# Algorithm for Generating 3D Geometric Representation Based on Indoor Point Cloud Data
## 2 Literature Review  
Previous studies focused on the automatic generation method for 3D indoor modeling over the past decades. Recently, there has been an increasing number of studies on generating 3D indoor representation by using the continuity of scanning and a mobile laser scanner (MLS) system to extract trajectory data [1]. Related works on data refinement and processing of indoor PCD are reviewed and analyzed.  
Regarding the process of data refinement that serves as preliminary work to achieve precise results, methods of converting 2D geometric representation into a 2.5D model [12] and generating 3D geometric representation by first partitioning the walls [13] are presented. [PERSON] et al. [14] first created a floor plan of an interior using backpack laser scanners (BLSs) and then generated a 2.5D model by vertically extruding the floor plan using height information acquired through scanning. Because the floor plan and height information are included in the algorithm, furniture and other objects that are not related to the building's main structural members (i.e., ceiling, floor, walls) are removed. However, the maximum error of the generated results was 27 cm because of a height difference inside the building. [PERSON] et al. [13] aimed to detect structural elements based on the geometric characteristics of the PCD. The PCD of nonstructural elements are partitioned into rooms through visibility analysis and a combination of the structural member constraints. The 3D geometry of every room was constructed through optimization based on multiple contiguous fixed partition allocation (MFT). However, the error rate is low only inside a simple building with a rectangular structure. A high possibility of clutter in the openings of a building exists in the case of openings detection, resulting in a detection error. The limitation of the study was that the vector elements of reverse-engineered walls are given a fixed width that is different from that in the actual structure.  
Data processing after data refinement enables the interconnectivity of data [15] and separates structural and nonstructural elements [16]. To overcome the limitations of the previous research, [PERSON] et al. [15] presented an approach to construct a new 3D geometry by setting parameters, interconnectivity, and volume elements as essential components. Through this method, the walls between adjacent rooms are automatically reverse-engineered by generating the normal vector of each wall through given formulas. However, this method has a relatively low opening detection accuracy (85.02%) compared to average accuracy (90.34%) in artificial datasets caused by systemic differences such as vector elements that are not independent and identically distributed. [PERSON] et al. [16] constructed interior and exterior walls in the building with a 3D geometric representation and simplified the process through a graph cut. Even so, this method is also difficult for applications in buildings with complex interiors or nonrectangular floor plans.  
Despite these shortcomings, MLSs continue to be used to increase the efficiency of reverse engineering on large objects such as buildings. Research on the estimation of the normal vector is being conducted to overcome these limitations in that the dimension of a derivable geometric representation is restricted to 2D because of problems with data types and capacity. However, these studies have low applicability because they are limited to a single room or multiple simple-shaped rooms. Therefore, a new algorithm is required to expand the applicability of generating 3D geometric representation.