# Historic Timber Roof Structure Reconstruction through Automated Analysis of Point Clouds

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## Abstract

**:**

## 1. Introduction

#### Related Work

## 2. Materials and Methods

#### 2.1. Roof Structure Site

#### 2.2. Point Cloud Acquisition

#### 2.3. Method

#### 2.3.1. Overview

#### 2.3.2. Combining of Point Clouds

#### 2.3.3. Roof Cover Filtering

#### Preparation of Cutting Reference Surface

_{Center}is middle point of the bounding box of the input point cloud, $(X,Y,Z)$

_{Min}and $(X,Y,Z)$

_{Max}are the limits of the input point cloud.

#### Point Cloud Split into Roof and Interior

_{signed}values mostly represent the roof structure interior, positive values mean that the points are outside of the cutting reference surface point cloud. With the signed distance information, a threshold value t

_{distance}can be specified taking the roof cover material thickness into account to separate the interior part. Usage of the threshold value may exclude some of the beam side face points that are close to the roof cover. This can be avoided by additionally considering the angles between the normal vectors.

_{distance}value. To achieve this, $\alpha $, angle between normal vectors of cutting reference point cloud and input point cloud (Equation (5)), is used for an additional thresholding in Equation (6). The $\alpha $ is visually shown in Figure 5 (right) for both green and blue regions. The points fulfilling Equation (6) are the interior roof point cloud.

#### 2.3.4. Segmentation

- Region-growing-based segmentation.
- Planar sub-segmenting.

_{max}= 0.05 m) is used as homogeneity rule for a region-growing-based segmentation.

_{max}is a threshold value for local angular homogeneity (e.g., 5°).

_{max}value, segmentation result may contain not only planar segments but also non-planar ones. The least squares fitting plane [35] is calculated for all segment points. The root mean square error (RMSE) of plane fitting is the reference value for decision of searching for planar sub-segments. If the plane is not fitting well to all segment points (e.g., RMSE > 0.04 m), the RANSAC algorithm [36] is used to detect multiple planar sub-segments as explained in [19,20].

#### 2.3.5. Shape Classification

- Type-1: Linear shaped segments.
- Type-2: Non-linear segments with separable sub-segments.
- Type-3: Non-linear compact segments.

_{l}and $\lambda $

_{w}, “length” and “width” of a segment, are the largest and second-largest eigenvalues, which are computed for all segment points with principle component analysis [37], A

_{$\alpha $}and A

_{MBR}are the area of the alpha-shape [38] and its minimum bounding rectangle (MBR) for a segment. In conclusion, for a segment, if ${f}_{\mathrm{elong}}$ > 5 and ${f}_{\mathrm{area}}$ > 0.5 then it refers to type-1, if ${f}_{\mathrm{elong}}$ < 4.5 and ${f}_{\mathrm{area}}$ > 0.8 then it corresponds to type-3, while all other cases considered type-2 [20].

#### 2.3.6. Linear Shaped Segment Splitting

#### 2.3.7. Cuboid Fitting and Modeling

- Identification of adjacent beam segments.
- Fit cuboids for beams.
- Intersect beams and analyze the structure.

- Distance of centroid of reference to plane of candidate:$$\left(\right)open="|"\; close="|">{C}_{\mathrm{A}}-{P}_{\mathrm{B}}$$
- Angle between normal vectors:$$arccos(\overrightarrow{{n}_{\mathrm{A}}}\xb7\overrightarrow{{n}_{\mathrm{B}}})\approx [0,90,180,270]$$
- Angle between longitudinal axes:$$arccos(\overrightarrow{{l}_{\mathrm{A}}}\xb7\overrightarrow{{l}_{\mathrm{B}}})\approx [0,180]$$

## 3. Results

^{h}52′52″. The final result (cuboid model) of the main workflow for the entire roof structure of St. Michael is presented in Figure 11 (bottom).

## 4. Discussion

_{max}= 0.05 m, $\alpha $

_{max}= ${5}^{\circ}$ and 600 minimum segment points. The segmentation process resulted in 5533 segments when roof cover is included, while roof cover filtered data resulted with 5165 segments. Thus, roof cover filtering reduced the number of segments by 7%, while the number of points was reduced by 28%. Furthermore, roof cover segments may have shapes similar to beam faces, and thus their removal does not only reduce computation time in later stages but also avoids building beams which are, wrongly, composed of beam faces and roof cover segments.

^{h}45′ manual work duration for both regions. Method 3 is results with 75% of beams modeled.

^{h}18′ for the entire roof structure.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 5.**Side beam faces cut by reference surface (light-blue), interior side face regions (gray) and equivalent orthogonal face (green).

**Figure 7.**Region growing segmentation result (in the

**middle**), planar sub-segmentation with RANSAC (

**left**) and non-linear segment with separable sub-segments (

**right**).

**Figure 9.**Image of a roof cover part from inside (

**a**), point cloud data of the region (

**b**), filtered roof cover (

**c**), interior points after roof cover filtering (

**d**), segmentation result of roof interior after roof cover filtered (

**e**) and segmentation result of the point cloud including roof cover (

**f**).

**Figure 10.**Type-2 segment (

**a**), 2D region growing segmentation on alpha-shape (

**b**), multi-line fitting with RANSAC (

**c**) and linear split sub-segments (

**d**).

**Figure 12.**An example of type-2 segment points that cannot be split automatically (

**left**), the alpha-shape (turquoise) and minimum bounding box (black) of the segment (

**right**).

Process Name | Number of Points | Percentage (%) | |
---|---|---|---|

Before | After | ||

Laser scanning | - | 634,065,068 | 100 |

Sub-sampling | 634,065,068 | 58,816,336 | 9.28 |

Roof cover filtering | 58,816,336 | 42,351,765 | 6.68 |

Segmentation | 42,351,765 | 22,922,973 | 3.62 |

Segment Class | Number of Segments | |
---|---|---|

Planar | Non-Planar | |

Type-1 | 3208 | 117 |

Type-2 | 1757 | 264 |

Type-3 | 79 | - |

Region | Number of Beams | Method 1 | Method 2 | Method 3 |
---|---|---|---|---|

Northern transept | 199 | 61 | 129 | 150 |

Southern transept | 194 | 53 | 117 | 146 |

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**MDPI and ACS Style**

Özkan, T.; Pfeifer, N.; Styhler-Aydın, G.; Hochreiner, G.; Herbig, U.; Döring-Williams, M.
Historic Timber Roof Structure Reconstruction through Automated Analysis of Point Clouds. *J. Imaging* **2022**, *8*, 10.
https://doi.org/10.3390/jimaging8010010

**AMA Style**

Özkan T, Pfeifer N, Styhler-Aydın G, Hochreiner G, Herbig U, Döring-Williams M.
Historic Timber Roof Structure Reconstruction through Automated Analysis of Point Clouds. *Journal of Imaging*. 2022; 8(1):10.
https://doi.org/10.3390/jimaging8010010

**Chicago/Turabian Style**

Özkan, Taşkın, Norbert Pfeifer, Gudrun Styhler-Aydın, Georg Hochreiner, Ulrike Herbig, and Marina Döring-Williams.
2022. "Historic Timber Roof Structure Reconstruction through Automated Analysis of Point Clouds" *Journal of Imaging* 8, no. 1: 10.
https://doi.org/10.3390/jimaging8010010