*3.2. Methods*

3.2.1. Three-Dimensional Object Recognition

As soon as the point cloud assessment was completed, the as-built model was incorporated into the Revit interface. Therefore, a transformation matrix was established where a planned model was fixed. The point cloud model was then transformed to match the reference model automatically. It was stated that the point cloud was clumsy enough to be recognized. Thus, the point cloud set was transformed into a geometry-based model, as mentioned thoroughly in Algorithm 1.

After the geometry-based model was established, the proposed approach was introduced to initiate this recognition system representing the correspondence between the BIM-planned model and the as-built model. The proposed approach depended on three main aspects. Firstly, the alignment accuracy between the two models was vital to object recognition. Secondly, the recognition approach was based on three distinctive features called the Lalonde features [44]. It was also used for the linerarness, surfaceness, and scatterness of a 3D point cloud set [45,46]. Finally, at least 95% of an element would intersect with the geometry model to be considered a recognized element, as declared thoroughly in Algorithm 2. In other words, Algorithm 2 searches through the BIM-planned model to find the closest geometry to each BIM-placed object. If the BIM-planned object is found, the actual component is classified based on the object type in the BIM-planned model.


**Algorithm 2**: Comparison between the geometry-based model and BIM-planned elements


Then, a color-coding system was established to demonstrate the condition of each element based on its recognition and scheduling state, as illustrated in Table 2. Each color would represent the recognition and scheduling state and determine whether it would be included in the calculation for automated schedule and cost.

**Table 2.** Color Coding of elements according to Algorithm 2.


### 3.2.2. Automated Schedule and Cost Control

To update the project's status in terms of schedule and cost (4D, 5D), the authors developed two algorithms based on the results of the object recognition system. On one hand, Algorithm 3 calculated the 4D updated status based on the BCWS and BCWP estimated from the BIM-planned model and the geometry-based model, respectively, where budgeted unit cost was inserted into the algorithm. The element's color would also determine whether its cost would be included. Then, the schedule performance index (SPI) was calculated automatically to review the schedule status of a project.

**Algorithm 3:** Calculate the automated schedule progress

```
Input: Structural elements E, Linkstructural elements LE, Budget unit cost BCost
Concrete Volume Vc
Output: Geometry Model Cost GM Cost, BIM-planned model total cost BIMM TC, SPI
1 For Each Category in E
2 Get Vc For category
3 Calculate Category cost From BCost and Vc
4 BIMM TC = Category Cost
5 End
6 For Each L in Redelement
7 Calculate Red TC From BCost and Vc Red
8 End
9 For Each LE in Greenelement
10 Calculate Green TC From BCost and Vc Green
11 End
12 For Each LE in Yellowelement
13 Calculate Yellow TC From BCost and Vc Yellow
14 End
15 GM Cost = BIMM TC − Red TC + Green TC + Yellow TC
16 SPI = GM Cost/BIMM TC
17 If SPI > 1
18 Then Print "Ahead of schedule."
19 Else If SPI < 1
20 Print "Behind schedule."
21 Else Print "Within schedule."
22 End If
23 End
```
On the other hand, Algorithm 4 calculated the 5D updated status based on the BCWP and ACWP estimated from the geometry-based model and the revised BIM-planned model, respectively, where the actual unit cost was inserted into the algorithm. The element's color would determine whether its cost would be included. Then, the cost performance index (CPI) was calculated automatically to review the cost status of the project.



#### *3.3. Case Study*

The data comprises a set of four field laser scans obtained from an investment building in The Rawda Administration Center, mainly consisting of reinforced concrete frame structure and Hardy slabs. The project location is [24.795813, 46.839646] beside Shaikh Isa Bin Salman Al Khalifah Rd, Al Maizilah, Riyadh. The site image of the case study is shown in Figure 2.

**Figure 2.** Site Image of the case study.

The construction site was scanned using Faro Focus3D [47] between 25 December 2020 and 20 January 2021. The weather on the days of the survey was hot; however, with a clear sky and low wind.
