines: extend the method to non-flat walls and generate B-rep models including details (paintings, panels, etc.) and parts of the walls (moldings, doorframes, windows frames, etc.) in inhabited buildings. As other potential applications, these 3D models can be helpful to create, in an automatic manner, virtual scenes in which digitized objects are introduced in order to generate virtual exhibitions as the ones shown in [24–26].