Three-Dimensional Reconstruction of Indoor Building Components Based on Multi-Dimensional Primitive Modeling Method

Abstract

The integration of Building Information Modeling (BIM) and Digital Twin (DT) has emerged as an innovative tool in the architecture, engineering, and construction (AEC) domain. To successfully utilize BIM and DT, it is crucial to update the 3D model in a timely and accurate manner. However, limitations remain when handling massive point clouds to reconstruct complex indoor structures with varying ceiling and floor heights. This study proposes a semi-automatic 3D model reconstruction method. First, point clouds are aligned with 3D Cartesian axes and the spatial extent of the indoor space is measured. Subsequently, the point clouds are projected onto each coordinate plane to hierarchically extract structural elements of a building component, such as boundary lines, rectangles, and cuboids. Boolean operations are then applied to the cuboids to reconstruct a 3D wireframe model. Additionally, wall points are segmented to identify openings like doors and windows. For validation, the method was applied to three typical building components with Manhattan-world structures: an office, a hallway, and a stairway. The reconstructed models were evaluated using reference points, resulting in positional accuracies of 0.033 m, 0.034 m, and 0.030 m, respectively. Finally, the resulting wireframe model served as a reference to build an as-built BIM model.

1. Introduction

1.1. Background

With the increasing complexity and scale of modern buildings, the integration of Building Information Modeling (BIM) and Digital Twin (DT) has emerged as an innovative technical paradigm in the architecture, engineering, and construction (AEC) domain [1,2,3]. A three-dimensional (3D) model in BIM, which encapsulates both geometric and semantic properties of indoor building components, has served as a centralized information platform from the design to construction and maintenance of buildings [4,5]. For example, a 3D model enables multiple stakeholders to collaborate and exchange information, enhancing the design process while satisfying requirements from various disciplines, such as architecture, structural engineering, and construction management [6,7]. In construction planning and scheduling, a 3D model-based simulation over time, often referred to as 4D simulation, optimizes a construction sequence by mitigating misconceptions and information gaps, thereby reducing the risk of rescheduling and project delivery delays [8,9,10]. Additionally, 3D visualization of building facilities provides a clear and comprehensive representation of the building and its system, enhancing understanding and decision-making for maintenance tasks [11,12].

Recently, DT technology has been integrated with BIM, exploiting an Internet-of-Things (IOT) sensor network and big data analytics. The static nature of the 3D model is consequently improved with advanced capabilities to visualize and analyze the real-time status of physical assets and systems in buildings [1,3,13,14,15]. The synchronization between the 3D model and real-time data from IoT sensors creates a dynamic digital replica of structural and functional properties of the built environments. Numerous applications have been proposed, including real-time monitoring and visualization of indoor environments such as air quality, temperature, and luminance [16,17,18]; continuous monitoring and predictive analysis of structural health properties [19,20]; and facility management to optimize building operations, maintenance scheduling, and energy efficiency [21,22]. The spatiotemporal integration of BIM and DT empowers stakeholders to make more informed, data-driven decisions throughout the building’s lifecycle. However, most 3D models in BIM are often as-designed, generated during the initial project phase [23,24,25]. These models may not fully reflect sequent changes or modifications occurring throughout the building’s operational and maintenance phases. The discrepancy between an outdated 3D model and an actual building environment constrains the accuracy and responsiveness of integrated DT and BIM applications [24,26,27].

1.2. Related Works

The timely reconstruction of an accurate and detailed 3D model is one of the crucial factors for the successful integration of BIM and DT. However, conventional methods, such as surveying techniques (e.g., total station and tape) and computer-aided design (CAD) drawings, are inadequate for as-built modeling, leading to inaccuracies and insufficient detail [28,29]. As the laser scanning system has the capability to capture highly accurate and detailed point clouds efficiently, Scan-to-BIM has become a standard process in the AEC domain [24,28,30,31]. In common practice, point clouds obtained from laser scanning are integrated into BIM authoring tools (e.g., Autodesk Revit and Graphisoft ArachiCAD) and used as a reference for manually creating as-built 3D models [31,32]. However, manual interpretation of unstructured point clouds remains unavoidable. Modelers are required to identify and classify structural elements of interest. Occlusions caused by various types of clutter within buildings lead to information loss and making the process labor-intensive, error-prone, and time-consuming, particularly for complex structures [31,33,34,35]. Also, the significantly large file sizes of point cloud further hinder efficiency and scalability in terms of data storage, processing, and management within limited computing resources [36,37,38]. These limitations necessitate the development of automated 3D reconstruction methods to streamline the geometric modeling process in Scan-to-BIM.

Numerous studies have proposed automatic or semi-automatic 3D modeling approaches for explicitly representing building interiors, which can be broadly classified into two categories: global optimization and local heuristic [39,40,41,42]. The global optimization approach, also known as the top-down approach, reconstructs a 3D model from the entire point cloud, encompassing complete rooms and hallways. Prior knowledge of the built environment (e.g., vertical walls and parallelism between ceilings and floors) can be incorporated as geometrical constraints to ensure a structurally coherent 3D model [43,44,45]. In addition, for modeling regular and repetitive spatial patterns in building interiors, a set of formal rules and transformations can be formulated to recursively combine simple primitives (e.g., cubic, cuboid and cylindrical shape) into a complex 3D model [46,47]. The global optimization method is effective for the automated reconstruction of 3D as-built models, particularly in the absence of architectural drawings for large-scale and complex indoor structures. However, the holistic constraints and rules impose limitations on modeling local structural irregularities and variations in individual building components (e.g., rooms, hallways, and stairways). In contrast, the local heuristic approach, also known as the bottom-up approach, focuses on modeling individual structural elements (e.g., floors, walls, and ceilings) from point cloud data. These elements are then gradually combined to create a 3D model. The local heuristic approach was initially developed for modelling a single building component [26,27,36,37] and has gradually expanded to the modelling of large-scale building interiors [39,48,49].

The primary concern in this study is the timely update of an as-designed (or outdated) 3D model in BIM. The local heuristic approach is adaptive as the fundamental principle remains consistent regardless of scale. Reconstruction begins with the segmentation of each building components from the entire point cloud. The identical process for segmenting and extracting structural elements is repeated for individual building components, which are then assembled into a coherent 3D model. This approach, which focuses on modeling a single building component, can be subdivided into 2.5D and 3D modeling approaches (

Table 1. Overview of the local heuristic approaches for the reconstruction of indoor 3D model.

Approach	Type	Highlight and Detail	Limitation
Hong et al. [26]	2.5D Approach	Model a floor boundary with line tracing and segmentation, followed by a constrained least square method Estimate a ceiling-to-floor height using RANSAC applied to zmax and zmin values of point cloud	Unable to detect and model wall openings Restrict to a uniform ceiling-to-floor height
Jung et al. [23]	2.5D Approach	Improve the 2.5D approach by Hong et al. [26] Model wall openings including windows and doors	Restrict to a uniform ceiling-to-floor height
Abdollahi et al. [48]	2.5D Approach	Model-driven approach based on a 2D rectangular primitive to generate a 2D floor model Estimate a ceiling-to-floor height using a point height histogram	Unable to detect and model wall openings Restrict to the uniform ceiling-to-floor height
Mahmoud et al. [50]	2.5D Approach	Floor boundary modeling with α-shape and RANSAC Compute an average ceiling height of a point cloud Detect and model wall openings	Restrict to the uniform ceiling-to-floor height
Xiong et al. [27]	3D Approach	Employ a region growing to detect planar patches Model wall openings including windows and doors	Lack of a geometric consistency Require the position information of scanning sites
Xiao and Furukawa [49]	3D Approach	Create volumetric 3D models textured with images Reconstruct a large-scale building using an inverse CSG	Unable to detect and model wall openings Unable to identify and model individual structural elements
Jung et al. [37]	3D Approach	Planar segmentation using 3D RANSAC 3D tracing boundary to planar segments	Computationally intensive for 3D segmentation Extract irregular 3D outlines caused by over-segmentation

). The 2.5D modeling approach is used to create a 3D Model by vertically extruding a 2D floor model (or a footprint) with a height estimate. For example, Hong et al. [26] proposed the parametric reconstruction method that converts a projected point cloud into a binary image to extract the floor boundary, followed by a refinement process that sequentially involves the Douglas-Peuker-based segmentation and the constrained least square method. Meanwhile, to estimate the height between the ceiling and the floor, the random sample consensus (RANSAC)-based plane fitting method is employed to detect point cloud data with minimum and maximum heights. Jung et al. [23] further enhanced this method, where the inverse binary image of wall-segmented point cloud is employed to detect and model windows and doors, thereby enhancing the semantic representation of the 3D model. The model-driven reconstruction method, presented by Abdollahi et al. [48], also utilized the binary image to generate 2D floor models. In this method, a predefined rectangular primitive is used to model major parts of building interiors. The remaining intrusion and protrusion parts are additionally modeled to increase the level of detail (LOD) of the floor model. To create a 3D model, the point height histogram is applied to estimate the floor-ceiling height. The model-driven reconstruction method is ideal for automation only when predefined primitives conform to the geometrical configuration of a building component. However, over-segmentation or under-segmentation issues persist, potentially leading to inaccuracies in geometric representation and requiring additional post-processing to refine the reconstructed model. In another study, Mahmoud et al. [50] generated a 2D floor model by projecting a ceiling-segmented point cloud using the 3D RANSAC method. The Alpha shape algorithm and 2D RANSAC methods are applied to extract line segments of the 2D floor model. The average ceiling height of the point cloud is then used to create a 3D model. The 2.5D modeling approach is widely adopted for as-built BIM due to its computational efficiency. By projecting 3D point clouds onto a 2D plane while retaining height as an attribute, this approach significantly reduces data volume and computational resource requirements, particularly for large-scale building components. However, accurately modeling building components with non-uniform floor and ceiling heights, especially for stairways, remains a significant challenge.

The 3D modeling approach has the potential to create complex indoor structures of building components, as a 3D model is directly created from raw point clouds. However, few methods have been developed, due to its significant computational complexity and cost associated with processing and structuring massive, unorganized point clouds. Xiong et al. [27] proposed the automatic 3D modeling method that employs the region growing method to detect planar patches from the voxelized point cloud. The shape grammar and contextual relationships are formulated to semantically interpret each planar patch such as wall, floor, and ceiling. Adjacent planar patches are then intersected to form the 3D model. However, the intersection of planar patches is not mathematically rigorous, and the locations of openings require the position of the laser scanner. Xiao and Furukawa [49] developed the inverse constructive solid geometry (CSG)-based method to reconstruct a 3D model, where the Hough transformation is used for segmentation of point cloud into horizontal slices. Cuboid primitives are then fitted and combined to reconstruct a 3D model for each slice. The stacked slices approximately represent large-scale built environments. The resulting model has a non-parametric mesh structure textured by captured images that depict windows and doors. Despite its visually realistic representations, structural elements cannot be individually identified or edited within BIM environments. Jung et al. [37] employed the 3D RANSAC method to segment point clouds for 3D plane extraction. Noise points are subsequently removed, and outlines of planar segments are traced to create a 3D model. The resulting model demonstrates complex building interiors, including doors and windows. However, a computationally intensive process is required for segmentation and refinement of the point cloud. Moreover, the 3D model exhibits an irregular shape, due to over-segmentation artifacts.

1.3. Problem Statement and Research Objective

The need for up-to-date 3D indoor models has risen substantially in the rapid and dynamic nature of integrated applications of DT and BIM. In the BIM maintenance workflows, it is common to update the specific building component where changes occurred rather than reconstructing the entire building interior at once. As indicated from the previous sub-section, the 2.5D modeling approach is feasible to update an as-designed (or outdated) 3D model in BIM, due to its ability to focus on a building component, leveraging geometrical constraints and incremental integration of structural elements. However, several challenges remain: (1) reliance on a 2D floor model as a base primitive for reconstruction imposes limitations on the modeling of a building component with varying floor and ceiling heights, and (2) opening detection and modeling are essential to enrich the semantic representation of a 3D model.

In this regard, the main objective of this study is to develop a semi-automatic 3D model reconstruction method that improves the accuracy and efficiency of as-built BIM updates while addressing the limitations of the 2.5D modeling approach. Despite the increasing prevalence of complex and non-rectilinear architectural designs in contemporary buildings for aesthetic purposes, a majority of building structures still adhere to the Manhattan-world design due to its advantages in spatial optimization, construction process simplification, and resource utilization [39]. Thus, for verification and validation purposes, the proposed method is specifically applied to the Manhattan-world structured building components including an office room, a hallway, and a stairway. The present paper is organized as follows: In Section 2, the developed methodology is fully described from a theoretical standpoint. Section 3 shows case studies to demonstrate the feasibility of the proposed method. Finally, in Section 4, the main findings of the study are discussed along the future research.

2. Methodology

2.1. Overview

The proposed method is illustrated in Figure 1, in which indoor point clouds are processed to create a 3D wireframe model that is used to generate a 3D as-built BIM model. The reconstruction process consists of three main steps: preprocessing, multi-dimensional primitives modeling, and 3D as-built modeling.

In the preprocessing step, the virtual points are created for the pose normalization that refers to reorienting the dominant axes of the point cloud along the axes of the Cartesian coordinate system. The spatial extent of original point cloud, associated with virtual points, is then measured using an Axis-Aligned Bounding Box (AABB). In the multi-dimensional primitives modeling, lines, rectangles, and cuboids are progressively extracted from the point clouds in each coordinate plane (i.e., XY, YZ, and XZ-planes). Initially, original point clouds are projected onto each coordinate plane to create 2D binary images. Boundary lines are extracted using a tracing grid, followed by a refinement process based on a line segmentation. Then, the enclosed area defined by the boundaries is divided into sets of rectangles along vertical lines. Each rectangle is extruded into a cuboid based on the measured indoor extent. In the 3D as-built modeling, a wireframe model is reconstructed through Boolean operations. Specifically, cuboids on each coordinate plane are merged using union operations to create 3D solid models, which are then intersected to derive a model that retains only the common space. In addition, a wall opening model is generated to represent elements such as windows and open doors in the main structural model. The point clouds are segmented for each corresponding wall and then projected onto 2D grid plane to create inverse binary images. Subsequently, rectangular wall openings are identified through histogram analysis, and their boundaries are extracted. The wall opening model is then re-projected into the main structural model.

2.2. Preprocessing

In the preprocessing step, the virtual points, created from the point cloud, are primarily utilized for pose normalization. Once the virtual points are rotated and realigned with the axes of the Cartesian coordinate system, the point cloud associated with each virtual point are retrieved for spatial dimension estimation.

2.2.1. Three-Dimensional Virtual Point Creation

Although laser scanner is capable of acquiring high-density point clouds with millimeter-level precision, the huge size of data requires a significant amount of time to process all points. In order to expedite point processing, the point clouds are resampled using 3D virtual grid. The virtual point is a voxel-centered representative point that stores indices of the original points within the voxel. These virtual points are generated based on the coordinates of the original points according to a predefined voxel size, as follows:

$$\begin{array}{c}{X}_{vp}=Round({\displaystyle \frac{X_{op}}{S}})\times S\\ Y_{vp}=Round({\displaystyle \frac{Y_{op}}{S}})\times S\\ Z_{vp}=Round({\displaystyle \frac{Z_{op}}{S}})\times S\end{array}$$

(1)

In Equation (1), $X_{vp},Y_{vp},Z_{vp}$ denote the virtual point coordinates, $X_{op},Y_{op},Z_{op}$ denote the original point coordinates, and $s$ is the voxel size. Figure 2 illustrates the original points from the laser scanner and the creation of 3D virtual points in Cartesian coordinates. In Figure 2, each virtual point corresponds to the center of a voxel and stores 3D coordinates of the original points within the voxel. The data structure not only significantly reduces the number of points but also enables efficient access to the original points when required.

2.2.2. Pose Normalization and Dimension Estimation

Although the virtual point reduces the number of points from the laser scanner, they may have arbitrary orientations in the coordinate system, as illustrated in Figure 3a. Direct projection onto the XY, YZ, and XZ planes can result in geometric distortion. This distortion makes it difficult to accurately extract geometric primitives for reconstructing structural elements. Therefore, the pose normalization is conducted to align the point clouds with the coordinate axes (Figure 3b).

In Manhattan-world structures, the pose normalization can be simplified to the problem of minimizing the volume of the AABB of the point cloud [51]. Meanwhile, according to [52], if the areas of the bounding boxes of a 3D object’s projections onto the coordinate planes are minimized, then the volume of the bounding box is also minimized. Consequently, pose normalization can be formulated as the process of finding a transformation that minimizes the area of the 2D bounding boxes of the point cloud projected onto the coordinate planes.

In the pose normalization of the virtual points, only the XY plane is considered since terrestrial laser scanner collects point clouds in a fixed orientation with respect to the gravity direction (Z-axis). Figure 4 shows the flowchart of the pose normalization process, where the x and y coordinates of virtual points are rotated counterclockwise around the Z-axis from 0° to 90° at 0.1° steps, and the area of the 2D bounding box is calculated at each angle. The angle that yields the minimum area is selected and applied to the original point clouds to align them with the coordinate axes.

To extend the geometric primitives extracted from each coordinate plane into 3D, it is necessary to determine the spatial extent of the indoor environment. In the dimension estimation, the original point cloud is retrieved from the virtual point. The AABB, computed from the minimum and maximum coordinates along the x, y, and z axes, is then used to measure the width, length, and height of the indoor space. These dimensions are used to extrude the planar primitives into volumetric primitives for 3D modeling described in the next section.

2.3. Multi-Dimensional Primitive Modeling

In the multi-dimensional primitive modeling step, the geometric primitives of the building component are progressively reconstructed from the point cloud projected onto the XY-, YZ-, and XZ-planes. For each plane, the boundary enclosing the projected point cloud is extracted and partitioned into 2D rectangles. The length, width, and height, which are estimated from the AABB in the preprocessing step, are then selectively applied according to the projection plane to extrude the 2D rectangles for cuboid generation.

2.3.1. Boundary Line Modeling

In this process, boundary lines are extracted to delineate the outer shape of the building component on the XY-, YZ-, and XZ-planes. Initially, point clouds, aligned with the Cartesian coordinate system, are projected onto each coordinate plane. Binary images at the predefined gird size are then generated (Figure 5a). Subsequently, boundary tracing is applied to sequentially search the outermost occupied pixels, extracting the outline connected by line segments. However, the traced boundary appears irregular due to the inherent noise (Figure 5b). Therefore, in this study, the refinement process is designed to merge multiple line segments into a single straight line, preceded by a line segmentation process. The line segmentation method based on the Douglas–Peucker algorithm is employed to identify the corner points of boundary lines and to group the line segments between them into a single line component [26]. However, when noise is severe, the segmentation process may result in over- or under-segmentation. Therefore, a further process is applied to two adjacent segmentation groups. In the sequentially grouped line segments, if the angle between two consecutive segments is less than or equal to 45 degrees, the two groups are merged into a single group (Figure 5c).

To obtain a compact geometric representation, a straight line is modeled from each group of line segments (Figure 5d). As the boundary line components under the Manhattan-world structure should be either vertical or horizontal, the Hessian line model is used to stably represent lines in all directions. The formulation is presented based on the XZ-plane projection (Equation (2)), where $\theta$ is the angle between the normal vector of the line and the X-axis, and $\rho$ is the shortest distance between the origin and the line; $x$ and $z$ denote the coordinates of the points on the line segment.

$$xcos\theta +zsin\theta =\rho$$

(2)

To calculate the line parameters, Hough transform is applied to the points that constitute each line segment. A straight line is sequentially modeled from each segmented group, and the boundary corners are then computed by the intersections of adjacent lines.

In the boundary line modeling, the geometric properties of the building component must be considered for selecting parameters. The grid size, which defines the resolution of the binary image, should be less than half the size of the smallest structural element in the building component, ensuring that its length and orientation can be correctly extracted. For example, Figure 6a shows the sample binary image generated by projecting the stairway point cloud on the XZ-plane. When the grid is smaller than half the smallest structural element, the stepped shape in Figure 6a is approximately preserved as illustrated in Figure 6b. In contrast, the larger grid size causes the stairway to become indistinguishable (Figure 6c). For the line segmentation using the Douglas–Peucker, the threshold should be selected within the range between the grid size and the length of the smallest structural element. When the threshold is smaller than the grid size, the extracted line in Figure 6b is over-segmented into many fragmented segments (Figure 7a). Conversely, when the threshold exceeds the smallest structural element, the under-segmentation merges multiple stairs into a single segment (Figure 7b). In Figure 7c, by selecting a threshold within the optimal range, the extracted line segments are appropriately grouped into distinct structural elements of the stairway.

2.3.2. Rectangle and Cuboid Modeling

In the rectangle and cuboid modeling, the boundary extracted on each coordinate plane (i.e., XY-, YZ-, and XZ-planes) is converted into a set of rectangles. The dimension measurements (i.e., length, width, and height) estimated from the AABB in the preprocessing step are then selectively applied to these rectangles to generate cuboids from the three coordinate planes. For example, in Figure 8, the boundary line defines the structural outline of a building component on the XZ-plane. The rectangles are sequentially generated by extending the vertical line segments, to which the width measurement is used to extrude the rectangles along the Y axis. The resulting cuboids represent the full volumetric extent from the boundary line on the XZ plane.

2.4. Three-Dimensional As-Built Modeling

2.4.1. Three-Dimensional Wireframe Modeling

The cuboids generated from each coordinate plane represent the 3D shape of the indoor space along their respective planes. However, they are limited in representing geometric space along the other coordinate axes. Therefore, an integration process is followed to completely reconstruct the main structure of the indoor space. In this process, Boolean operations are applied to the cuboids to create a 3D indoor model (Figure 9). First, a union operation is used on the cuboids generated from the same plane to form a 3D model. Next, an intersection operation is performed on these three plane-wise solid models (XY, YZ, and XZ models). This intersection process creates the final shape by retaining only the common volumetric space, effectively cropping the extruded boundaries to match the main structure of the indoor space. Finally, a wireframe model is generated by extracting the boundaries of the solid model, which simplifies the representation and allows for easy identification of the main structure of the indoor space.

2.4.2. Wall Opening Modeling

In the building components, openings in wall structures are usually categorized as either doors or windows. The wall opening modeling involves segmenting wall points and detecting openings using histogram analysis. The vertical faces of the integrated solid model serve as a reference for segmenting wall points. A buffer zone is formed around each vertical face to determine its corresponding wall points. To expedite querying, virtual points from a preprocessing step are used. If a virtual point is within the buffer zone, the points linked to it are segmented as the wall points to that face.

Since doors and windows are generally represented as rectangular forms in most buildings, opening detection is based on bounding box processing. After the wall points segmentation, the points in each wall are projected onto the wall coordinate system at a predefined grid size. An inverse binary image is then generated where occupied pixels are represented as 0 and others as 1 (Figure 10a). Subsequently, clustering based on pixel connectivity is conducted on the unoccupied pixels in the binary image (Figure 10b). Then, clusters with a small bounding box size are excluded from the candidate set (Figure 10c).

The opening of a rectangular form has consistent width and height, which results in a uniform distribution of white pixels along each row and column. Therefore, this characteristic can be used to determine the shape of the cluster through a histogram analysis (Figure 11). The row histogram is calculated according to the white pixels in each row of the bounding box, as shown in Figure 11a. If the proportion of rows where the number of white pixels exceeds half of the peak white pixel count in the row histogram is above a threshold, the cluster is retained. Otherwise, it is excluded from the opening candidates. The same process is applied to columns, where a column histogram is constructed by counting white pixels in each column, as shown in Figure 11b.

After valid openings are identified, boundary tracing is conducted. The Hough transform is applied to extract the four sides of a rectangle, such as doors or windows, by deriving two vertical and two horizontal lines. The corner points are then calculated from the intersections of these lines. Finally, their coordinates in each wall coordinate system are transformed into the coordinate system of the 3D wireframe model. However, in case where a window (or door) protrudes from the wall, the identical opening may be redundantly detected on the multiple planes. To determine the valid opening, the wall outline of the 3D wireframe model is used as the criterion for filtering redundant openings. The openings are preserved only if they lie within the wall outline. Otherwise, they are discarded as invalid detections.

3. Test Site and Application

3.1. Overview

To validate the performance of the proposed method, three test sites were selected with different levels of structural complexity and clutter: an office, a hallway, and a stairway, as shown in Figure 12. The office has varying ceiling heights and contains various types of clutter (i.e., desks, chairs, and partitions), whereas the hallway has a consistent ceiling height but is relatively large and includes a corner. The stairway is more complex due to variations in floor height. In scanning test sites, point clouds were collected using FARO Focus M70 Laser scanner, which was moved to several locations to minimize occluded regions caused by clutter.

Table 2. Scanning results of the test sites.

	Office	Hallway	Stairway
Number of scans	3	17	7
Number of points	3,567,835	13,052,382	3,835,159
Data size(.xyz)	160 mb	637 mb	168 mb

shows the scanning results after registration and the removal of outdoor noise. The proposed method is implemented in MATLAB R2021b and Python 3.7 and performed on Windows 10(64bit) with Intel(R) Core (TM) i9-12900F CPU @ 2.40 GHz, 128GB RAM.

3.2. Three-Dimensional Virtual Point Creation and Pose Normalization

To expedite the time-consuming pose normalization of massive point clouds, virtual points were generated as an initial step. As the virtual points and the pose normalization process are directly influenced by the voxel size, the experiment was conducted with voxel sizes ranging from 1 cm to 13 cm at 1 cm intervals (

Table 3. Effect of voxel size for pose normalization and processing time.

Voxel Size	Office			Hallway			Stairway
	Rotation Angle (°)	Time (s)	Unique Virtual Points (Number)	Rotation Angle (°)	Time (s)	Unique Virtual Points (Number)	Rotation Angle (°)	Time (s)	Unique Virtual Points (Number)
Original	27.6	48.9		29.7	185.4		32.5	66.7
1 cm	27.6	19.8	373,186	29.7	63.4	1,300,555	32.5	18.2	201,797
2 cm	27.6	6.4	93,906	29.7	19.5	326,919	32.5	4.8	50,882
3 cm	27.6	2.9	41,950	29.7	10.5	146,021	32.5	2.6	22,777
4 cm	27.6	2.0	23,731	29.7	6.8	82,554	32.5	1.6	12,904
5 cm	27.6	1.4	15,256	29.7	4.7	53,112	32.5	1.2	8322
6 cm	27.6	1.1	10,648	29.7	3.9	37,061	32.5	0.9	5817
7 cm	27.6	0.9	7862	29.7	3.4	27,369	32.5	0.8	4302
8 cm	27.6	0.8	6051	29.7	3.0	21,057	32.2	0.7	3318
9 cm	27.6	0.7	4805	29.7	2.6	16,715	32.5	0.6	2639
10 cm	27.6	0.7	3913	29.7	2.4	13,609	32.5	0.6	2153
11 cm	27.5	0.7	3251	29.7	2.2	11,299	32.1	0.6	1790
12 cm	27.6	0.7	2746	29.6	1.9	9537	33.4	0.5	1516
13 cm	27.6	0.6	2348	29.7	1.7	8171	33.3	0.5	1298

). The optimal voxel size threshold was then determined for the pose normalization within a reasonable time. The experiment results show that the rotation angle remains nearly identical to that of the original point cloud until a specific voxel size threshold is reached. However, the processing time is significantly affected by the number of virtual points with unique x and y coordinates (referred to as unique virtual points hereinafter) and their horizontal extents on the XY plane. As shown in Table 2, although the stairway contains more original points than the office, the number of unique virtual points in the stairway is smaller than that in the office, resulting in a shorter processing time for the stairway. In particular, the vertically oriented stairway requires less processing time compared to the horizontally expansive hallway. This confirms that unique virtual points effectively reduce the number of points and processing time. Based on these results, a voxel size of 10 cm was selected for virtual point creation across all test sites, as it commonly provided the most significant reduction in processing time without compromising the accuracy of the pose normalization. As Figure 13 illustrates, original point clouds with arbitrary orientations are correctly aligned with the coordinate axes after the pose normalization.

3.3. Three-Dimensional Wireframe Model Reconstruction

In this step, boundary lines, rectangles, and cuboids are hierarchically extracted to reconstruct a 3D wireframe model. As the boundary lines directly influence the model’s accuracy and level of detail, it is necessary to determine the optimal grid size and the threshold for the line segmentation method. Figure 14 shows the results of boundary tracing. The 3D point clouds were projected onto a 2D grid plane, creating a binary image in which a pixel is occupied if it contains at least one point (Figure 14a). In the boundary tracing, a smaller grid size delineates more precise outlines but is more sensitive to noise and increases the computational load (Figure 14b). In contrast, a larger grid size allows faster outline extraction, but it excessively simplifies the outlines, limiting the representation of detailed shapes (Figure 14c). The optimal grid size should be selected based on the precision of model and processing time. Figure 14d illustrates an example with the optimal grid size, where the outlines were clearly extracted.

However, as the initial boundary extraction produces irregular line segments due to noisy points (Figure 15a), a refinement process using a line segmentation was applied. A low threshold subdivides the line segments, enabling the representation of complex indoor structures, but the segments become over-segmented and are depicted in irregular shapes (Figure 15b). On the other hand, a high threshold can effectively simplify the outlines, but the segments become under-segmented, limiting the representation of details (Figure 15c). Figure 15d shows the boundary modeled with the optimal threshold. The grid size and threshold were experimentally selected for each test site and coordinate plane, as shown in

Table 4. Parameter selection for the boundary line modeling.

Plane	Office		Hallway		Stairway
	Grid Size (cm)	Threshold (cm)	Grid Size (cm)	Threshold (cm)	Grid Size (cm)	Threshold (cm)
XY	3	3	1	7	1	1
YZ	1.5	1.5	2	4	2	2
XZ	0.5	1.5	0.5	2.5	2.5	5

.

Assuming a Manhattan-world structure, the rectangular modeling process divides the area enclosed by the boundaries into rectangular units according to the vertical line components. The number of rectangles depends on the complexity of the boundaries. The rectangles are then extruded into cuboids based on the spatial extent of the indoor space measured during the preprocessing step, representing the 3D shape of the interiors. Figure 16 illustrates the 3D wireframe model reconstructed by applying union and intersection operations to the multi-dimensional geometric primitives hierarchically extracted on each coordinate plane. The 3D wireframe models of an office and a hallway, generated by the identical process as the stairway, are shown in Figure 17.

3.4. Wall Opening Model Reconstruction

In wall opening modeling, wall point segmentation was initially performed. Since walls are vertical, wall points can be segmented using a 20cm buffer zone around the vertical faces of the 3D wireframe model (Figure 18a). As the wall opening model is reconstructed by tracing the boundaries of the void areas in an inverse binary image, it is necessary to consider the optimal grid size. While a small grid size can precisely represent an opening, it poses constraints on modeling because it is time-consuming and results in an irregular shape due to complex outlines. Conversely, a large grid size is robust to noise but lacks precision. With the optimal grid size, the result is shown in Figure 18b. The grid size was determined experimentally: 2.5 cm for the office and stairway, and 2 cm for the hallway. However, due to noisy points, the traced boundary appeared irregular instead of a straight line. Therefore, a refinement process was followed using the Hough transformation to represent the four sides of the rectangular shape as straight lines (Figure 18c). The wall opening models in each wall coordinate system were then transformed into the coordinate system of the 3D wireframe model (Figure 18d). Figure 19 illustrates the 3D wireframe models, which include the opening models, created for an office and a hallway, respectively.

Table 5. Processing time for each modeling step.

Process	Office	Hallway	Stairway
Pre-processing (s)	0.855	2.531	0.724
Multi-dimensional primitive modeling (s)	1.833	7.014	1.867
3D wireframe modeling (s)	0.054	0.969	0.156
Wall opening modeling (s)	0.812	9.471	0.985
Total (s)	3.554	19.985	3.732

shows the processing time for each step, with total time consumptions of 3.554 s, 19.985 s, and 3.732 s for the office, hallway, and stairway, respectively. In the office and stairway, the multi-dimensional primitives modeling step required the most time, due to the repeated processing of binary image pixels to extract lines. For the hallway, considerable time was required not only on primitives modeling but also on wall opening modeling. Since the hallway is composed of multiple walls, the wall opening modeling was performed repeatedly for each wall, which significantly increased the total processing time.

3.5. Accuracy Assessment

The final 3D wireframe model was compared with a set of total station measurements as reference points. The reference points were selected from clearly identifiable vertices. Also, to estimate overall quality of the wireframe models, reference points are well-distributed throughout the test sites (Figure 20). In the office and stairway, 15 and 17 reference points were measured, respectively, while in the hallway, which is relatively larger in scale, 23 reference points were measured. A 3D rigid transformation was performed to transform the coordinates of the 3D model into the coordinate system of reference points. The accuracy of the 3D wireframe model was evaluated by the Euclidean average distance error (${\delta }_{avg}$) between corresponding points on the model and the reference points (Equation (3)), where $n$ is the number of measured points, $a_i$ is the $i$-th corner point of the 3D wireframe model, $b_i$ is the $i$-th reference point, and $R$ and $t$ represent the rotation matrix and translation vector, respectively.

$${\delta }_{avg}={\displaystyle \frac{1}{n}}{\sum }_{i=1}^n‖R{a}_i+t-b_i‖$$

(3)

Figure 20 illustrates the vertices of the 3D wireframe model corresponding to the reference points and

Table 6. Accuracy assessment results for the office (bold indicates comparatively larger errors).

Reference Point	X (m)	Y (m)	Z (m)	Error (m)
1	0.002	−0.018	−0.002	0.018
2	−0.008	−0.018	−0.006	0.020
3	−0.010	−0.026	0.022	0.035
4	−0.005	−0.022	0.006	0.023
5	−0.026	−0.002	0	0.026
6	−0.037	−0.013	−0.010	0.040
7	−0.008	0	−0.010	0.013
8	−0.026	−0.002	−0.007	0.027
9	0.011	0.005	−0.006	0.014
10	0.016	0.005	0.015	0.023
11	−0.002	0.003	0.021	0.021
12	0.012	0.011	0.002	0.016
13	0.042	0.028	−0.042	0.066
14	0.050	0.025	0.023	0.061
15	−0.012	0.024	−0.006	0.028
Average	0.018	0.013	0.012	0.029
RMSE	0.023	0.017	0.016	0.033

,

Table 7. Accuracy assessment results for the hallway (bold indicates comparatively larger errors).

Reference Point	X (m)	Y (m)	Z (m)	Error (m)
1	−0.040	0.010	0.015	0.044
2	−0.001	−0.017	0.021	0.027
3	−0.008	0.018	−0.037	0.042
4	−0.002	−0.004	−0.032	0.033
5	0.008	−0.010	0.016	0.021
6	0.004	−0.002	−0.036	0.037
7	0.010	−0.018	0.031	0.038
8	−0.002	0.003	0.021	0.021
9	0.009	−0.004	0.021	0.023
10	0.020	−0.009	−0.033	0.040
11	0.007	−0.010	0.019	0.023
12	0.019	−0.027	0.007	0.033
13	0.025	0	0.005	0.026
14	0.019	−0.005	−0.017	0.026
15	0.028	0.005	−0.031	0.042
16	0.030	0.028	0.013	0.043
17	−0.015	0.015	−0.014	0.025
18	−0.004	−0.015	0.022	0.027
19	−0.022	−0.007	0.027	0.036
20	−0.008	−0.014	−0.015	0.022
21	−0.032	−0.006	0	0.032
22	−0.003	0.047	0.008	0.048
23	−0.042	0.024	−0.010	0.049
Average	0.016	0.013	0.020	0.033
RMSE	0.020	0.017	0.022	0.034

and

Table 8. Accuracy assessment results for the stairway (bold indicates comparatively larger errors).

Reference Point	X (m)	Y (m)	Z (m)	Error (m)
1	0.001	0.026	0.035	0.043
2	−0.004	−0.017	−0.043	0.046
3	0.005	−0.015	0.018	0.024
4	−0.018	0.013	0.018	0.028
5	0.024	−0.022	0.014	0.035
6	0.003	0	−0.014	0.014
7	−0.010	−0.030	−0.021	0.038
8	−0.025	0.016	−0.015	0.034
9	0.026	−0.008	0.010	0.028
10	−0.002	0.013	−0.018	0.022
11	0.031	0	−0.003	0.031
12	−0.023	0.002	0.007	0.024
13	0.013	−0.010	−0.008	0.019
14	−0.026	0.006	−0.002	0.027
15	0.012	0.003	0.010	0.016
16	−0.032	0.009	0.009	0.035
17	0.026	0.015	0.004	0.031
Average	0.017	0.012	0.015	0.029
RMSE	0.020	0.015	0.018	0.030

list the error vectors. The quality of the model was quantified by average errors of 0.029 m, 0.033 m, and 0.029 m for the office, hallway, and stairway, respectively. Additionally, the 3D wireframe model was assessed using Root Mean Square Error (RMSE), which is more sensitive to outliers (Equation (4)).

$$RMSE=\sqrt{{\displaystyle \frac{1}{n}}{\sum }_{i=1}^n{‖{Ra}_i+t-b_i‖}^2}$$

(4)

The RMSE for the office, hallway, and stairway was calculated as 0.033 m, 0.034 m, and 0.030m, respectively, with the RMSE values for each axis direction listed in Table 6, Table 7 and Table 8. Since the 3D wireframe models were reconstructed by integrating the models created from each coordinate plane, the errors along the X, Y, and Z axes were compared. In each test site, the deviation was within 5–7 mm, indicating a relatively uniform accuracy without directional bias. In particular, relatively large errors were concentrated on the vertices of openings, as highlighted by the yellow markers in Figure 20. These deviations could be due to reduced point cloud precision caused by discontinuities at frame edges, as well as uncertainty in the positions of corner points caused by silicone sealant between the glass and the frame.

3.6. Three-Dimensional As-Built BIM Creation

In this study, the 3D wireframe model serves as a reference for creating the 3D as-built BIM model. The wireframe models significantly reduced data sizes compared to the point clouds, enhancing the efficiency of processing, storage, and management. Also, structural elements (i.e., walls, ceilings, floors, doors, and windows) with simplified lines completely depict even occluded areas, enabling modelers to easily identify the structural elements and facilitating the reconstruction of accurate models. The wireframe models, formatted as DXF files, were imported into the BIM tool (AutoCAD Revit 2024) to create 3D as-built BIM models that reflected the structural elements while excluding clutter such as furniture (Figure 21).

4. Discussion and Conclusions

Recently, indoor digital twins, integrated with BIM, IoT sensors, and big data analytics, have been utilized in a variety of applications such as air quality monitoring and energy optimization. To maximize the effectiveness of these technologies, it is crucial to reconstruct an up-to-date 3D model rapidly and accurately. Although numerous methods have been proposed to reconstruct a 3D model, limitations still remain in modeling building components with varying floor and ceiling heights. Therefore, to improve the accuracy and efficiency of as-built BIM updates, this study proposes a semi-automatic 3D modeling method consisting of three main steps: preprocessing, multidimensional primitive modeling, and 3D as-built modeling.

The major contributions of this study are as follows. First, a simple pose normalization process was proposed to enable direct projection onto each coordinate plane, thereby ensuring rapid and accurate alignment of point clouds. Second, applying Boolean operations to geometric primitives enables the simple reconstruction of complex indoor structures while eliminating redundancies, resulting in a coherent 3D model. Additionally, the extracted lines from the multi-dimensional primitives modeling can also serve as architectural drawings. Third, the proposed method produces a complete 3D indoor wireframe model that incorporates the main structural elements, including ceilings, floors, walls, windows, and open doors, even in the presence of clutter and occlusion. In particular, the method can also handle complex indoor designs, such as variations in ceiling and floor heights or protruding window frames. The proposed method was assessed by using point clouds collected from a single building component with Manhattan-world structure, an office, a hallway, and a stairway. The accuracy evaluation showed an RMSE of approximately 3 cm, which is well within the Level 1 tolerance (±5.1 cm) specified in the GSA BIM Guide [53].

Although the proposed method is effective for reconstructing 3D as-built BIM models, several limitations remain. First, the proposed method needs to be developed for a large scale of a building interior composed of multiple-room and multi-story environments. Second, the proposed method is limited to reconstructing closed doors, window surfaces obscured by opaque materials such as blinds or curtains, and small subdivided window panes. Therefore, in future work, a deep learning-based point cloud segmentation needs to be developed to distinguish individual building components as well as to various opening objects. Since the modeling parameters must be determined heuristically depending on the indoor environment, a new adaptive method is required that can automatically adjust the parameters according to the characteristics of the indoor space. Furthermore, the proposed method is based on the strong Manhattan-world assumption, where the main structural elements are rectangular and intersect orthogonally. To broaden its generality, a novel approach should be developed to model irregular angled or curved walls, slanted ceilings, and other atypical structural configurations. Also, a building DT includes a broader range of indoor structures and facilities. To fully realize a building DT, it is essential to develop the 3D modeling method to reconstruct Mechanical, Electrical, and Plumbing (MEP) systems (i.e., pipes and cables).