# Surface Reconstruction Assessment in Photogrammetric Applications

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## Abstract

**:**

## 1. Introduction

#### Paper’s Motivation and Aim

- In a traditional photogrammetric pipeline, the meshing step interpolates a surface over the input 3D points. This is usually disjointed from the 3D point cloud generation DIM but can potentially leverage and take advantage of additional information from the previous steps of the workflow, i.e., visibility constraints and photo-consistency measures which are generally not considered in popular meshing algorithms as Poisson [14].
- Dense point clouds can be heavily affected by poor image quality or textureless areas, resulting in high frequency noise, holes and uneven point density. These issues can be propagated during the mesh generation process.
- Volumetric approaches for surface reconstruction based on depth maps are well-established, time-efficient methods for depth sensors, also known as RGB-D [15], and might be a valid approach also for pure image-based approaches.

- Method 1: Surface generation and refinement are incorporated in the 3D reconstruction pipeline. The mesh is generated after depth maps and dense point clouds are estimated and is subsequently refined considering visibility information (i.e., image orientation) to optimize a photo-consistency score over the reconstructed surface [13,16].

## 2. On DIM and MVS

## 3. Benchmarks and Assessment of Surface Reconstruction Approaches

#### 3.1. DIM/MVS Benchmarks

#### 3.2. Surface Reconstruction and Assessment Criteria

## 4. Investigated Surface Generation Methods

#### 4.1. Photo-Consistent Volume Integration and Mesh Refinement (Method 1, M1)

#### 4.2. Surface Generation from Point Cloud (Method 2, M2)

^{d}× 2

^{d}× 2

^{d}. The octree level is automatically adapted to the original point sampling density, with the selected reconstruction depth being an indication of the maximum achievable mesh resolution. Beside the depth value, another critical parameter is the samples per node. It defines the number of points included in each voxel grid or node: the more noisy are the input data, the higher should be the number of points falling in each node of the octree, which may result in a loss of geometric details. If the original points have color information, as in our experiments, the RGB values are interpolated and transferred to the vertices of the generated mesh.

#### 4.3. TSDF Volume Integration (Method 3, M3)

## 5. Datasets and Evaluation Metrics

#### 5.1. Datasets

#### 5.2. Evaluation Approach and Criteria

- Accuracy was evaluated as the signed Euclidean distance between the vertices of the (photogrammetric) data mesh and the (scanner) reference mesh. The signed Euclidean distance was chosen instead of the Hausdorff distance to highlight any possible systematic error. For this, both CloudCompare and Meshlab [85] implementations were tested, providing equivalent results. The following values were computed: mean, standard deviation (STDV), median and normalized maximum absolute deviation from the median (NMAD = 1.4826 × MAD), root mean square (RMS) and outliers percentage.
- Completeness was defined as the signed Euclidean distance between the (scanner) reference mesh and the (photogrammetric) data mesh. The percentage of vertices of photogrammetric data mesh falling within the defined threshold (in%) was adopted as a measure for completeness.
- Local roughness was computed as the absolute distance between the mesh vertex and the best fitting plane estimated on its nearest neighbors within a defined kernel size. The method implemented in CloudCompare was adopted. Adapting the standard parameters generally used to quantify the roughness [86], mean and RMS roughness values are reported to describe the local behavior of the vertices in their local region (i.e., within the selected kernel). The kernel size was carefully selected according to surface resolution.
- Local noise was assessed on selected planar regions where the plane fitting RMS was computed.
- Sections were extracted from the meshes and the mean and RMS signed distance values from data to reference are reported.
- Local curvature variation, expressed as normal change rate, was computed over a kernel size, i.e., the radius defining the neighbor vertices around each point where the curvature was estimated. As for the roughness metric, the kernel size was decided according to the surface resolution and size of the geometric elements (3D edges). The normal change rate is shown as a color map to highlight high geometric details (e.g., 3D edges), which appear as sharp green to red contours, and high frequency noise, shown as scattered green to red areas. The method implemented in CloudCompare was here adopted.
- The topology of each generated surface is evaluated in terms of the percentage of self-intersecting triangles over the total number of faces.

## 6. Results and Discussion

#### 6.1. Evaluation without a Reference Mesh: The Aerial Case Study

#### 6.2. Evaluation with a Reference Mesh

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**(

**a**) Orthographic view of the urban area, with details of the extracted areas for the plane fitting analysis (P1 and P2) and sections (S1 and S2); (

**b**) profiles of the extracted sections; and (

**c**) normal change rate maps on a building.

**Figure 5.**Shaded surface models of evaluated datasets. From left to right: Reference, M1, M2 and M3. From top to bottom: Fountain, Modena’s bas-relief, Ignatius and Wooden ornament.

**Figure 6.**Section profiles (

**top**); roughness (

**middle**); and normal change rate maps (

**bottom**) for the Fountain dataset.

**Figure 7.**Section profiles (

**top**); roughness (

**middle**); and normal change rate maps (

**bottom**) for the Modena dataset.

**Figure 8.**Section profiles (

**top**); roughness (

**middle**); and normal change rate maps (

**bottom**) for the Ignatius dataset.

**Figure 9.**Section profiles (

**top**); roughness (

**middle**); and normal change rate maps (

**bottom**) for the Wooden ornament dataset.

Dataset | Type of Scene | Type of Acquisition | Num of Images/Total Mpx | Scene Size/Mean Image GSD | Ground Truth | Evaluation Criteria |
---|---|---|---|---|---|---|

FBK/AVT | Urban | Aerial nadir—single shots | 4/120 | (1 × 1 × 0.1) km^{3}/10 cm | - | Profiles, plane fitting, topology correctness |

Strecha Fountain | Building facade | Terrestrial—single shots | 11/66 | (5 × 4 × 5) m^{3}/30 mm | Mesh from laser scanner | Accuracy, completeness, roughness, profiles, topology correctness |

FBK/3DOModena | Building facade | Terrestrial—single shots | 14/320 | (11 × 3 × 9) m^{3}/20 mm | Mesh from laser scanner | Accuracy, completeness, roughness, profiles, topology correctness |

Tanks and Temples—Ignatius | Statue | Terrestrial—video | 263/535 | (2 × 2 × 3) m^{3}/30 mm | Mesh from laser scanner | Accuracy, completeness, roughness, profiles, topology correctness |

FBK/3DOM wooden ornament | Asset | Terrestrial—single shots | 32/740 | (305 × 95 × 25) mm^{3}/0.6 mm | Mesh from structured light scanner | Accuracy, completeness, roughness, profiles, topology correctness |

FBK/AVT | Strecha Fountain | Tanks and Temples—Ignatius | FBK/3DOM Modena | FBK/3DOM Wooden Ornament | ||
---|---|---|---|---|---|---|

Image Resolution for Depth Maps and Dense Point Cloud Generation | ¼ | Full | Full | ¼ | Full | |

M1 | Regularity weight | 0.4 | 0.4 | 0.4 | 0.4 | 0.4 |

Resolution (mm) | 80.0 | 1.3 | 1.2 | 3.0 | 0.04 | |

M2 | Voxel grid size (mm) | 160.0 | 0.7 | 0.3 | 1.5 | 0.02 |

Samples per node | 20 | 1.5 | 20 | 1.5 | 20 | |

Resolution (mm) | 160.0 | 0.3 | 0.2 | 0.7 | 0.01 | |

M3 | Voxel grid size (mm) | 500.0 | 3.8 | 15 | 6.2 | 1.4 |

Resolution (mm) | 160.0 | 2.7 | 5.0 | 3.0 | 0.07 |

**Table 3.**Quantitative and topological analyses for the aerial dataset: plane fitting and percentage of self-intersecting faces.

Method | Plane Fitting RMS (m) | Percent of Self-Intersecting Faces | |
---|---|---|---|

P1 | P2 | ||

M1 | 0.352 | 0.602 | - |

M2 | 0.391 | 0.606 | 0.01% |

M3 | 0.385 | 0.547 | 0.5% |

**Table 4.**Quantitative and topological analyses for the Fountain dataset. Values are in mm. Threshold and kernel values are set equal to 9.0 and 10 mm, respectively. Mean and RMS values in the Sections columns are double as we considered two sections (Figure 6).

Method | Accuracy | Completeness | F-Score | Roughness | Sections | % of Self-Intersecting Faces | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

MEAN | STDV | RMS | MEDIAN | NMAD | OUT% | IN% | MEAN | RMS | MEAN | RMS | |||

M1 | 3.3 | 11.0 | 11.5 | 1.7 | 6.8 | 3.7 | 73.4 | 0.886 | 1.0 | 1.3 | 6.5 | 14.9 | - |

0.4 | 15.9 | ||||||||||||

M2 | 2.1 | 12.6 | 12.7 | 0.4 | 6.7 | 4.1 | 73.6 | 0.898 | 1.7 | 2.2 | 6.9 | 16.2 | 0.03% |

0.1 | 15.0 | ||||||||||||

M3 | 3.6 | 27.9 | 28.1 | 2.1 | 8.6 | 7.8 | 71.1 | 0.827 | 1.8 | 2.3 | 8.7 | 18.3 | 0.07% |

−0.2 | 27.7 |

**Table 5.**Quantitative and topological analyses for the Modena dataset. Values are in mm. Threshold and kernel values are set equal to 4.5 and 20 mm, respectively. Mean and RMS values in the Sections columns are double as we considered two sections (Figure 7).

Method | Accuracy | Completeness | F-Score | Roughness | Sections | % of Self-Intersecting Faces | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

MEAN | STDV | RMS | MEDIAN | NMAD | OUT% | IN% | MEAN | RMS | MEAN | RMS | |||

M1 | 5.4 | 21.2 | 21.9 | −0.1 | 5.6 | 9.8 | 54.3 | 0.779 | 1.0 | 1.4 | −0.1 | 6.0 | - |

1.3 | 8.4 | ||||||||||||

M2 | 5.0 | 17.5 | 18.2 | 0.8 | 6.4 | 7.5 | 52.7 | 0.758 | 1.5 | 2.0 | 1.0 | 8.0 | - |

2.0 | 9.0 | ||||||||||||

M3 | 7.1 | 20.9 | 22.1 | 1.3 | 7.1 | 9.1 | 52.7 | 0.736 | 2.1 | 2.8 | 0.9 | 7.2 | - |

1.7 | 9.0 |

**Table 6.**Quantitative and topological analyses for the Ignatius dataset. Values are in mm. Threshold and kernel values are set equal to 3 and 10 mm, respectively. Mean and RMS values in the Sections columns are double as we considered two sections (Figure 8).

Method | Accuracy | Completeness | F-Score | Roughness | Sections | % of Self-Intersecting Faces | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

MEAN | STDV | RMS | MEDIAN | NMAD | OUT% | IN% | MEAN | RMS | MEAN | RMS | |||

M1 | 1.6 | 3.2 | 3.6 | 1.4 | 2.7 | 1.5 | 65.3 | 0.820 | 0.4 | 0.5 | 3.4 | 7.3 | - |

0.5 | 2.7 | ||||||||||||

M2 | 1.7 | 7.4 | 7.6 | 1.0 | 3.0 | 2.7 | 85.7 | 0.798 | 1.2 | 1.5 | 2.5 | 7.8 | 0.02% |

−0.2 | 3.1 | ||||||||||||

M3 | 4.9 | 11.4 | 12.4 | 3.0 | 3.0 | 9.2 | 58.8 | 0.643 | 3.6 * | 3.3 * | 5.4 | 9.7 | - |

2.4 | 4.3 |

**Table 7.**Quantitative and topological analyses for the Wooden ornament dataset. Values are in mm. Threshold and kernel values are set equal to 0.225 and 0.5 mm, respectively. Mean and RMS values in the Sections columns are double as we considered two sections (Figure 9).

Method | Accuracy | Completeness | F-Score | Roughness | Sections | % of Self-Intersecting Faces | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

MEAN | STDV | RMS | MEDIAN | NMAD | OUT% | IN% | MEAN | RMS | MEAN | RMS | |||

M1 | 0.06 | 0.23 | 0.24 | 0.03 | 0.11 | 5.5 | 99.9 | 0.80 | 0.02 | 0.03 | 0.05 | 0.12 | - |

0.05 | 0.14 | ||||||||||||

M2 | 0.05 | 0.13 | 0.14 | 0.04 | 0.11 | 1.9 | 90.8 | 0.93 | 0.06 | 0.07 | 0.04 | 0.14 | 0.002% |

0.07 | 0.10 | ||||||||||||

M3 | 0.36 | 1.34 | 1.4 | 0.03 | 0.14 | 10.1 | 77.9 | 0.86 | 0.04 | 0.05 | 0.09 | 0.17 | 0.06% |

0.61 | 0.13 |

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## Share and Cite

**MDPI and ACS Style**

Nocerino, E.; Stathopoulou, E.K.; Rigon, S.; Remondino, F.
Surface Reconstruction Assessment in Photogrammetric Applications. *Sensors* **2020**, *20*, 5863.
https://doi.org/10.3390/s20205863

**AMA Style**

Nocerino E, Stathopoulou EK, Rigon S, Remondino F.
Surface Reconstruction Assessment in Photogrammetric Applications. *Sensors*. 2020; 20(20):5863.
https://doi.org/10.3390/s20205863

**Chicago/Turabian Style**

Nocerino, Erica, Elisavet Konstantina Stathopoulou, Simone Rigon, and Fabio Remondino.
2020. "Surface Reconstruction Assessment in Photogrammetric Applications" *Sensors* 20, no. 20: 5863.
https://doi.org/10.3390/s20205863