# Point Cloud Stacking: A Workflow to Enhance 3D Monitoring Capabilities Using Time-Lapse Cameras

^{1}

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## Abstract

**:**

## 1. Introduction

#### 1.1. Photogrammetry vs. LiDAR 3D Point Cloud Errors

**geometric errors**, will be more or less significant depending on the quality of the homologous points and the bundle adjustment, which depends on the quality of the photographs.

**random error**, was easily solved and was the theoretical basis of the development of many algorithms for the processing of LiDAR data [14,20].

#### 1.2. Landslide Monitoring Using Photogrammetry

#### 1.3. Techniques for Image Stacking (2D)

#### 1.4. Aim and Objectives

## 2. Materials and Methods

#### 2.1. PCStacking Workflow

#### 2.1.1. Automatic 3D Reconstruction from Time-Lapse Camera Systems

#### 2.1.2. Point Cloud Stacking Algorithm

Algorithm 1 PCStacking is |

1 Start |

2 get the number of Point Clouds (m) from a designated folder |

3 load m Point Clouds into the workspace |

4 merge all Point Clouds into a single matrix (PC-Stack) [step 1] |

5 input search radius value (r_{1}) |

6 for each Point in PC-Stack |

7 create a subset_{1} of PC-Stack inside r_{1}, with coordinates (x,y,z) |

8 apply axes transformation (PCA), being normal vector -> Z_{1} axes [step 2] |

9 compute median value of the subset_{1} along eigen vectors (X, Y, Z) [step 3] |

10 end |

11 output the mean coordinates of the stacked Point Cloud |

12 End |

#### 2.2. Experimental Design (I): Synthetic Test

#### 2.2.1. Synthetic Point Clouds Creation

**Photogrammetric Point Clouds**(Phot-PC) was performed, in order to assess the PCStacking algorithm. In the first instance, a regular perfect surface (without any geometric error) was created using Equation (1). This surface is considered the

**Reference Point Cloud**(Ref-PC):

_{1},d

_{2}} are calculated randomly using predefined ranges. That means the synthetic test suite generates a different error (z

_{sin}) in each iteration (Figure 2):

**Synthetic Point Cloud**(Synt-PC) is obtained from the sum of the Ref-PC coordinates, the geometric deformation obtained by the sinusoidal function (Equation (2)) and the Gaussian scattering errors (Equations (3)–(5)):

**Enhanced Point Cloud**(Enh-PC), 20 random functions were generated, and 20 different Gaussian scattering errors were calculated in order to obtain 20 Synt-PC. This allowed analysis of the performance of the PCStacking algorithm, as well as the sensitivity of the method.

#### 2.2.2. PCStacking Application

_{n}(n being the number of Synt-PCs considered). The resulting Enh-PC

_{n}was then compared with the Ref-PC. The Synt-PCs were introduced into the algorithm in an incremental way, from two to 20 Synt-PCs. Then, each Enh-PC

_{n}was compared with the Ref-PC in order to assess the performance of the designed method, as well as its sensitivity to the number of Synt-PCs introduced.

- -
- Design a Reference PC (Ref-PC)
- -
- Create 20 Synthetic PCs (Synt-PC)
- -
- Application of the PCStacking algorithm: (n -> 2:20)
- o
- Input: n Synthetic PCs (Synt-PC)
- o
- Output: Enhanced PC (Enh-PC
_{n}) - o
- Comparison between the Enhanced PCs (Enh-PC
_{n}) and the Reference PC (Ref-PC)

- -
- Analysis of computed differences

_{n}vs. Ref-PC comparison was carried out using the Point to Mesh algorithm to avoid the influence of statistical averaging of the results using other comparison methods such as the M3C2 algorithm [14]. In this case, the conversion of the Ref-PC into a mesh does not introduce errors because the Ref-PC is a regular surface. For this reason, the distances obtained in the comparison correspond to the real distance between each point of the Enh-PC

_{n}and the synthetic surface computed from the Ref-PC. The performance of the developed method was evaluated through the statistical values of the differences between Enh-PC

_{n}and Ref-PC, assuming that an improvement means achieving an Enh-PC

_{n}more and more similar to the Ref-PC. Thus, the differences obtained in the comparison must tend to zero.

#### 2.2.3. Redundancy Test

_{n}vs. Ref-PC comparison was calculated. As this process was repeated 20 times in an iterative way, 20 standard deviation values were obtained for each Enh-PC

_{n}vs. Ref-PC comparison. This procedure allowed us to evaluate whether the described method works independently of the random parameters introduced to produce the Synt-PC. This redundancy test was carried out because in some tests the random values of the Synt-PC were too low, which resulted in a Synt-PCs with little error that generated a much improved Enh-PCs. With the generation of 400 Synt-PCs and the computation of the standard deviation of the 400 comparisons (Ref-PC vs. Enh-PC1:2020 times) the median values showed the real range of the PCStacking algorithm.

#### 2.3. Experimental Design (II): 3D Reconstruction of a Rocky Cliff

#### 2.3.1. Pilot Study Area

#### 2.3.2. Field Setup and Data Acquisition

#### 2.3.3. Point Cloud Reconstruction

^{2}. The computational cost to perform the entire process for a given radius in this small area is around 60 minutes to generate the 3D models with Agisoft Metashape and 70 minutes to apply the PCStacking algorithm. These times have been achieved with a commercial medium-high performance equipment (Intel(R) Core(TM) i9—7900X up to 4.30 GHz, 64GB RAM and NVIDIA GeForce GTX 1080 Ti). The raw point clouds obtained by the Metashape software are composed by approximately 150,000 points.

**Photogrammetric Point Clouds**(Photo-PC) were generated. The calculated models were aligned and scaled with a reference LiDAR to produce metric values for comparison. Figure 6a shows the X and Y cross-sections of four Photo-PCs. It demonstrates the correct alignment of the models but shows clearly different surfaces due to the poor quality of the acquisition system.

## 3. Results

#### 3.1. Synthetic Test

_{n}and the Ref-PC (Figure 7a) provide a quantitative assessment of the improvement achieved with the PCStacking algorithm. The increase in the number of input models (Synt-PCs) resulted in a better fit between Enh-PC

_{n}and Ref-PC.

_{n}vs. Ref-PC. The boxplot depicts a decrease in the errors when more inputs were used. The 25th and 75th percentiles progressively reduced to 50% after using 18 models. Specifically, the percentiles were progressively reduced from ±3.2 cm to ±1.4 cm after using the PCStacking algorithm with 18 models. Likewise, the minimums and maximums shown in the boxplot also showed a reduction close to 50%. The comparisons between Enh-PC

_{n}vs. Ref-PC in the redundancy test (Figure 8a) reveal a considerable reduction of the standard deviation when increasing the number of models introduced. The average standard deviations of the comparisons of all iterations decreased from 4.9 cm to 1.8 cm when 20 PC were used.

_{n}) accumulates all the points of the different Synt-PCs used, producing both a more accurate and denser Enh-PC. The plot in Figure 8b depicts the number of points available to average the Z coordinate, which depends on the number of Synt-PCs used as input data and on the search radius defined. This value is a great indicator of when the algorithm has enough input points to compute the new Z coordinate.

#### 3.2. 3D Reconstruction on a Rocky Cliff

_{n=2:15}from the February 25th PCs; (b) Calculation of the Enh-PC

_{n=2:15}from the February 26th PCs; (c) Point to mesh comparison (in CloudCompare) between a February 25th Photo-PC and a February 26th Photo-PC without applying any enhancement algorithm; and (d) Point to mesh comparison (in CloudComapre) between all Enh-PC

_{(2:15)}

^{25 feb}vs. Enh-PC

_{(2:15)}

^{26 feb}. The outputs from these comparisons are the distances in metric values existing between the two models studied. Given that between 25th and 26th February 2019 there was no change in the analyzed cliff, the expected difference in an ideal case must be zero.

_{15}

^{25 feb}vs. Enh-PC

_{15}

^{26 feb}.

_{n}

^{25 feb}and Enh-PC

_{n}

^{26 feb}. Each plotted line represents different parameters in the search radius (r) of the PCStacking algorithm (Section 2.1 and Figure 1). Note that for the smaller radius (r = 0.1 cm) the algorithm does not produce any improvement, because as in the synthetic test (Figure 8b), the small search radius does not provide enough points to average the Z coordinate in the direction of the normal.

_{15}

^{25 feb}and Enh-PC

_{15}

^{26 feb}for the different search radii described.

## 4. Discussion

#### 4.1. Synthetic Test vs. Real Data

#### 4.2. The PCStacking Method

_{18}comparison (Figure 7). In contrast, real photogrammetric models had a smaller comparison error that ranged from ±1.5 cm to ±0.5 cm when 15 PCs were used. In this case, 50% reduction in error was achieved when using only five PCs (Figure 9). This is because: (a) the synthetic PCs were designed with a higher geometric error with a distribution dependent on random parameters (see Equation (2)); and (b) the errors in the real photogrammetric PCs are not homogeneous and tend to be concentrated in areas where the software has more difficulty identifying homologous points. Consequently, synthetic data has larger and more distributed errors, thus, the algorithm needs more input point clouds to reduce the error. Even so, the algorithm succeeded in reducing the errors in both the synthetic test and the real case, and the number of PCs used was sufficient to stabilize the error reduction.

_{n}vs. Ref-PC.

#### 4.3. Current Limits and Margins for Improvement

_{n}

^{25 feb}and Enh-PC

_{n}

^{26 feb}in the real case test, were calculated using the Point to Mesh comparison algorithm. Since the application of this algorithm does not produce any improvement by itself, the error reduction shown in Figure 4 and Figure 9 can be associated with the PCStacking algorithm. On the other hand, when a real representation of the distribution of differences between two PCs was needed (Figure 3, Figure 8 and Figure 10), the M3C2 algorithm was used, since this allows better visualization of the results as well as discrimination between positive and negative values of the differences obtained.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The three steps developed by the Point Cloud Stacking algorithm. Step 1: All points are stored in the PC-Stack cloud. Step 2: Coordinates system change. Step 3: Point averaging on the normal axis.

**Figure 2.**Functions developed to create the Synthetic Point Clouds (Synt-PC) First row: Function without error, representing the reference PC (Ref-PC) (Equation (1)). Rows (2 to 4): Synthetic functions created with errors based on random parameters (Equation (2)). Columns (left to right): Error function; sum of Ref-PC + Error function, X cross-section, Y cross-section. Dotted lines correspond to the Ref-PC and continuous lines to the Synt-PC.

**Figure 3.**(

**a**) X cross-sections of 5 Synt-PC (each color corresponds to a different Synt-PC), the black line corresponds to the sections of the Ref-PC. (

**b**) Y cross-sections of 5 Synt-PC (each color corresponds to a different Synt-PC), the black line corresponds to the sections of the Ref-PC. (

**c**) Distribution of differences between two Synt-PC computed by M3C2.

**Figure 4.**(

**a**) Puigcercós location (Pallars Jussà—Catalonia—NE Spain). (

**b**) Geomorphological scheme of the Puigcercós cliff and main rockfall mechanism (modified from Royán et al. [8]).

**Figure 5.**Low-cost photogrammetric systems developed ad-hoc for rockfall monitoring on the Puigcercós cliff. (

**a**,

**b**,

**c**) Images of the installation on the Puigcercos cliff. (

**d**) Main electronic components (left to right): WittyPi2, Raspberry Pi Zero W, Raspberry Camera Module v2 and MicroSD card.

**Figure 6.**(

**a**) X cross-sections of four Photo-PCs generated using five images (each color corresponds to a different Photo-PC). (

**b**) Y cross-sections of four Photo-PCs generated using five images (each color corresponds to a different Photo-PC). (

**c**) Distribution of differences of two Photo-PCs computed by M3C2. (x) and (y) shows the cross section represented in (

**a**) and (

**b**).

**Figure 7.**Results from the application of the PCStacking algorithm with synthetic data. (

**a**) Histogram of the differences between the Enh-PC

_{n}and the Ref-PC. Each colored line represents a different number of Synt-PCs introduced into the PCStacking algorithm. (

**b**) Boxplot with the errors of the differences obtained in the different comparisons (Enh-PC

_{n}vs. Ref-PC).

**Figure 8.**(

**a**) Evolution of the standard deviation of the comparison Enh-PC

_{n}vs. Ref-PC in the redundancy test. The standard deviation decreased from 4.9 cm to 1.8 cm. A total of 400 Synt-PCs were used to compute this plot. (

**b**) Number of averaged points according to the search radius (r). Each colored line represents a different number of Synt-PCs introduced into the PCStacking algorithm.

**Figure 9.**Results from the application of the PCStacking algorithm to real images. (

**a**) Histogram of the differences between the Enh-PC

_{n}

^{25 feb}and Enh-PC

_{n}

^{26 feb}. Each colored line represents a different number of PCs introduced into the PCStacking algorithm. (

**b**) Error of the differences obtained in the different comparisons (Enh-PC

_{n}

^{25 feb}vs. Enh-PC

_{n}

^{26 feb}).

**Figure 10.**Influence of the search radius (r) on the PCStacking results. (

**a**) Standard deviation of the Enh-PC

_{n}

^{25 feb}vs. Enh-PC

_{n}

^{26 feb}comparison. (

**b**) Comparisons between Enh-PC

_{15}

^{25 feb}and Enh-PC

_{15}

^{26 feb}for different search radii (r).

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**MDPI and ACS Style**

Blanch, X.; Abellan, A.; Guinau, M.
Point Cloud Stacking: A Workflow to Enhance 3D Monitoring Capabilities Using Time-Lapse Cameras. *Remote Sens.* **2020**, *12*, 1240.
https://doi.org/10.3390/rs12081240

**AMA Style**

Blanch X, Abellan A, Guinau M.
Point Cloud Stacking: A Workflow to Enhance 3D Monitoring Capabilities Using Time-Lapse Cameras. *Remote Sensing*. 2020; 12(8):1240.
https://doi.org/10.3390/rs12081240

**Chicago/Turabian Style**

Blanch, Xabier, Antonio Abellan, and Marta Guinau.
2020. "Point Cloud Stacking: A Workflow to Enhance 3D Monitoring Capabilities Using Time-Lapse Cameras" *Remote Sensing* 12, no. 8: 1240.
https://doi.org/10.3390/rs12081240