# Multisource Point Clouds, Point Simplification and Surface Reconstruction

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## Abstract

**:**

## 1. Introduction

## 2. Related Works

#### 2.1. Point Cloud Simplification and Uniformity

#### 2.2. Surface Reconstruction from Point Clouds

#### 2.2.1. Parametric Surface Reconstruction Methods

#### 2.2.2. Triangulation/Mesh-based Algorithms

#### 2.2.3. Comparison of Surface Reconstruction Methods from Literature

## 3. Materials

#### 3.1. Car

#### 3.2. Human Bodies

#### 3.3. Bookshelf Data Acquisition

#### 3.4. Acquisition of Indoor Objects: Two Chairs and A Stool

## 4. Methods

#### 4.1. Phase 1: Point Simplification

#### 4.1.1. PCA of the Objects

#### 4.1.2. Object 2D Projection

#### 4.1.3. Edge Points Resampling

#### 4.1.4. Resampling of the Remaining Points

- Percentage-based resamplingA random resampling method needs to specify the percentage of reduced points. The points are randomly selected from the original points, without replacement. The advantage is its high computational efficiency.
- Grid/box-based resamplingThe grid-based resampling method selects points using a fixed size grid, retaining a single point in each cell. Replacement or interpolation is needed in this case. The advantage of this method is that, after resampling, the points are distributed evenly over the shape surface.
- Number of points in a box resampling (also called non-uniform resampling)In this method, the points are located in cubes. The maximum number of points within a cube is specified. The resampling is conducted by selecting a certain number of points in a cube using the applied criteria/method.

#### 4.2. Phase 2: Surface Reconstruction

#### 4.3. The Method for Assessing Point Simplification

_{t}is the distance from point t in the compared point cloud to its nearest neighbor in reference point cloud. $\overline{Y}$ is the mean distance. t = 1, 2, 3, …, n and n is the number of points.

## 5. Results

#### 5.1. Results from Phase 1

#### 5.2. Assessment of Phase 1

#### 5.3. Result of Phase 2

#### 5.4. Recommendation of Surface Reconstruction Methods

## 6. Discussion and Future Work

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Point simplification and surface reconstruction with different algorithms. (

**a**): point simplification with feature preservation and uniform resampling; (

**b**): surface reconstruction by different methods: Alpha shapes, algebraic point set surfaces (APSS), the Crust, and Screened Poisson reconstruction (SPR).

**Figure 3.**The car was scanned by a FARO Focus3D X330 terrestrial laser scanner. The scanner was mounted on the yellow tripod, seen near the right. Three of the five white reference spheres are also visible.

**Figure 5.**An object point cloud reconstructed with a hand-held scanner shown with the measurement trajectory and automatically detected markers mounted adjacent to the object on the table surface.

**Figure 6.**Workflow of the point simplification and surface reconstruction. Two phases: the first phase in the red frame concerns the point simplification; the second phase within the green frame concerns surface reconstruction.

**Figure 7.**The difference between before principal component analysis (PCA) transformation and after PCA transformation for human body scanning data. (See the axis for the difference). Because both images are in local coordinate systems, there are no units for the axes.

**Figure 11.**Comparing our method with the Poisson sampling method. (

**Left**): our method; (

**Right**): Poisson sampling method.

**Figure 12.**Car reconstruction from different point densities by the methods of the Crust and SPR. Left two images: the Crust with the resampling points of 0.01 m and 0.05 m, respectively; Right three images: the SPR with the original points and the resampling points of 0.01 m and 0.05 m, respectively.

**Table 1.**Comparison of the evaluated methods with respect to the considered criteria ranging from +++ (very good) to --- (very poor) (From Wiemann et al. [32]).

Open Geometry | Closed Geometry | Sharp Features | Topological Correctness | Noise Robustness | Run Time | |
---|---|---|---|---|---|---|

Poisson Reconstruction | -- | +++ | - | ++ | +++ | o |

Ball Pivoting | o | o | o | -- | --- | - |

Alpha Shapes | o | o | o | -- | --- | - |

APSS Marching Cubes | ++ | ++ | o | ++ | o | - |

LVR Planar Marching Cubes | +++ | ++ | ++ | ++ | ++ | + |

Kinect Fusion | ++ | ++ | -- | --- | +++ | +++ |

Original Points | Simplification1 | Simplification2 | Simplification3 |
---|---|---|---|

Object | Number of: Original Points | The Number of Points (Edge Points + Internal Points) | Percentage of Reduction (%) | ||||
---|---|---|---|---|---|---|---|

Grid = 0.01 (m) * | Grid = 0.02 (m) * | Grid = 0.05 (m) * | Grid = 0.01 (m) * | Grid = 0.02 (m) * | Grid = 0.05 (m) * | ||

Car | 5,549,404 | 331,207 | 87,213 | 18,249 | 94.032 | 98.428 | 99.671 |

Human1 | 21,041 | 14,682 | 6551 | 3015 | 30.222 | 68.865 | 85.671 |

Human2 | 16,848 | 12,034 | 5694 | 2839 | 28.573 | 66.204 | 83.149 |

Human3 | 23,979 | 16,635 | 7287 | 2995 | 30.627 | 69.611 | 87.510 |

BS | 252,418 | 145,688 | 57,769 | 13,880 | 42.283 | 77.114 | 94.501 |

Chair1 | 202,803 | 13,322 | 5724 | 3901 | 93.431 | 97.178 | 98.076 |

Chair2 | 436,849 | 27,351 | 7472 | 2526 | 93.739 | 98.290 | 99.422 |

Stool | 146,000 | 8782 | 4649 | 3580 | 93.985 | 96.816 | 97.548 |

Average | 63.362 | 84.063 | 93.194 |

Object | NumP: Original Points * | NumP: Edge Points * | Runtime (s) | NumP: Resampled Edge Points Grid = 0.005 m * | Number of Internal Point Resampling | Accuracy in all Points (std) (cm) | ||||
---|---|---|---|---|---|---|---|---|---|---|

Grid = 0.01 m | Grid = 0.02 m | Grid = 0.05 m | Grid = 0.01 m | Grid = 0.02 m | Grid = 0.05 m | |||||

Car | 5,549,404 | 5785 | 125.45 | 4850 | 326,357 | 82,363 | 13,399 | 0.086 | 0.113 | 0.203 |

Human1 | 21,041 | 2065 | 0.508 | 2064 | 12,618 | 4487 | 951 | 0.177 | 0.214 | 0.207 |

Human2 | 16,848 | 2016 | 0.404 | 2016 | 10,018 | 3678 | 823 | 0.173 | 0.218 | 0.195 |

Human3 | 23,979 | 1928 | 0.538 | 1928 | 14,707 | 5359 | 1067 | 0.179 | 0.229 | 0.262 |

BS | 252,418 | 3317 | 5.673 | 3233 | 142,455 | 54,536 | 10,647 | 0.156 | 0.227 | 0.389 |

Chair1 | 202,803 | 4884 | 5.024 | 3585 | 9737 | 2139 | 316 | 0.087 | 0.106 | 0.099 |

Chair2 | 436,849 | 1927 | 11.82 | 1735 | 25,616 | 5737 | 791 | 0.087 | 0.114 | 0.173 |

Stool | 146,000 | 5524 | 3.673 | 3385 | 5397 | 1264 | 195 | 0.066 | 0.08 | 0.075 |

Average | 0.116 | 0.163 | 0.200 |

Alpha Shape | APSS (Grid Resolution = 500) | Crust | SPR | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Run Time (s) | Number of Meshes | Hole (Y/N) | Run Time (s) | Number of Meshes * | Hole (Y/N) | Run Time (s) | Number of Meshes | Hole (Y/N) | Run Time (s) | Number of Meshes | Hole (Y/N) | |

Car_org | failed | failed | 1814.5 | 12,529,297 | N | 11 | 188,088 | N | ||||

Car_1 | 25.6 | 932,630 | Y | 53.2 | 655,075 | Y | 93.8 | 737,790 | N | 7.8 | 206,516 | N |

Car_2 | 4.3 | 359,902 | Y | 17.5 | 742,331 | Y | 22.8 | 175,961 | N | 7.4 | 202,206 | N |

Car_5 | 0.7 | 76,117 | Y | 12.7 | 827,202 | Y | 4.8 | 34,533 | N | 3.3 | 79,684 | N |

Hu1_org | 3.8 | 32,034 | Y | 8.4 | 339,328 | Y | 5.9 | 45,339 | N | 3.6 | 91,014 | N |

Hu1_1 | 0.8 | 89,868 | Y | 7.1 | 310,857 | Y | 3.9 | 29,116 | N | 3.5 | 79,142 | N |

Hu1_2 | 0.2 | 31,409 | Y | 6.3 | 337,071 | Y | 1.9 | 12,919 | N | 1.7 | 27,436 | N |

Hu1_5 | 0.1 | 9279 | Y | 6.2 | 372,628 | Y | 1.1 | 5948 | N | 1.5 | 20,746 | N |

Hu2_org | 1.1 | 116,032 | Y | 7.4 | 295,369 | Y | 4.9 | 36,758 | N | 3.2 | 205,132 | N |

Hu2_1 | 0.7 | 72,574 | Y | 6.1 | 258,619 | Y | 3.4 | 23,747 | N | 2.9 | 80,854 | N |

Hu2_2 | 0.3 | 28,056 | Y | 6.0 | 282,096 | Y | 1.9 | 11,261 | N | 1.7 | 25,606 | N |

Hu2_5 | 0.1 | 9544 | Y | 5.8 | 314,521 | Y | 1.0 | 5588 | N | 1.4 | 19,400 | N |

Hu3_org | 5.1 | 31,124 | Y | 6.7 | 338,799 | Y | 6.5 | 47,814 | N | 3.6 | 90,042 | N |

Hu3_1 | 0.9 | 82,919 | Y | 6.6 | 339,403 | Y | 4.5 | 33,127 | N | 3.4 | 85,250 | N |

Hu3_2 | 0.3 | 32,058 | Y | 5.7 | 347,050 | Y | 2.2 | 14,420 | N | 1.7 | 26,622 | N |

Hu3_5 | 0.1 | 8022 | Y | 5.5 | 359,493 | Y | 0.9 | 5867 | N | 1.4 | 19,868 | N |

BS_org | 25.3 | 500,103 | Y | 113 | 2,343,075 | Y | 63.9 | 489,601 | Y | 19.1 | 556,746 | N |

BS_1 | 17.5 | 359,227 | Y | 87.0 | 2,505,295 | Y | 37.4 | 290,048 | Y | 18.3 | 535,830 | N |

BS_2 | 2.2 | 203,125 | Y | 45.4 | 2,606,712 | Y | 15.0 | 114,724 | Y | 8.5 | 210,352 | N |

BS_5 | 0.5 | 44,995 | Y | 41.6 | 2,663,567 | Y | 4.1 | 26,523 | Y | 2.8 | 42,560 | N |

Ch1_org | 7.4 | 174,942 | N | 86.4 | 1,288,477 | N | 8.6 | 452,190 | N | 7.2 | 168,126 | N |

Chr1_1 | 0.4 | 40,203 | N | 18.2 | 838,936 | N | 4.0 | 27,316 | N | 2.3 | 42,612 | N |

Ch1_2 | 0.2 | 18,870 | Y | 13.9 | 814,207 | N | 1.8 | 11,280 | N | 2.2 | 32,738 | N |

Ch1_5 | 0.1 | 11,578 | Y | 12.9 | 803,961 | Y | 1.4 | 7381 | Y | 1.8 | 32,600 | N |

Ch2_org | 16.3 | 228,214 | N | 148 | 1,813,631 | N | 126 | 869,919 | N | 10.2 | 218,433 | N |

Ch2_1 | 1.0 | 72,423 | N | 22.4 | 1,082,339 | N | 7.6 | 45,657 | N | 4.4 | 98,350 | N |

Ch2_2 | 0.3 | 24,359 | Y | 14.9 | 989,877 | N | 2.4 | 11,831 | N | 2.1 | 36,265 | N |

Ch2_5 | 0.1 | 6799 | Y | 13.9 | 1,162,428 | Y | 1.0 | 4023 | Y | 1.5 | 20,510 | N |

Stool_org | 5.1 | 189,983 | N | 50.7 | 902,489 | N | 39.7 | 314,142 | N | 7.0 | 187,248 | N |

Stool_1 | 0.3 | 29,506 | N | 17.5 | 657,254 | N | 2.6 | 17,468 | N | 2.1 | 42,390 | N |

Stool_2 | 0.2 | 15,257 | Y | 15.6 | 652,582 | N | 1.5 | 9088 | N | 1.8 | 35,644 | N |

Stool_5 | 0.1 | 12,415 | Y | 15.2 | 620,818 | Y | 1.2 | 6974 | Y | 1.7 | 29,880 | N |

Alpha shapes | APSS | The Crust | SPR | |
---|---|---|---|---|

Reconstruction with complete data | ||||

Reconstruction with data imperfections |

Alpha Shape | APSS | Crust | SPR | |
---|---|---|---|---|

Car | x | x | ||

Human | x | x | x | |

Bookshelf | x | x | x | x |

Chair | x | x | ||

Stool | x | x |

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## Share and Cite

**MDPI and ACS Style**

Zhu, L.; Kukko, A.; Virtanen, J.-P.; Hyyppä, J.; Kaartinen, H.; Hyyppä, H.; Turppa, T.
Multisource Point Clouds, Point Simplification and Surface Reconstruction. *Remote Sens.* **2019**, *11*, 2659.
https://doi.org/10.3390/rs11222659

**AMA Style**

Zhu L, Kukko A, Virtanen J-P, Hyyppä J, Kaartinen H, Hyyppä H, Turppa T.
Multisource Point Clouds, Point Simplification and Surface Reconstruction. *Remote Sensing*. 2019; 11(22):2659.
https://doi.org/10.3390/rs11222659

**Chicago/Turabian Style**

Zhu, Lingli, Antero Kukko, Juho-Pekka Virtanen, Juha Hyyppä, Harri Kaartinen, Hannu Hyyppä, and Tuomas Turppa.
2019. "Multisource Point Clouds, Point Simplification and Surface Reconstruction" *Remote Sensing* 11, no. 22: 2659.
https://doi.org/10.3390/rs11222659