# Accuracy Assessment of Cultural Heritage Models Extracting 3D Point Cloud Geometric Features with RPAS SfM-MVS and TLS Techniques

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Data Collection and Database Construction

#### 2.2. RPAS Digital Photogrammetry

#### 2.3. TLS

#### 2.4. Geometric Feature Extraction and 3D Point Cloud Accuracy Assessment

_{1}, λ

_{2}and λ

_{3}) of the 3D covariance matrix S, also known as the 3D structural tensor [41]. These eigenvalues express the dispersion relevance along their eigenvector and allow defining the structure typology: when λ

_{1}» λ

_{2}, λ

_{3}, the structure is unidimensional, since the points are distributed along one main axis; while, when λ

_{1}and λ

_{2}» λ

_{3}the structure is bidimensional because all the selected points are essentially arranged along two axes only; lastly, when λ

_{1}, λ

_{2}and λ

_{3}show similar values, the structure is tridimensional. S was estimated by considering the spatial information of all 3D points (X = (X, Y, Z)) within a local neighborhood V, defined by applying a sphere of a fixed radius r

_{s}[42]. The size of r

_{s}was determined in accordance with the proposal by Demantké et al. (2011) [43]. Thus, the radius was set as 0.05 m in accordance with the study area heterogeneity.

_{λ}, Anisotropy A

_{λ}, Sphericity S

_{λ}, Planarity P

_{λ}, Omnivariace O

_{λ}, Curvature C

_{λ}, Eigenvalues’ sum ∑

_{λ}) were computed. In the following, the formal definition of such parameters is reported:

_{95%}value, computed by applying Equation (8).

_{1}(d)

^{2}and σ

_{2}(d)

^{2}are the variances of the two clouds’ positions, while n

_{1}and n

_{2}are the numbers of points of RPAS- and TLS-extracted clouds, respectively. Lastly, reg represents the co-registration error between the two considered dense point clouds. The outcome of this procedure was used as a benchmark to evaluate the accuracy.

#### 2.5. The Gaussian Law of Variance Propagation

_{x}, σ

_{y}, σ

_{z}). Nevertheless, their values are not homogeneous over the entire 3D structure since each individual point can show a different deviation standard. The variance of a function f (f = f (x

_{1}, …, x

_{n})) of random variables x

_{i}can be appreciated through the application of the variance propagation law. Commonly, the Taylor series, reported in Equation (9), was adopted to address such a purpose.

## 3. Case Study

## 4. Results and Discussion

^{®}CoreTM i7-3970X CPU @3.50GHz with 16 GB RAM was applied in this case.

_{x}, RMSE

_{y}, and RMSE

_{z}) and the total errors (RMSE

_{T}) are reported in Table 2. 3D reconstruction generated by handling TLS data was slightly more accurate than the one produced by processing RPAS input data.

_{1}, λ

_{2}and λ

_{3}) of the 3D covariance matrix S were extracted from TLS and RPAS dense point clouds (Figure 6). To easily compare their values, the corresponding histograms were computed and are reported in Figure 7. λ

_{1}, λ

_{2}and λ

_{3}values were within the same order of magnitude for both models albeit the number of points were different for the two resultant clouds, as previously highlighted. Moreover, λ

_{1}and λ

_{3}had the same trend in contrast to the second eigenvalue, which showed a more complex distribution of around 0.0007 for the TLS-based model compared to the RPAS one. This indicated that the size and the shape of the point clouds generated by RPAS and TLS were similar along the most elongated direction (identified by λ

_{1}) as well as along the “flat” dimension (defined by λ

_{3}). Conversely, some divergences were detected along the second elongation direction (underlined by λ

_{2}). As depicted in Figure 6, these differences are mainly located on the vegetated areas and on the ground, and thus, they did not affect the point clouds’ performance in the area under investigation. This indicated that no significant differences were detected among them.

_{1}. The features trends as a function of λ

_{2}and λ

_{3}were nearly similar and, thus, only the values according to λ

_{1}variation were reported. The variance contribution was significant at low values for all examined properties, except linearity, curvature, and omnivariance were the most affected by that noise. In particular, as to the linearity, the variance effect was more evident in the RPAS model than in the TLS model. As previously stated, in both models the low values of λ

_{1}corresponded to the vegetation, considered to be the noisiest and least accurate zone. This indicated that the noise particularly affected the vegetated areas. In contrast, the noise impact was less relevant in accordance with the increment of λ

_{1}values.

## 5. Conclusions

- RPAS allowed reducing the time required to collect the input data while TLS permitted generating the final 3D model in a shorter operational time;
- The RPAS-based point cloud was less dense than the one produced by TLS and thus more easily manageable;
- The point distribution of the TLS-derived cloud was not homogeneous and, consequently, the accuracy of the 3D reconstruction was not uniform in the final model;
- RPAS allowed surveying the entire study area while TLS did not permit the collection of data concerning the roof of the Monastery, the vegetated areas, and the grounds;
- RPAS was a low-cost tool while TLS was a highly expensive instrument.

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## Abbreviation

3D | Three-Dimensional |

AGL | Above Ground Level |

BBA | Bundle Block Adjustment |

CORS | Continuous Operation Reference Stations |

CPs | Check Points |

EPSG | European Petroleum Survey Group |

GCPs | Ground Control Points |

GNSS | Global Navigation Satellite System |

GSD | Ground Sample Distance |

IMU | Inertial Measurement Unit |

INS | Inertial Navigation System |

LoD | Level of Detection |

M3C2 | Model-to-Model Cloud Comparison |

MSV | MultiView Stereo |

nRTK | Network Real-Time Kinematic |

RMSE | Root Mean Square Error |

RPAS | Remotely Piloted Aircraft Systems |

SfM | Structure from Motion |

TLS | Terrestrial Laser Scanner |

v. | version |

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**Figure 1.**Operative workflow implemented to assess the accuracy and reliability of RPAS-photogrammetric and TLS-based 3D point clouds and to compare both models’ performances.

**Figure 3.**Study area: All Saints’ Monastery of Cuti, located in the province of Bari (Southern Italy). The RGB orthophoto and the 3D scene representation produced by handling RPAS-photogrammetric data are reported on the left and on the right of the panel, respectively. Ground Control Points (GCPs) (in yellow) and Check Point (in light blue) locations are represented on the orthophoto. (Coordinate Reference System: WGS84/Pseudo-Mercator (EPSG:3857)).

**Figure 4.**Volume density levels generated from RPAS-based and TLS-based point clouds are reported on the (

**top**) and on the (

**bottom**), respectively. This parameter was computed within a sphere with a radius equal to 0.05 m.

**Figure 5.**M3C2 distance and Distance Uncertainty are depicted at the (

**top**) and at the (

**bottom**), respectively. The unit measurement is the meter.

**Figure 6.**λ

_{1}, λ

_{2}and λ

_{3}estimated within a local sphere with a radius 0.05 m from RPAS-based (on the (

**top**)) and TLS-based (on the (

**bottom**)) point clouds, respectively.

**Figure 7.**Histogram of λ

_{1}, λ

_{2}and λ

_{3}estimated within a local sphere with a radius 0.05 m from RPAS-based (on the (

**top**)) and TLS-based (on the (

**bottom**)) point clouds, respectively.

**Figure 8.**Histogram of eigenvalues-based geometric features extracted from the RPAS dense point cloud.

**Figure 9.**Histogram of eigenvalues-based geometric features extracted from the TLS dense point cloud.

**Figure 10.**Anisotropy, planarity, linearity, mean curvature, eigenvalue sum, omnivariance extracted from RPAS.

**Figure 11.**Anisotropy, planarity, linearity, mean curvature, eigenvalue sum, omnivariance extracted from TLS.

**Figure 12.**The variance of geometric features computed from the RPAS (on the (

**left**)) and TLS (on the (

**right**)) models.

RPAS | TLS | |
---|---|---|

ACQUISITION TIME (min) | ~14 | ~150 |

PROCESSING TIME (min) | ~974 | ~300 |

DENSE POINT CLOUDS NUMEROSITY (n° points) | 28,202,789 | 195,939,535 |

**Table 2.**RMSE referring to the point cloud extracted using RPAS-photogrammetry for both GCPs and CPs. The total values and their components along the three axes (x, y, and z) are reported.

GCPs | CPs | |
---|---|---|

RMSE_{x} (m) | 0.014 | 0.009 |

RMSE_{y} (m) | 0.016 | 0.013 |

RMSE_{z} (m) | 0.026 | 0.022 |

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**MDPI and ACS Style**

Capolupo, A. Accuracy Assessment of Cultural Heritage Models Extracting 3D Point Cloud Geometric Features with RPAS SfM-MVS and TLS Techniques. *Drones* **2021**, *5*, 145.
https://doi.org/10.3390/drones5040145

**AMA Style**

Capolupo A. Accuracy Assessment of Cultural Heritage Models Extracting 3D Point Cloud Geometric Features with RPAS SfM-MVS and TLS Techniques. *Drones*. 2021; 5(4):145.
https://doi.org/10.3390/drones5040145

**Chicago/Turabian Style**

Capolupo, Alessandra. 2021. "Accuracy Assessment of Cultural Heritage Models Extracting 3D Point Cloud Geometric Features with RPAS SfM-MVS and TLS Techniques" *Drones* 5, no. 4: 145.
https://doi.org/10.3390/drones5040145