# An Improved RANSAC Outlier Rejection Method for UAV-Derived Point Cloud

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

#### Related Works

- number of inliers found;
- lower number of iterations;
- increased convergence rate;
- the refinement of the final inlier output (reducing the remaining outliers in the last stage of the loop).

## 2. Methods

#### 2.1. An Overview of the RANSAC-Based Methods

Algorithm 1: Standard RANSAC procedure. |

Inputs: M: all tie points, s: minimum number of points required to solve the unknown parameters of the model, and $\theta $: a predefined threshold. |

Output: ${I}_{global-best}$: global-best-inliers |

$iteration=0$, ${I}_{current-best}=0$ |

While $iteration$ < $N$ |

Select an initial random sample (s points) |

Generate the hypothesis using the initial sample (collinearity equations) |

Evaluate the hypothesis (i.e., Euclidian distance for all tie data points (M)) |

Count the supporting points (${I}_{iteration}$) |

If ${I}_{iteration}$ > ${I}_{current-best}$ |

${I}_{current-best}={I}_{iteration}$ |

Update N based on the new ${I}_{current-best}$ (Equation (2)) |

End If |

$iteration=iteration$ + 1 |

End While |

${I}_{global-best}={I}_{current-best}$ Re-estimate the Collinearity equations or the Fundamental matrix using ${I}_{global-best}$ |

#### 2.2. ELISAC: Empowered Locally Iterative SAmple Consensus

#### 2.3. Locally Iterative Least Squares (LILS) Loop

#### 2.3.1. Basic LILS

Algorithm 2: Basic LILS. |

Inputs: M: all match points, s: minimum number of points required to solve the unknown parameters of a model, and $\theta $: a predefined threshold. |

Output: ${I}_{global-best}$: global-best-inliers |

$iteration=0$, ${I}_{current-best}=0$, ${I}_{save-best}=0$ |

While $iteration$ < $N$ |

Select an initial random sample (s points) |

Generate a hypothesis using the initial sample |

Evaluate the hypothesis (evaluation procedure against all data points (M)) |

Count the support data (${I}_{iteration}$) |

If ${I}_{iteration}$ > ${I}_{current-best}$ |

${I}_{current-best}={I}_{iteration}$ |

${I}_{loop-best}=0$ |

While (${I}_{loop-best}$ > ${I}_{current-best}$ OR ${I}_{loop-best}=0$) |

If ${I}_{loop-best}$ ≠ 0 |

${I}_{current-best}={I}_{loop-best}$ |

End If |

Select all inliers (${I}_{current-best}$) as initial sample |

Generate a hypothesis (least-squares-based) using the initial sample |

Evaluate the hypothesis (evaluation procedure against all data points (M)) |

Count the supporting data (${I}_{loop-best}$) |

End While |

If ${I}_{current-best}$ ≥ ${I}_{save-best}$ |

${I}_{save-best}$ = ${I}_{current-best}$ |

Else |

${I}_{current-best}$ = ${I}_{save-best}$ |

End If |

Check the ST criterion (optional) and terminate the program if it is satisfied. |

Update N based on the new ${I}_{current-best}$ (AT-Basic criterion) |

End If |

$iteration=iteration$ + 1 |

End While |

${I}_{global-best}={I}_{current-best}$ Re-estimate the Collinearity equations or the Fundamental matrix using ${I}_{global-best}$ |

#### 2.3.2. Aggregated LILS

Algorithm 3: Aggregated LILS. |

Inputs: M: all match points, s: minimum number of points required to solve the unknown parameters of a model, and $\theta $: a predefined threshold. |

Output: ${I}_{global-best}$: global-best-inliers |

$iteration=0$, ${I}_{current-best}=0$, ${I}_{save-best}=0$, ${I}_{Aggregate-best}=0$ |

While $iteration$ < $N$ |

Select an initial random sample (s points) |

Generate a hypothesis using the initial sample |

Evaluate the hypothesis (evaluation procedure against all data points (M)) |

Count the support data (${I}_{iteration}$) |

If ${I}_{iteration}$ > ${I}_{current-best}$ |

${I}_{current-best}={I}_{iteration}$ |

${I}_{loop-best}=0$ |

While (${I}_{loop-best}$ > ${I}_{current-best}$ OR ${I}_{loop-best}=0$) |

If ${I}_{loop-best}$ ≠ 0 |

${I}_{current-best}={I}_{loop-best}$ |

End If |

Select all inliers (${I}_{current-best}$) as the initial sample |

Generate a hypothesis (least-squares-based) using the initial sample |

Evaluate the hypothesis (evaluation procedure against all data points (M)) |

Count the supporting data (${I}_{loop-best}$) |

End While |

If ${I}_{current-best}$ ≥ ${I}_{save-best}$ |

If ${I}_{save-best}\ne 0$ |

${I}_{Aggregate-best}=Aggregate\left({I}_{Aggregate-best}{I}_{current-best}\right)$ |

Check the ST criterion (optional) and terminate the program if it is satisfied. |

${I}_{save-best}$ = ${I}_{current-best}$ |

Else If ${I}_{save-best}=0$ |

${I}_{save-best}$ = ${I}_{current-best}$ |

${I}_{Aggregate-best}$ = ${I}_{current-best}$ |

End If |

Else |

Check the ST criterion (optional) and terminate the program if it is satisfied. |

${I}_{current-best}$ = ${I}_{save-best}$ |

${I}_{Aggregate-best}=Aggregate\left({I}_{Aggregate-best}{I}_{current-best}\right)$ |

End If |

Update N based on the new ${I}_{current-best}$ (AT-Basic criterion) or ${I}_{Aggregate-best}$ (AT-Improved) |

End If |

$iteration=iteration$ + 1 |

End While |

${I}_{global-best}={I}_{Aggregate-best}$ Re-estimate the Collinearity equations or the Fundamental matrix using obtained ${I}_{global-best}$ |

#### 2.4. The Similarity Termination (ST) Criterion

#### 2.5. Post-Processing Procedure

## 3. Experiments and Results

#### 3.1. Dataset

#### 3.2. Performance Evaluation

#### 3.3. Point Cloud and DSM Comparison

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Chart 1.**Processing steps in MSAC and the proposed ELISAC method (gray boxes show the three enhancements steps).

**Figure 1.**The image samples of the first dataset (Books (

**a**), Box (

**b**), Kampa (

**c**), Kyoto (

**d**), Plant (

**e**), Valbonne (

**f**)).

**Figure 2.**The image sequence samples of the UAV dataset (image pairs: (

**a**,

**b**), (

**a**,

**c**), (

**a**,

**d**), (

**a**,

**e**), (

**a**,

**f**), (

**a**,

**g**), (

**a**,

**h**), and (

**a**,

**i**)).

**Figure 7.**Three different stereo UAV images over dense (

**a**), semi-dense (

**b**), and sparse (

**c**) forestry areas.

**Figure 8.**The generated sparse point cloud by the proposed procedure (

**a–c**) and Agisoft (

**d–f**) from the first, second, and third datasets, respectively.

**Figure 9.**The generated dense point clouds based on the proposed procedure (

**a–c**) and Agisoft (

**d–f**) from the first, second, and third datasets.

**Figure 10.**The differences between the generated point clouds by Agisoft and the proposed method from (

**a**) the first, (

**b**) second, and (

**c**) third datasets.

**Figure 11.**The image captured at the desired area (

**a**), the generated DSM by Agisoft (

**b**), as well as the proposed method, (

**c**) are also shown from the first dataset. The subtraction of two DSMs, in addition to the profile graph, is also demonstrated (

**d**).

**Figure 12.**The image captured at the desired area (

**a**), the generated DSM by Agisoft (

**b**), as well as the proposed method, (

**c**) are also shown from the second dataset. The subtraction of two DSMs, in addition to the profile graph, is also demonstrated (

**d**).

**Figure 13.**The image captured at the desired area (

**a**), the generated DSM by Agisoft (

**b**), as well as the proposed method, (

**c**) are also shown from the third dataset. The subtraction of two DSMs, in addition to the profile graph, is also demonstrated (

**d**).

Image Pairs | Books (a) | Box (b) | Kampa (c) | Kyoto (d) | Plant (e) | Valbonne (f) |
---|---|---|---|---|---|---|

Number of SIFT points | 167 | 418 | 227 | 730 | 157 | 97 |

Weight (g) | 1280 | |

Diagonal size (mm) | 350 | |

Max speed (m/s) | 16 | |

UAV model | DJI Phantom 3 | |

Camera | Model | FC330 |

Sensor | 1/2.3″ CMOS (Effective pixels: 12.4 M) | |

Lens | FOV 94°20 mm | |

Hover Accuracy Range | Vertical | ±0.5 m (with GPS Positioning) |

Horizontal | ±1.5 m (with GPS Positioning) | |

Max. flight time (minute) | 23 | |

Image size (pixels) | 4000 × 3000 | |

Ground resolution size of images (cm/pix) | 2 | |

Average flight altitude (m) | 53.8 | |

Focal length in 35 mm format (mm) | 20 | |

ISO speed | 174 | |

Exposure | 1/60 | |

Aperture Value | 2.8 | |

Image area coverage (m^{2}) | 81 × 61 |

Image Pairs | a and b | a and c | a and d | a and e | a and f | a and g | a and h | a and i |
---|---|---|---|---|---|---|---|---|

Number of SIFT points | 7791 | 2621 | 1083 | 420 | 4265 | 2400 | 1324 | 728 |

Books (a) | Box (b) | Kampa (c) | Kyoto (d) | Plant (e) | Valbonne (f) | ||
---|---|---|---|---|---|---|---|

Inliers’ average-RMSEI(min-max) | MSAC | 80.0 ± 5.6 (67–93) | 221.7 ± 9.8 (200–247) | 70.1 ± 3.6 (61–79) | 245.7 ± 10.1 (214–266) | 52.1 ± 4.1 (41–63) | 39.1 ± 2.3 (30–44) |

Basic LILS | 102.0 ± 6.0 (84–118) | 278.7 ± 15.2 (234–303) | 110.1 ± 8.8 (85–136) | 338.5 ± 28.6 (257–392) | 70.45 ± 5.4 (56–83) | 51.7 ± 4.1 (39–61) | |

Aggregated LILS | 90.0 ± 6.9 (71–98) | 222.8 ± 15.6 (186–249) | 65.3 ± 4.9 (53–79) | 249.4 ± 12.7 (202–266) | 51.7 ± 4.8 (41–64) | 40.3 ± 3.5 (31–46) | |

Ratio of inliers w.r.t MSAC | Basic LILS | 1.275 | 1.2571 | 1.5706 | 1.3776 | 1.3522 | 1.3222 |

Aggregated LILS | 1.125 | 1.0049 | 0.9315 | 1.015 | 0.9923 | 1.0306 | |

Ratio of computational time w.r.t MSAC | Basic LILS | 0.174 | 0.277 | 0.040 | 0.122 | 0.127 | 0.139 |

Aggregated LILS | 0.197 | 0.377 | 0.049 | 0.127 | 0.112 | 0.150 |

**Table 5.**The obtained results from all image pairs (a and b, a and c, a and d, a and e, a and f, a and g, a and h, and a and i).

a and b | a and c | a and d | a and e | a and f | a and g | a and h | a and i | ||

Inliers’ average-RMSE (min-max) | MSAC | 4516.5 ± 245.9 (4001–5128) | 1374.3 ± 68.2 (1228–1566) | 491.3 ± 20.1 (447–552) | 119.2 ± 4.7 (104–131) | 2416.1 ± 130.5 (2145–2699) | 1243.3 ± 66.4 (1100–1383) | 618.8 ± 30.0 (540–688) | 248.6 ± 10.5 (227–274) |

Basic LILS | 5380.4 ± 51.4 (4935–5420) | 1593.6 ± 35.8 (1511–1644) | 556.1 ± 8.0 (531–570) | 132.6 ± 2.5 (124–137) | 2882.9 ± 14.4 (2828–2909) | 1435.5 ± 14.3 (1384–1463) | 722.1 ± 11.9 (681–743) | 279.1 ± 7.0 (243–290) | |

Aggregated LILS | 5394.4 ± 19.8 (5301–5439) | 1598.8 ± 34.7 (1456–1644) | 559.1 ± 7.5 (538–571) | 133.5 ± 2.7 (123–139) | 2889.5 ± 13.2 (2844–2913) | 1442.3 ± 16.7 (1380–1478) | 720.2 ± 13.6 (680–746) | 282.0 ± 7.4 (260–296) | |

Ratio of inliers w.r.t MSAC | Basic LILS | 1.1912 | 1.2505 | 1.1318 | 1.1124 | 1.1932 | 1.1545 | 1.1669 | 1.1226 |

Aggregated LILS | 1.1943 | 1.2546 | 1.1380 | 1.1199 | 1.1959 | 1.1600 | 1.1638 | 1.1343 | |

Ratio of computational time w.r.t MSAC | Basic LILS | 1.522 | 1.051 | 0.407 | 0.220 | 0.814 | 0.539 | 0.402 | 0.355 |

Aggregated LILS | 1.678 | 0.769 | 0.310 | 0.131 | 0.819 | 0.545 | 0.360 | 0.105 |

Method | Number of Points in the Generated Sparse Point Clouds | ||
---|---|---|---|

First Dataset (a) | Second Dataset (b) | Third Dataset (c) | |

The proposed procedure | 4870 | 5755 | 11,292 |

Agisoft software | 3306 | 4225 | 7418 |

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## Share and Cite

**MDPI and ACS Style**

Salehi, B.; Jarahizadeh, S.; Sarafraz, A.
An Improved RANSAC Outlier Rejection Method for UAV-Derived Point Cloud. *Remote Sens.* **2022**, *14*, 4917.
https://doi.org/10.3390/rs14194917

**AMA Style**

Salehi B, Jarahizadeh S, Sarafraz A.
An Improved RANSAC Outlier Rejection Method for UAV-Derived Point Cloud. *Remote Sensing*. 2022; 14(19):4917.
https://doi.org/10.3390/rs14194917

**Chicago/Turabian Style**

Salehi, Bahram, Sina Jarahizadeh, and Amin Sarafraz.
2022. "An Improved RANSAC Outlier Rejection Method for UAV-Derived Point Cloud" *Remote Sensing* 14, no. 19: 4917.
https://doi.org/10.3390/rs14194917