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

^{1}

^{2}

^{3}

^{*}

## 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:$$\left|{C}_{\mathrm{A}}-{P}_{\mathrm{B}}\right|<dis{t}_{\mathrm{max}}$$
- 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

## References

- Liebich, H.A. The Vienna Roof Register—Investigating Historic Wooden Roof Structures in Vienna’s City Centre; Eberhardsteiner, J., Winter, W., Fadai, A., Pöll, M., Eds.; WCTE 2016 e-book; TU-Verlag: Vienna, Austria, 2016; pp. 3030–3038. ISBN 978-3-903024-35-9. [Google Scholar]
- Liebich, H.A. Dachwerke der Wiener Innenstadt. Konstruktion—Typologie—Bestand, Österreichische Denkmaltopographie 4; Verlag Berger: Horn, Austria, 2021; ISSN 2616-4957. [Google Scholar]
- Vosselman, G.; Maas, H.G. Airborne and Terrestrial Laser Scanning; Whittles Publishing: Dunbeath, Scotland, 2010. [Google Scholar]
- Westoby, M.J.; Brasington, J.; Glasser, N.F.; Hambrey, M.J.; Reynolds, J.M. ‘Structure-from-Motion’ photogrammetry: A low-cost, effective tool for geoscience applications. Geomorphology
**2012**, 179, 300–314. [Google Scholar] [CrossRef][Green Version] - McCarthy, J. Multi-image photogrammetry as a practical tool for cultural heritage survey and community engagement. J. Archaeol. Sci.
**2014**, 43, 175–185. [Google Scholar] [CrossRef] - Chandler, J.; Buckley, S. Structure from Motion (SFM) Photogrammetry vs. Terrestrial Laser Scanning; American Geosciences Institute: Alexandria, VA, USA, 2016. [Google Scholar]
- Peña-Villasenín, S.; Gil-Docampo, M.; Ortiz-Sanz, J. Professional SfM and TLS vs a simple SfM photogrammetry for 3D modelling of rock art and radiance scaling shading in engraving detection. J. Cult. Herit.
**2019**, 37, 238–246. [Google Scholar] [CrossRef] - Kamnik, R.; Perc, M.N.; Topolšek, D. Using the scanners and drone for comparison of point cloud accuracy at traffic accident analysis. Accid. Anal. Prev.
**2020**, 135, 105391. [Google Scholar] [CrossRef] - Alexiou, S.; Deligiannakis, G.; Pallikarakis, A.; Papanikolaou, I.; Psomiadis, E.; Reicherter, K. Comparing High Accuracy t-LiDAR and UAV-SfM Derived Point Clouds for Geomorphological Change Detection. ISPRS Int. J. Geo-Inf.
**2021**, 10, 367. [Google Scholar] [CrossRef] - Son, H.; Kim, C.; Kim, C. 3D reconstruction of as-built industrial instrumentation models from laser-scan data and a 3D CAD database based on prior knowledge. Autom. Constr.
**2015**, 49, 193–200. [Google Scholar] [CrossRef] - Volk, R.; Stengel, J.; Schultmann, F. Building Information Modeling (BIM) for existing buildings—Literature review and future needs. Autom. Constr.
**2014**, 38, 109–127. [Google Scholar] [CrossRef][Green Version] - Kaiser, A.; Ybanez Zepeda, J.A.; Boubekeur, T. A Survey of Simple Geometric Primitives Detection Methods for Captured 3D Data. Comput. Graph. Forum
**2018**, 38, 167–196. [Google Scholar] [CrossRef] - Rabbani, T.; Heuvel, F. 3D Industrial Reconstruction by Fitting CSG Modles to a Combination of Images and Point Clouds. ISPRS Spat. Inf. Sci.
**2004**, 35, 7–15. [Google Scholar] - Masuda, H.; Tanaka, I. As-built 3D modeling of large facilities based on interactive feature editing. Comput. Aided Des. Appl.
**2010**, 7, 349–360. [Google Scholar] [CrossRef][Green Version] - Poullis, C. A Framework for Automatic Modeling from Point Cloud Data. IEEE Trans. Pattern Anal. Mach. Intell.
**2013**, 35, 2563–2575. [Google Scholar] [CrossRef] - Ochmann, S.; Vock, R.; Klein, R. Automatic reconstruction of fully volumetric 3D building models from oriented point clouds. ISPRS J. Photogramm. Remote Sens.
**2019**, 151, 251–262. [Google Scholar] [CrossRef][Green Version] - Balletti, C.; Berto, M.; Gottardi, C.; Guerra, F. Ancient Structures and New Technologies: Survey and Digital Representation of the Wooden Dome of SS. Giovanni E Paolo in Venice. ISPRS Ann. Photogramm.
**2013**, II-5, 25–30. [Google Scholar] [CrossRef][Green Version] - Cabaleiro, M.; Riveiro, B.; Arias, P.; Caamaño, J.C. Algorithm for the analysis of the geometric properties of cross-sections of timber beams with lack of material from LIDAR data. Mater. Struct.
**2016**, 49, 4265–4278. [Google Scholar] [CrossRef] - Pöchtrager, M.; Styhler-Aydin, G.; Döring-Williams, M.; Pfeifer, N. Automated Reconstruction of Historic Roof Structures from Point clouds—Development and Examples. ISPRS Ann. Photogramm. Remote. Sens. Spat. Inf. Sci.
**2017**, IV-2/W2, 195–202. [Google Scholar] [CrossRef][Green Version] - Pöchtrager, M.; Styhler-Aydin, G.; Döring-Williams, M.; Pfeifer, N. Digital reconstruction of historic roof structures: Developing a workflow for a highly automated analysis. Virtual Archaeol. Rev.
**2018**, 9, 21–33. [Google Scholar] [CrossRef][Green Version] - Murtiyoso, A.; Grussenmeyer, P. Virtual Disassembling of Historical Edifices: Experiments and Assessments of an Automatic Approach for Classifying Multi-Scalar Point Clouds into Architectural Elements. Sensors
**2020**, 20, 2161. [Google Scholar] [CrossRef] [PubMed][Green Version] - Eßer, G.; Styhler-Aydın, G.; Hochreiner, G. The historic roof structures of the Vienna Hofburg: An innovative interdisciplinary approach in architectural sciences laying ground for structural modeling. In World Conference of Timber Engineering; Eberhardsteiner, J., Winter, W., Fadai, A., Pöll, M., Eds.; WCTE 2016 e-book; TU Verlag: Vienna, Austria, 2016; pp. 3039–3047. [Google Scholar]
- Styhler-Aydın, G.; Eßer, G. Das Dachwerk der Kirche St. Michael in Wien—Baudokumentation und Bauanalyse; Die Wiener Hofburg im Mittelalter. Von der Kastellburg bis zu den Anfängen der Kaiserresidenz; Schwarz, M., Ed.; Verlag der Österreichischen, Akademie der Wissenschaften: Vienna, Austria, 2016; pp. 527–538. ISBN 978-3-7001-7656-5. [Google Scholar]
- Wang, Q.; Tan, Y.; Mei, Z. Computational Methods of Acquisition and Processing of 3D Point Cloud Data for Construction Applications. Arch. Comput. Methods Eng.
**2020**, 27, 479–499. [Google Scholar] [CrossRef] - Rashidi, M.; Mohammadi, M.; Sadeghlou, K.; Abdolvand, M.M.; Truong-Hong, L.; Samali, B. A Decade of Modern Bridge Monitoring Using Terrestrial Laser Scanning: Review and Future Directions. Remote Sens.
**2020**, 12, 3796. [Google Scholar] [CrossRef] - Besl, P.J.; McKay, N.D. A method for registration of 3-D shapes. IEEE Trans. Pattern Anal. Mach. Intell.
**1992**, 14, 239–256. [Google Scholar] [CrossRef] - Riegl (VZ-2000i Terrestrial Laser Scanner). Available online: http://www.riegl.com/nc/products/terrestrial-scanning/produktdetail/product/scanner/58/ (accessed on 20 September 2021).
- RiScanPRO (Version 2.0). Available online: http://www.riegl.com/products/software-packages/riscan-pro/ (accessed on 20 September 2021).
- Pfeifer, N.; Mandlburger, G.; Otepka, J.; Karel, W. OPALS—A framework for Airborne Laser Scanning data analysis. Comput. Environ. Urban Syst.
**2014**, 45, 125–136. [Google Scholar] [CrossRef] - OPALS Data Manager (ODM) (Version 2.3.2). Available online: https://opals.geo.tuwien.ac.at/html/stable/ref_odm.html (accessed on 16 September 2021).
- Van Rossum, G.; Drake, F.L., Jr. Python Tutorial; Centrum voor Wiskunde en Informatica: Amsterdam, The Netherlands, 1995. [Google Scholar]
- ASPRS LAS File Format (Version 1.4). Available online: https://www.asprs.org/divisions-committees/lidar-division/laser-las-file-format-exchange-activities (accessed on 22 September 2021).
- Katz, S.; Tal, A.; Basri, R. Direct visibility of point sets. ACM Trans. Graph.
**2007**, 26, 24–40. [Google Scholar] [CrossRef] - Levin, D. The approximation power of moving least-squares. Math. Comput.
**1998**, 67, 1517–1532. [Google Scholar] [CrossRef][Green Version] - Shakarji, C.M. Least-Squares Fitting Algorithms of the NIST Algorithm Testing System. J. Res. Natl. Inst. Stand. Technol.
**1998**, 103, 633–641. [Google Scholar] [CrossRef] - Fischler, M.A.; Bolles, R.C. Random sample consensus: A paradigm for model fitting with applications to image analysis and automated cartography. Commun. ACM
**1981**, 24, 381–395. [Google Scholar] [CrossRef] - Hoppe, H.; DeRose, T.; Duchamp, T.; McDonald, J.; Stuetzle, W. Surface reconstruction from unorganized points. ACM SIG-GRAPH Comput. Graph.
**1992**, 21, 71–82. [Google Scholar] [CrossRef] - Edelsbrunner, H.; Kirkpatrick, D.G.; Seidel, R. On the shape of a set of points in the plane. IEEE Trans. Inf. Theory
**1983**, 29, 551–559. [Google Scholar] [CrossRef][Green Version] - DXF Open Data Exchange Format (Version AC1014). Available online: https://knowledge.autodesk.com/support/autocad/learn-explore/caas/CloudHelp/cloudhelp/2019/ENU/AutoCAD-Core/files/GUID-D4242737-58BB-47A5-9B0E-1E3DE7E7D647-htm.html (accessed on 14 October 2021).
- STEP. Industrial Automation Systems and Integration—Product Data Representation and Exchange. (Version ISO 10303-21:2016). Available online: https://www.loc.gov/preservation/digital/formats/fdd/fdd000448.shtml (accessed on 14 October 2021).
- Laney, D. 3D data management: Controlling data volume, velocity and variety. META Group Res. Note
**2001**, 6, 1. [Google Scholar]

**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 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**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