# Experimental Tests and Simulations on Correction Models for the Rolling Shutter Effect in UAV Photogrammetry

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. State-of-the-Art in RS Modelling

#### 1.2. Experimental Tests on Rolling Shutter Correction

^{2}has been surveyed with two flights at 8 m/s and 12 m/s speed with a Phantom 4 Pro, equipped with a mechanical shutter and a CMOS sensor. The block has been adjusted with Agisoft Photoscan (the version number is unspecified) with and without RS compensation. No information is provided on image overlaps, GSD or whether camera calibration parameters have been estimated in the BBA. The correction model effectiveness is measured over the residuals of 24 well-distributed GCPs rather than at independent checkpoints. The improvement on such residuals with RS correction active is 25–35% in horizontal coordinates and 25–50% in elevation, with the lower gain at lower speed.

#### 1.3. Paper Goals

- (i).
- Following the results presented in [23] over flat terrain, the paper aims primarily to investigate the performance of the 10-parameter Fraser model over rough terrain, where the image scale varies considerably also within a single frame and therefore may result in less effective results. In this respect, evidence will also be sought on whether it is better to estimate a single set of affine parameters for the whole block or to work on an image-by-image basis. Alongside these new contributions, as the photogrammetric processing will be performed with Metashape, an evaluation of the effectiveness and a comparison with the 10-parameter camera calibration model of the two RS correction methods available in the 1.8.0 version will be performed on the test flight results. Besides the evaluation of the accuracy on the ground, an analysis of the estimated correction parameters and their correlations with flight or drone characteristics has been performed. Likewise, an analysis of the interior and exterior orientation parameters estimates from the BBA shows their correlations (particularly between principal distance and camera elevation a.g.l.) to be even stronger than usual with RS-distorted images.
- (ii).
- Adding the RS correction parameters as unknowns in the BBA might weaken the stability of the solution, introducing correlations that may require a denser ground control. To this aim, an analysis of the optimal number of GCP necessary, their density and their spatial distribution will be performed over the experimental test fields.
- (iii).
- The costs and operational benefits for drone surveys of hosting on-board global navigation satellite systems (GNSS) receivers capable of measuring with cm-level accuracy the camera stations are today largely acknowledged. On the one hand, drone manufacturers are recognising that the RS technology is an objective obstacle to the metric use of images and switching to global shutters in their latest products. On the other hand, apart from the turn-key RTK plug-in modules offered by virtually all main drone manufacturers, many kits are available on the market that allow users to render their RS platforms RTK-capable. Though, therefore, the problem of RS may fade in the medium or long term, the paper investigates with a series of simulations whether using drones with RS sensors and such enhanced-performance receivers helps to contrast the RS effect by reducing the number of GCP.

## 2. Materials and Methods

#### 2.1. Equipment and Test Site Characteristics

#### 2.2. Image and Reference Data Acquisition

#### 2.3. Test Overview

#### 2.3.1. Analysis of Check Point Accuracy as a Function of the Number of GCP

- -
- without RS modelling and with an 8-parameter camera calibration model;
- -
- without RS modelling and with a 10-parameter camera calibration model;
- -
- with Metashape 2-parameter RS model and with an 8-parameter camera calibration model;
- -
- with Metashape 6-parameter RS model and with an 8-parameter camera calibration model.

- RMSE(all): RMSE on CP of the BBA with all GCP fixed
- RMSE(i): RMSE on CP of the BBA with i GCP fixed, i = {22, 18, 14, 9, 6}

#### 2.3.2. Analysis of Rolling Shutter Compensation Model Performance

#### 2.3.3. A Simulation Study on RS Modelling with GNSS-Assisted Block Orientation

## 3. Results

#### 3.1. CP Accuracy as a Function of the Number of GCP

#### 3.2. Rolling Shutter Compensation Strategies

#### Parameters’ Value Evaluation

^{2}= 0.94) and confirms that a large portion of the RMSE is due to the RS effect and that just the b1 parameter is effective in correcting it. In fact, after corrections, the RMSE is leveraged even among all the drones.

#### 3.3. Rolling Shutter and GNSS-Assisted BBA

## 4. Discussion

^{2}, approximately 1000 images), using more than eight GCP did not improve the horizontal coordinate accuracy by more than 0.9–2.1 GSD; elevation accuracy improved much less or not at all. On the other hand, in a rectangular block (0.2 km

^{2}, approximately 400 images) with eight GCP only, the accuracy was already better than one GSD in horizontal coordinates, while in elevation, it ranged between 2.6 and 8.3 GSD. Though the GCP density is quite different from our experiment, the conclusions are similar, in particular, that too few GCP affect primarily the accuracy of elevation. In [23], in an area 200 × 150 m wide, out of 15 points, 8 and 7 were used alternately as GCP and CP in each of the various tests; the RMSE changed up to more than 50% when switching CP and GCP. Though taking into account the small GCP and CP sample sizes, this also hints that GCP layout matters and cannot easily be optimised. Still, in the [23] paper, it has been mentioned that in the block corridor case, only the MicMac and the 10-parameter camera models were effective, while Metashape had large errors, especially in elevation. Though we did not investigate a corridor case, as the number of GCP used (five over a 400-m-long strip) is limited, this could be seen as consistent with our analysis of errors in elevation with poor ground control.

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Figure A1.**Graphs of δ (see Equation (1)) for Air2s platform flights over Site B in four BBA processing configurations. (

**Left**): horizontal coordinates; (

**right**): elevations. Please notice that the scale limits are not the same.

**Figure A2.**Graphs of δ (see Equation (1)) for Mavic Mini platform flights over Site A in four BBA processing configurations. (

**Left**): horizontal coordinates; (

**right**): elevations. Please notice that the scale limits are not the same.

**Figure A3.**Graphs of δ (see Equation (1)) for Mavic Mini platform flights over Site B in four BBA processing configurations. (

**Left**): horizontal coordinates; (

**right**): elevations. Please notice that the scale limits are not the same.

**Figure A4.**Graphs of δ (see Equation (1)) for Phantom 4 Pro platform flights at 4 m/s over Site A in two BBA processing configurations. (

**Left**): horizontal coordinates; (

**right**): elevations. Please notice that the scale limits are not the same.

**Figure A5.**Graphs of δ (see Equation (1)) for Phantom 4 Pro platform flights at 4 m/s over Site B in two BBA processing configurations. (

**Left**): horizontal coordinates; (

**right**): elevations. Please notice that the scale limits are not the same.

## Appendix B

**Figure A6.**Graphs of RMSE on CP in four BBA processing configurations for Phantom 4 Pro platform at Site A. (

**Left**): horizontal coordinates; (

**right**): elevations. Please notice that the scale limits are not the same.

**Figure A7.**Graphs of RMSE on CP in four BBA processing configurations for Phantom 4 Pro platform at Site B. (

**Left**): horizontal coordinates; (

**right**): elevations. Please notice that the scale limits are not the same.

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**Figure 1.**Characteristics of the case study sites: (

**a**) Site A—Parma University Campus; (

**b**) Site B—Pasture Grassland in Aosta Valley. Top: orthophoto with white circles showing camera stations along strips; bottom: digital elevation model. Grid coordinates are defined in the RDN2008/UTM Zone 32N (EPSG: 6707) system.

**Figure 2.**GCPs and CPs locations for the two sites: (

**a**) Site A, (

**b**) Site B. CPs, represented by yellow circles, do not change (45 CP in Site A and 24 CP in Site B); GCPs, represented by red circles, increase from 6 to 22 in five steps.

**Figure 3.**Workflow of the simulation study on RS modelling with GNSS-assisted block orientation. Adjusted camera station positions are exported from three cases, corrupted with random errors, and oriented in a GNSS-assisted BBA.

**Figure 4.**Graphs of δ (see Equation (1)) for all Air2s flights over Site A in processing Cases A, B, F, E (see Table 4). Left: horizontal coordinates; right: elevations. Please notice that the scales limits are not the same.

**Figure 5.**Graphs of RMS on CP in processing configuration A, for all the platforms and Sites. Left: horizontal coordinates; right: elevations. Please notice that the scales limits are not the same.

**Figure 6.**Graphs of RMSE on CP in seven BBA processing configurations, for Air2s and Mavic Mini platforms in Site A.

**Left**: horizontal coordinates;

**right**: elevations. Please notice that the scales limits are not the same.

**Figure 7.**Graphs of RMSE on CP in seven BBA processing configurations, for Air2s and Mavic Mini platforms in Site B.

**Left**: horizontal coordinates;

**right**: elevations. Please notice that the scales limits are not the same.

**Figure 8.**Scatter chart showing the relationship between the RMSE on CP (xyz coordinates) obtained in Case A and the corresponding b1 values computed in Case B for the same flight.

**Figure 9.**Estimated values of Sx and Sy camera shifts (Case E) due to RS effect. (

**a**) Graphical representation of camera movements during readout times for Air2S at Site A at 2 m/s and 4 m/s flight speeds: camera y-axis is represented with a red line, and estimated camera movement is depicted by a green line. (

**b**) Table of the combined Sx and Sy movements (averaged over each block) at different speeds for each drone and site, and 100% staked bar of their relative proportion at different speeds.

Drone | Pixel Size [μm] | Resolution [pix] | Shutter Type | Sensor | Focal Length [mm] |
---|---|---|---|---|---|

Air2S | 2.4 | 5472 × 3648 | Rolling | 1″ CMOS | 22 * |

Mavic Mini | 1.8 | 4000 × 2250 | Rolling | 1/2,3″ CMOS | 24 * |

Phantom 4 Pro | 2.4 | 5472 × 3648 | Global | 1″ CMOS | 24 * |

Site | Number of Images | Height | Forward Overlap | Side Overlap |
---|---|---|---|---|

A | 68 | 45 m a.g.l. | 70% | 60% |

B | 108 | 50 m a.g.l. | 80% | 70% |

Site | Air2S | Mavic Mini | Phantom P4 Pro |
---|---|---|---|

A | 11 mm | 13 mm | 10 mm |

B | 15 mm | 17 mm | 12 mm |

Site | Air2S | Mavic Mini | Phantom P4 Pro | |
---|---|---|---|---|

A | 1 m/s | 0.93 | 0.47 | 0.47 |

2 m/s | 0.93 | 0.48 | 0.51 | |

4 m/s | 0.96 | 0.49 | 0.49 | |

B | 1 m/s | 0.96 | 0.48 | 0.48 |

2 m/s | 0.98 | 0.51 | 0.43 | |

4 m/s | 1.06 | 0.51 | 0.47 |

**Table 5.**Specification of the parameters adopted for camera calibration and RS modelling in each of the seven test cases were executed to explore different strategies for RS compensation.

Case | Camera Calibration Model | Rolling Shutter Model |
---|---|---|

A | 8-parameter (f, c_{x}, cy, k1, k2, k3, p1, p2) | None |

B | 10-parameter (f, c_{x}, cy, k1, k2, k3, p1, p2, b1, b2) | None |

C | 8-parameter + b1 only | None |

D | 10-parameter (f, c_{x}, cy, k1, k2, k3, p1, p2, b1, b2) with b1 and b2 computed image by image | None |

E | 8-parameter | Sx, Sy |

F | 8-parameter | Tx, Ty, Tz, Rx, Ry, Rz |

G | 10-parameter (f, c_{x}, cy, k1, k2, k3, p1, p2, b1, b2) | Tx, Ty, Tz, Rx, Ry, Rz |

**Table 6.**Estimated values of the scaling parameter b1 for each block in Cases B, C and G to highlight the correlation with the platform speed.

B | C | G | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

Site | 1 m/s | 2 m/s | 4 m/s | 1 m/s | 2 m/s | 4 m/s | 1 m/s | 2 m/s | 4 m/s | |

A | Air2S | −4.74 | −8.95 | −17.41 | −4.73 | −8.95 | −17.41 | −10.32 | −14.87 | −21.30 |

Mavic Mini | −2.02 | −3.87 | −7.89 | −2.03 | −3.87 | −7.9680 | −9.13 | −9.95 | −13.03 | |

Phantom | −0.01 | 0.01 | 0.04 | −0.04 | −0.02 | 0.01 | - | - | - | |

B | Air2S | −5.26 | −8.88 | −16.76 | −5.19 | −8.92 | −16.73 | −8.63 | −13.47 | −16.69 |

Mavic Mini | −2.68 | −4.83 | −8.40 | −2.68 | −4.81 | −8.39 | −8.70 | −10.14 | −13.26 | |

Phantom | −0.23 | −0.49 | −0.72 | −0.31 | −0.49 | −0.71 | - | - | - |

**Table 7.**Correlations between the estimated parameters of Case D and Case E for each block and site. Top: correlation between b1 and Sy; bottom: correlation between b2 and Sx.

Site A | Site B | ||||
---|---|---|---|---|---|

Air2S | Mavic Mini | Air2S | Mavic Mini | ||

b1-Sy | 1 m/s | 0.910 | 0.944 | 0.776 | 0.444 |

2 m/s | 0.953 | 0.757 | 0.713 | 0.809 | |

4 m/s | 0.935 | 0.450 | 0.941 | 0.859 | |

b2-Sx | 1 m/s | −0.940 | −0.982 | −0.747 | −0.896 |

2 m/s | −0.973 | −0.861 | −0.568 | −0.972 | |

4 m/s | −0.980 | −0.666 | −0.686 | −0.908 |

**Table 8.**Differences between the principal distance and the average camera station elevation estimated in Case A and the corresponding values estimated in all the other cases.

Principal Distance Difference (pix) | Projection Centre Z Difference (m) | ||||||
---|---|---|---|---|---|---|---|

UAV-Site | Case | 1 m/s | 2 m/s | 4 m/s | 1 m/s | 2 m/s | 4 m/s |

MavicSite A | B | −1.4 | −80.4 | −242.4 | −0.03 | −1.11 | −3.40 |

E | −3.9 | −83.3 | −180.6 | −0.04 | −1.09 | −2.45 | |

F | 18.8 | −76.3 | −191.3 | 0.26 | −1.00 | −2.60 | |

MavicSite B | B | 9.8 | 27.7 | 39.4 | 0.14 | 0.39 | 0.54 |

E | 0.2 | 8.0 | 10.9 | 0.02 | 0.11 | 0.22 | |

F | −1.8 | 5.5 | 23.0 | −0.03 | 0.09 | 0.36 | |

Air2sSite A | B | −13.4 | −19.3 | −59.1 | −0.17 | −0.25 | −0.75 |

E | −6.1 | −22.9 | −49.1 | −0.04 | −0.20 | −0.44 | |

F | −69.2 | −61.1 | −95.5 | −0.75 | −0.63 | −0.97 | |

Air2sSite B | B | 22.3 | 35.1 | 73.8 | 0.26 | 0.41 | 0.90 |

E | 6.2 | 9.3 | 40.7 | 0.09 | 0.14 | 0.64 | |

F | −1.8 | −1.3 | 28.1 | −0.01 | 0.01 | 0.47 |

**Table 9.**RMSE on the CP of the simulated GNSS-assisted BBA, all processed in Case B. Fictitious PC sets were derived from GCP-only BBA in different cases. As a reference for comparison, the RMSE of Case B with 14 GCP is also included (last row).

PC Set | X (cm) | Y (cm) | Z (cm) | |
---|---|---|---|---|

Original | A | 2.3 | 1.5 | 3.6 |

E | 1.1 | 1.0 | 1.6 | |

F | 2.0 | 1.5 | 2.5 | |

With random errors | A1 | 2.3 | 1.6 | 3.6 |

E1 | 1.1 | 1.0 | 1.7 | |

F1 | 1.2 | 1.1 | 1.6 | |

14 GCP Case B | 1.2 | 0.9 | 1.6 |

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**MDPI and ACS Style**

Bruno, N.; Forlani, G.
Experimental Tests and Simulations on Correction Models for the Rolling Shutter Effect in UAV Photogrammetry. *Remote Sens.* **2023**, *15*, 2391.
https://doi.org/10.3390/rs15092391

**AMA Style**

Bruno N, Forlani G.
Experimental Tests and Simulations on Correction Models for the Rolling Shutter Effect in UAV Photogrammetry. *Remote Sensing*. 2023; 15(9):2391.
https://doi.org/10.3390/rs15092391

**Chicago/Turabian Style**

Bruno, Nazarena, and Gianfranco Forlani.
2023. "Experimental Tests and Simulations on Correction Models for the Rolling Shutter Effect in UAV Photogrammetry" *Remote Sensing* 15, no. 9: 2391.
https://doi.org/10.3390/rs15092391