# Impact of Stereo Camera Calibration to Object Accuracy in Multimedia Photogrammetry

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Calibration Techniques in Multimedia Photogrammetry

#### 2.1. Planar Interfaces

#### 2.2. Hemispherical Interfaces

#### 2.3. System Configurations and Calibration Strategies

#### 2.4. Calibration Fixtures

## 3. Synthetic Datasets

^{−6}mm is added to the error-free image coordinates of the calibration fixture. These coordinates are named error-free coordinates in the following. By integrating a strict raytracing model using synthetic interfaces, the object points can also be projected into the image through refracting interfaces.

#### 3.1. Notation and Assumptions

_{single/multimedia}convergence-ratio

_{air/water}–calibration fixture

_{MM}10°-5/95-Cube describes an experiment with two cameras in a multimedia case (air-glass-water) with a convergence of 10° equipped with a glass interface at 5% of the distance for each camera (bundle-invariant case) to the object, based on the dataset with a cube as calibration fixture. In case of single-camera setting, of course, no convergence is part of the experiments naming. Datasets having a ratio of 1/99 assume the interface to be 20 mm in front of the principal point as in Figure 3.

- Isotropic glass interface of 10 mm thickness
- Refractive index of air = 1.000
- Refractive index of water = 1.3318
- Refractive index of glass = 1.490
- Perpendicular arrangement of the interface with respect to the optical axis

#### 3.2. Dataset Cube

^{3}, the average acquisition distance 3.5 m. Thus, this dataset represents a typical ROV application using an ideal spatial test-field, even though such a large object would be hard to handle underwater. Correlations should become as small as possible using such a dataset. By introducing bundle-invariant interfaces, this dataset is extended to a multimedia dataset. Variations of interface parameters and convergence of the stereo system will be discussed in Section 3.4 and Section 3.5.

#### 3.3. Dataset HS

#### 3.4. Variation of Convergence

#### 3.5. Variation of Air/Water Ratio

#### 3.6. Quality Evaluation in Object Space via Forward Intersection

## 4. Analysis of Calibration and Orientation for Planar Interfaces in Implicit Form

#### 4.1. Single-Camera Bundle Adjustment

_{SM}-1/99), image coordinates without any refractive effects are used for the bundle adjustment, whereas the datasets 3 and 4 (1

_{MM}-1/99) contain error-free refracted image coordinates. The interface is simulated 20mm in front of the lens, thus leading to an air/water depth ratio of approximately 1/99. The bundle adjustment was performed using standard software not introducing any interfaces as parameters, and using the standard collinearity equations with the distortion model according to [15]. The interior and exterior orientations are determined within the bundle adjustment employing the object points as fixed reference points. Table 3 shows that the principal distance is longer in the multimedia case by a factor of 1.42 compared to the nominal value. Furthermore, the values of the radial distortion parameters increase significantly. According to [39], the principal distance c increases underwater by a factor equivalent to the refraction index of water. The authors of [40] present ratios of 1.335 to 1.345 in experimental setups within identical environmental conditions and show that the principal distance as well as the exterior orientations of a stereo camera system exhibit high discrepancies between in-air and in-water calibration. In [41], it is suggested not to overcome the refraction effects by camera calibration and shown how the principal distance behaves in calibration depending on the ratio of air and water within the path of light.

#### 4.2. Stereo Camera Bundle Adjustment

- 2
_{SM}-0°-1/99 - 2
_{MM}-0°-1/99

#### 4.2.1. Variation of Convergence

#### 4.2.2. Variation of Air/Water Ratio

_{MM}-0°-50/50). The results are not stable, not even with synthetic data. They highly depend on the configuration of the bundle and the correlations between critical parameters. As expected, the principal distance becomes smaller when the percentage of water is decreased. As presented by [41], using standard software might lead to contrasting results regarding the principal distance. Compared with the results of convergent datasets (Section 4.2.1), the principal distance is calibrated significantly different. Furthermore, in contrast to the experiments of the previous section, the variation of the interface leads to large errors of the relative orientation in Z0, which represents the direction of the optical axis of the stereo camera (Table 8).

_{MM}-0-50/50) and have the largest scale in the dataset 50/50. At the range of ±2.5 m of the calibration distance, the 50/50 ratio shows the highest scale error.

#### 4.3. Assessment of Simulated Data

## 5. Analysis of Calibration and Orientation for Planar Interfaces in Explicit Form

#### 5.1. Explicit Modelling

n_{air} | = refractive index of air |

n_{glass} | = refractive index of glass |

n_{water} | = refractive index of water |

N1_{x}, N1_{y}, N1_{z}, d | = plane parameters of interface 1 |

N2_{x}, N2_{y}, N2_{z}, d2 | = plane parameters of interface 2 |

X0, Y0, Z0 | = translation of the relative orientation |

ω, φ, κ | = rotation of relative orientation |

#### 5.2. Synthetic Data

n_{water} | ± 0.01 |

Image coordinates | ± 1 pixel |

Translation of exterior orientations | ± 200 mm |

Rotation of exterior orientations | ± 1° |

## 6. Experiments

#### 6.1. Description of the Experiments

#### 6.2. Calibration Parameters

#### 6.3. Deviations in Object Space

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- kbvresearch.com. Underwater Camera Market Size. Available online: https://www.kbvresearch.com/underwater-camera-market-size/ (accessed on 28 November 2019).
- Datainsightspartner.com. Underwater Drones Market Size Estimation, in-Depth Insights, Historical Data, Price Trend, Competitive Market Share & Forecast 2019–2027. Available online: https://datainsightspartner.com/report/underwater-drones-market/61 (accessed on 28 November 2019).
- Shortis, M.; Ravanbakskh, M.; Shaifat, F.; Harvey, E.S.; Mian, A.; Seager, J.W.; Culverhouse, P.F.; Cline, D.E.; Edgington, D.R. A review of techniques for the identification and measurement of fish in underwater stereo-video image sequences. In SPIE Optical Metrology; Remondino, F., Shortis, M.R., Beyerer, J., Puente León, F., Eds.; SPIE: Munich, Germany, 2013. [Google Scholar]
- Torisawa, S.; Kadota, M.; Komeyama, K.; Suzuki, K.; Takagi, T. A digital stereo-video camera system for three-dimensional monitoring of free-swimming Pacific bluefin tuna, Thunnus orientalis, cultured in a net cage. Aquat. Living Resour.
**2011**, 24, 107–112. [Google Scholar] [CrossRef][Green Version] - Menna, F.; Nocerino, E.; Nawaf, M.M.; Seinturier, J.; Torresani, A.; Drap, P.; Remondino, F.; Chemisky, B. Towards real-time underwater photogrammetry for subsea metrology applications. In OCEANS 2019; IEEE: Marseille, France, 2019; pp. 1–10. [Google Scholar]
- Bruno, F.; Lagudi, A.; Collina, M.; Medaglia, S.; Davidde Petriaggi, B.; Petriaggi, R.; Ricci, S.; Sacco Perasso, C. Documentation and monitoring of underwater archaeological sites using 3d imaging techniques: The case study of the “nymphaeum of punta epitaffio” (baiae, naples). Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci.
**2019**, XLII-2/W10, 53–59. [Google Scholar] [CrossRef][Green Version] - Costa, E. The progress of survey techniques in underwater sites: The case study of cape stoba shipwreck. Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci.
**2019**, XLII-2/W10, 69–75. [Google Scholar] [CrossRef][Green Version] - Kahmen, O.; Rofallski, R.; Conen, N.; Luhmann, T. On scale definition within calibration of multi-camera systems in multimedia photogrammetry. Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci.
**2019**, XLII-2/W10, 93–100. [Google Scholar] [CrossRef][Green Version] - Shortis, M. Calibration Techniques for Accurate Measurements by Underwater Camera Systems. Sensors (Basel)
**2015**, 15, 30810–30826. [Google Scholar] [CrossRef][Green Version] - Boutros, N.; Shortis, M.R.; Harvey, E.S. A comparison of calibration methods and system configurations of underwater stereo-video systems for applications in marine ecology. Limnol. Oceanogr. Methods
**2015**, 13, 224–236. [Google Scholar] [CrossRef] - Massot-Campos, M.; Oliver-Codina, G. Optical Sensors and Methods for Underwater 3D Reconstruction. Sensors (Basel)
**2015**, 15, 31525–31557. [Google Scholar] [CrossRef] [PubMed][Green Version] - Höhle, J. Zur Theorie und Praxis der Unterwasser-Photogrammetrie; Deutsche Geodätische Kommission: München, Germany, 1971. [Google Scholar]
- Maas, H.-G. Digitale Photogrammetrie in der Dreidimensionalen Strömungsmesstechnik. Ph.D. Thesis, ETH Zürich—Dissertation Nr. 9665, Zürich, Switzerland, 1992. [Google Scholar]
- Mandlburger, G. A case study on through-water dense image matching. Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci.
**2018**, XLII-2, 659–666. [Google Scholar] [CrossRef][Green Version] - Brown, D.C. Close-Range Camera Calibration. Photogramm. Eng.
**1971**, 37, 855–866. [Google Scholar] - Kotowski, R. Zur Berücksichtigung Lichtbrechender Flächen im Strahlenbündel; Zugl.: Bonn, Univ., Diss., 1986; Beck: München, Germany, 1987; ISBN 3769693795. [Google Scholar]
- Bräuer-Burchardt, C.; Heinze, M.; Schmidt, I.; Kühmstedt, P.; Notni, G. Compact handheld fringe projection based underwater 3d-scanner. Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci.
**2015**, XL-5/W5, 33–39. [Google Scholar] [CrossRef][Green Version] - Maas, H.-G. A modular geometric model for underwater photogrammetry. Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci.
**2015**, XL-5/W5, 139–141. [Google Scholar] [CrossRef][Green Version] - Mulsow, C. A flexible multi-media bundle approach. Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci.
**2010**, XXXVIII/5, 472–477. [Google Scholar] - Menna, F.; Nocerino, E.; Remondino, F. Flat versus hemispherical dome ports in underwater photogrammetry. Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci.
**2017**, XLII-2/W3, 481–487. [Google Scholar] [CrossRef][Green Version] - Nocerino, E.; Menna, F.; Fassi, F.; Remondino, F. Underwater calibration of dome port pressure housings. Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci.
**2016**, XL-3/W4, 127–134. [Google Scholar] [CrossRef][Green Version] - Menna, F.; Nocerino, E.; Fassi, F.; Remondino, F. Geometric and Optic Characterization of a Hemispherical Dome Port for Underwater Photogrammetry. Sensors (Basel)
**2016**, 16, 48. [Google Scholar] [CrossRef][Green Version] - Menna, F.; Nocerino, E.; Remondino, F. Optical aberrations in underwater photogrammetry with flat and hemispherical dome ports. In Videometrics, Range Imaging, and Applications XIV; SPIE: Munich, Germany, 2017; pp. 26–27. [Google Scholar]
- Shortis, M.; Harvey, E.; Seager, J. A Review of the Status and Trends in Underwater Videometric Measurement. In Proceedings of the SPIE Conference 6491, Videometrics IX, IS&T/SPIE Electronic Imaging, San Jose, CA, USA, 28 January–1 February 2007. Invited paper. [Google Scholar]
- Menna, F.; Nocerino, E.; Troisi, S.; Remondino, F. A photogrammetric approach to survey floating and semi-submerged objects. In SPIE Optical Metrology; Remondino, F., Shortis, M.R., Beyerer, J., Puente León, F., Eds.; SPIE: Munich, Germany, 2013; 87910H. [Google Scholar]
- Johnson-Roberson, M.; Pizarro, O.; Williams, S.B.; Mahon, I. Generation and visualization of large-scale three-dimensional reconstructions from underwater robotic surveys. J. Field Robotics
**2010**, 27, 21–51. [Google Scholar] [CrossRef] - Rofallski, R.; Luhmann, T. Fusion von Sensoren mit optischer 3D-Messtechnik zur Positionierung von Unterwasserfahrzeugen. In Hydrographie 2018, Trend zu Unbemannten Messsystemen; Wißner-Verlag: Augsburg, Germany, 2018; pp. 223–234. ISBN 978-3-95786-165-8. [Google Scholar]
- Luhmann, T.; Fraser, C.; Maas, H.-G. Sensor modelling and camera calibration for close-range photogrammetry. ISPRS J. Photogramm. Remote Sens.
**2016**, 37–46. [Google Scholar] [CrossRef] - Wester-Ebbinghaus, W. Verfahren zur Feldkalibrierung von photogrammetrischen Aufnahmekammern im Nahbereich. In Kammerkalibrierung in der Photogrammetrischen Praxis; Reihe, B., Kupfer, G., Wester-Ebbinghaus, W., Eds.; Heft Nr. 275; Deutsche Geodätische Kommission: München, Germany, 1985; pp. 106–114. [Google Scholar]
- Luhmann, T. Erweiterte Verfahren zur Geometrischen Kamerakalibrierung in der Nahbereichsphotogrammetrie; Beck: München, Germany, 2010; ISBN 978-3-7696-5057-0. [Google Scholar]
- Bruno, F.; Bianco, G.; Muzzupappa, M.; Barone, S.; Razionale, A.V. Experimentation of structured light and stereo vision for underwater 3D reconstruction. ISPRS J. Photogramm. Remote Sens.
**2011**, 66, 508–518. [Google Scholar] [CrossRef] - Drap, P.; Seinturier, J.; Hijazi, B.; Merad, D.; Boi, J.-M.; Chemisky, B.; Seguin, E.; Long, L. The ROV 3D Project. J. Comput. Cult. Herit.
**2015**, 8, 1–24. [Google Scholar] [CrossRef] - Luhmann, T.; Robson, S.; Kyle, S.; Boehm, J. Close-Range Photogrammetry and 3D Imaging, 3rd ed.; De Gruyter: Berlin, Germany; Boston, MA, USA, 2020; ISBN 9783110607246. [Google Scholar]
- Wester-Ebbinghaus, W. Einzelstandpunkt-Selbstkalibrierung. Ein Beitrag zur Feldkalibrierung von Aufnahmekammern; Zugl.: Bonn, Univ., Habil.-Schr., 1982; Beck: München, Germany, 1983; ISBN 3769693396. [Google Scholar]
- Ekkel, T.; Schmik, J.; Luhmann, T.; Hastedt, H. Precise laser-based optical 3d measurement of welding seams under water. Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci.
**2015**, XL-5/W5, 117–122. [Google Scholar] [CrossRef] - VDI. VDI/VDE. 2634.1: Optical 3-D Measuring Systems—Imaging Systems with Point-by-Point Probing; VDI: Düsseldorf, Geramny, 2002. [Google Scholar]
- Costa, C.; Loy, A.; Cataudella, S.; Davis, D.; Scardi, M. Extracting fish size using dual underwater cameras. Aquac. Eng.
**2006**, 35, 218–227. [Google Scholar] [CrossRef] - Buschinelli, P.D.V.; Matos, G.; Pinto, T.; Albertazzi, A. Underwater 3D shape measurement using inverse triangulation through two flat refractive surfaces. In OCEANS 2016 MTS/IEEE, Monterey, CA, USA, 19–23 September 2016; IEEE: Piscataway, NJ, USA, 2016; pp. 1–7. ISBN 978-1-5090-1537-5. [Google Scholar]
- Lavest, J.M.; Rives, G.; Laprest, J.T. Dry camera calibration for underwater applications. Mach. Vis. Appl.
**2003**, 13, 245–253. [Google Scholar] [CrossRef] - Rahman, T.; Anderson, J.; Winger, P.; Krouglicof, N. Calibration of an Underwater Stereoscopic Vision System. In 2013 OCEANS—San Diego; IEEE: San Diego, CA, USA, 2013; pp. 1–6. [Google Scholar] [CrossRef]
- Agrafiotis, P.; Georgopoulos, A. Camera constant in the case of two media photogrammetry. Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci.
**2015**, XL-5/W5, 1–6. [Google Scholar] [CrossRef][Green Version] - Sedlazeck, A.; Koch, R. Calibration of Housing Parameters for Underwater Stereo-Camera Rigs. In British Machine Vision Conference 2011; Hoey, J., McKenna, S., Trucco, E., Zhang, J., Eds.; BMVA Press: Dundee, UK, 2011; pp. 118.1–118.11. [Google Scholar]
- Sedlazeck, A.; Koch, R. Perspective and Non-perspective Camera Models in Underwater Imaging—Overview and Error Analysis. In Outdoor and Large-Scale Real-World Scene Analysis; Hutchison, D., Kanade, T., Kittler, J., Kleinberg, J.M., Mattern, F., Mitchell, J.C., Naor, M., Nierstrasz, O., Pandu Rangan, C., Steffen, B., et al., Eds.; Springer: Berlin/Heidelberg, Germany, 2012; pp. 212–242. ISBN 978-3-642-34090-1. [Google Scholar]
- Maas, H.-G. On the Accuracy Potential in Underwater/Multimedia Photogrammetry. Sensors (Basel)
**2015**, 15, 18140–18152. [Google Scholar] [CrossRef] [PubMed]

**Figure 1.**System components, calibration approaches for underwater photogrammetric systems. The left side illustrates options of configuration for single-camera usage; the right side illustrates options for multi-camera systems. Approaches 1 can be declared as unreasonable strategies, approaches 2 are standard strategies using standard software, explicit modelling approaches 3 are not part of this work but theoretically possible, approaches 4 and 5 model refractive effects explicitly using a known IO.

**Figure 2.**Schema of the creation of synthetic datasets. After error-free images, the coordinates are calculated via strict ray tracing, the calibration is conducted using standard software and implicit modelling. The 3D coordinates are calculated via forward intersection of a stereo image pair, based on the standard model. These coordinates are compared to the nominal values of simulated test object coordinates.

**Figure 3.**Exemplarily configuration of the interfaces. A plane interface (10 mm in thickness) of isotropic glass is simulated 20 mm in front of the principal point.

**Figure 4.**Setup of the synthetic dataset Cube. Blue points (36) indicate the positions of the cameras, red points (100) indicate the cubic arranged object points (

**a**). Cubic test object, according to VDI/VDE 2634.1 (

**b**).

**Figure 5.**Half-sphere-shaped bundle. Green dots indicate 10 × 10 points of the calibration fixture. The points are spaced at 250 mm in each direction. Simulated stereo cameras are rotated around the optical axis by 90° at each position. The basis is 200 mm.

**Figure 7.**Illustration of the refractive effects with different air to water ratio. The ratios vary from 1% air and 99% water (

**a**) to a 50/50 configuration (

**b**).

**Figure 8.**Test object with five points moved 6 m in 100 mm steps along the optical axis of the left camera.

**Figure 9.**Setup of the synthetic datasets. Blue points indicate the positions of the cameras, red points indicate the cubically arranged object points of dataset Cube (

**a**) and object points of dataset HS (

**b**), respectively. The arrows indicate the offset of the camera positions of dataset 2 and 4 and of 3 and 5 according to Table 3.

**Figure 10.**Correlations between translation parameters of the relative orientation (X, Y, Z) and the principal distance c as a function of the convergence of the stereo configuration.

**Figure 11.**3D deviations of the forward intersected points to the reference object points for 6 m through the object space. Different datasets of varying convergence of Cube and the average calibration distance are visualised.

**Figure 12.**Factors of the scale of a 3D similarity parameter transformation of each five-point object in object space to the corresponding reference five-point object. The scale is calculated for 6 m (each 100 mm) and visualised for the object space. Different datasets of varying convergence of Cube and the average calibration distance are visualised.

**Figure 13.**Correlations between translation parameters of the relative orientation (X, Y, Z) and the principal distance c as a function of the air/water ratio of the stereo configuration.

**Figure 14.**3D deviations of spatially intersected points to the reference object points for 6 m through the object space. Different datasets of varying air/water ratios of Cube and the average calibration distance are visualised.

**Figure 15.**3D deviations of spatially intersected points to the reference object points for 6 m through the object space. Different datasets of varying air/water ratios of HS and the average calibration distance are visualised.

**Figure 16.**Factors of the scale of a 3D similarity parameter transformation of each five-point object in the object space to the corresponding reference five-point object. The scale is calculated for 6 m (each 100 mm) and visualised for the object space. Different datasets of varying convergence of Cube and the average calibration distance are visualised.

**Figure 17.**3D deviations of the forward intersected points to the reference object points as an exemplary for the dataset 2

_{MM}-5-10-90-Cube.

**Figure 18.**Stereo setups of experiments. The convergent arranged cameras in waterproofed housings observe the 3D calibration fixture (

**a**). The parallel setup (

**b**) is realised using two cameras placed just in front of an aquarium (top view). In (

**c**), two images are shown. The top one is acquired in air, the bottom one through glass and water.

**Figure 19.**Radial-symmetric distortion of the calibrated cameras of Table 11 in air (red) and water (blue).

**Figure 20.**Mean (

**left**) and Max (

**right**) deviation (3D) of intersected 3D points from stereo images 1–5. Parallel datasets (No. 1–4 of Table 12).

**Figure 21.**Mean (

**left**) and max (

**right**) deviation (3D) of intersected 3D points from stereo images 1–5. Convergent datasets (No. 5–8 of Table 12).

**Figure 22.**Mean absolute difference of intersected points underlying 2D calibration parameter and underlying 3D calibration parameters for parallel and convergent data at positions 1–5.

**Figure 23.**Vectors, exemplary showing differences of absolute coordinates of the forward intersected points of the 2D calibration object in parallel datasets 2D and 3D at position 4. The red vectors indicate the largest differences of ~1.2 mm, green the smallest of 0.8 mm. All vectors point towards the stereo camera.

**Table 1.**Simulated stereo datasets for different angles of convergence. The air/water ratio is not considered and named XX according to the notation (Section 3.1).

Cube | HS |
---|---|

2_{SM}-0-Cube | 2_{SM}-0-HS |

2_{MM}-0-XX-Cube | 2_{MM}-0-XX-HS |

2_{MM}-5-XX-Cube | 2_{MM}-5-XX-HS |

2_{MM}-10-XX-Cube | 2_{MM}-10-XX-HS |

2_{MM}-15-XX-Cube | 2_{MM}-15-XX-HS |

2_{MM}-20-XX-Cube | 2_{MM}-20-XX-HS |

2_{MM}-25-XX-Cube | 2_{MM}-25-XX-HS |

**Table 2.**Simulated stereo datasets for different air/water ratios. The angle of convergence is not considered and named XX according to the notation (Section 3.1).

Cube | HS |
---|---|

2_{SM}-XX-Cube | 2_{SM}-XX-HS |

2_{MM}-XX-1/99-Cube | 2_{MM}-XX-1/99-HS |

2_{MM}-XX-10/90-Cube | 2_{MM}-XX-10/90-HS |

2_{MM}-XX-20/80-Cube | 2_{MM}-XX-20/80-HS |

2_{MM}-XX-30/70-Cube | 2_{MM}-XX-30/70-HS |

2_{MM}-XX-40/60-Cube | 2_{MM}-XX-40/60-HS |

2_{MM}-XX-50/50-Cube | 2_{MM}-XX-50/50-HS |

**Table 3.**Interior orientation parameters (principal distance and radial distortion) of two single-medium and two multimedia datasets.

No. | Experiment | Principal Distance c [mm] | A1 | A2 | A3 |
---|---|---|---|---|---|

1 | nominal | −23.908 | 0.0 | 0.0 | 0.0 |

2 | 1_{SM}-1/99-Cube | −23.908 | 0.0 | 0.0 | 0.0 |

3 | 1_{SM}-1/99-HS | −23.908 | 0.0 | 0.0 | 0.0 |

4 | 1_{MM}-1/99-Cube | −33.980 | 3.1e-4 | 1.4e-7 | 1.3e-10 |

5 | 1_{MM}-1/99-HS | −33.979 | 3.1e-4 | 1.5e-7 | 1.1e-10 |

**Table 4.**Relative orientation and principal distance of convergent datasets of Cube as a result of the bundle adjustment running standard software for different datasets with varying angles of convergence.

No. | Dataset | Relative Orientation | c [mm] | |||||
---|---|---|---|---|---|---|---|---|

X0 [mm] | Y0 [mm] | Z0 [mm] | ω [°] | φ [°] | κ [°] | |||

0 | nominal | 200.000 | 0.000 | 0.000 | 0.000 | 0–25 | 0.000 | −23.908 |

1 | 2_{SM}-0°-1/99-Cube | 200.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | −23.908 |

2 | 2_{MM}-0°-1/99-Cube | 199.994 | 0.000 | 0.019 | 0.000 | 0.000 | 0.000 | −33.979 |

3 | 2_{MM}-5°-1/99-Cube | 200.572 | 0.000 | −0.062 | 0.000 | 5.001 | 0.000 | −33.978 |

4 | 2_{MM}-10°-1/99-Cube | 201.143 | −0.002 | −0.116 | 0.000 | 10.000 | 0.000 | −33.978 |

5 | 2_{MM}-15°-1/99-Cube | 201.715 | −0.007 | −0.192 | 0.000 | 15.003 | 0.000 | −33.979 |

6 | 2_{MM}-20°-1/99-Cube | 202.266 | −0.010 | −0.339 | −0.001 | 20.003 | 0.000 | −33.979 |

7 | 2_{MM}-25°-1/99-Cube | 202.884 | −0.011 | −0.378 | 0.001 | 25.004 | 0.000 | −33.981 |

**Table 5.**Relative orientation and principal distance of convergent datasets of HS as a result of the bundle adjustment running standard software for different datasets with varying angles of convergence.

No. | Dataset | Relative Orientation | c [mm] | |||||
---|---|---|---|---|---|---|---|---|

X0 [mm] | Y0 [mm] | Z0 [mm] | ω [°] | φ [°] | κ [°] | |||

0 | nominal | 200.000 | 0.000 | 0.000 | 0.000 | 0–25 | 0.000 | −23.908 |

1 | 2_{SM}-0°-1/99-HS | 200.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | −23.908 |

2 | 2_{MM}-0°-1/99-HS | 199.987 | 0.000 | 0.007 | 0.000 | 0.000 | 0.000 | −33.978 |

3 | 2_{MM}-5°-1/99-HS | 200.573 | 0.000 | −0.047 | 0.000 | 5.000 | 0.000 | −33.977 |

4 | 2_{MM}-10°-1/99-HS | 201.164 | −0.001 | −0.037 | 0.000 | 10.000 | 0.000 | −33.978 |

5 | 2_{MM}-15°-1/99-HS | 201.736 | −0.004 | −0.082 | 0.000 | 15.000 | 0.000 | −33.979 |

6 | 2_{MM}-20°-1/99-HS | 202.314 | −0.008 | −0.113 | 0.002 | 20.001 | 0.000 | −33.980 |

7 | 2_{MM}-25°-1/99-HS | 202.845 | −0.005 | −0.290 | 0.001 | 25.000 | 0.000 | −33.981 |

**Table 6.**Major correlations between selected interior and relative orientation parameters for dataset 2

_{MM}-25°-1/99-Cube and 2

_{MM}-25°-1/99-HS. Only correlations higher than |0.5| are listed. Grey cells indicate correlations lower than |0.5|.

Parameter | Dataset | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

Cube | HS | Cube | HS | Cube | HS | Cube | HS | Cube | HS | |

X | −0.58 | −0.65 | ||||||||

Y | ||||||||||

Z | −0.69 | −0.78 | ||||||||

ω | 0.75 | 0.81 | 0.76 | 0.80 | ||||||

φ | −0.82 | −0.82 | −0.79 | −0.74 | ||||||

κ | −0.88 | −0.90 | −0.85 | −0.87 | ||||||

c | Xh | Yh | B1 | B2 |

**Table 7.**Relative orientation and principal distance of ratio datasets of Cube as a result of the bundle adjustment running standard software for different datasets with varying air/water ratios.

No. | Dataset | Relative Orientation | c [mm] | |||||
---|---|---|---|---|---|---|---|---|

X0 [mm] | Y0 [mm] | Z0 [mm] | ω [°] | Φ [°] | κ [°] | |||

0 | nominal | 200.000 | 0.000 | 0.000 | 0.000 | 0–25 | 0.000 | −23.908 |

1 | 2_{SM}-0°-1/99-Cube | 200.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | −23.908 |

2 | 2_{MM}-0°-1/99-Cube | 199.994 | 0.000 | 0.019 | 0.000 | 0.000 | 0.000 | −33.979 |

3 | 2_{MM}-0°-10/90-Cube | 199.912 | −0.018 | 0.012 | −0.001 | −0.008 | 0.001 | −33.891 |

4 | 2_{MM}-0°-20/80-Cube | 199.780 | 0.021 | 1.491 | 0.003 | 0.018 | 0.001 | −33.806 |

5 | 2_{MM}-0°-30/70-Cube | 199.732 | 0.142 | 1.501 | 0.019 | 0.002 | −0.002 | −33.744 |

6 | 2_{MM}-0°-40/60-Cube | 199.664 | 0.219 | 1.594 | 0.018 | 0.015 | −0.001 | −33.654 |

7 | 2_{MM}-0°-50/50-Cube | 199.702 | 0.234 | 2.345 | 0.021 | 0.033 | 0.000 | −33.549 |

**Table 8.**Relative orientation and principal distance of ratio datasets of HS as a result of the bundle adjustment running standard software for different datasets with varying air/water ratios.

No. | Dataset | Relative Orientation | c [mm] | |||||
---|---|---|---|---|---|---|---|---|

X0 [mm] | Y0 [mm] | Z0 [mm] | ω [°] | Φ [°] | κ [°] | |||

0 | nominal | 200.000 | 0.000 | 0.000 | 0.000 | 0–25 | 0.000 | −23.908 |

1 | 2_{SM}-0°-1/99-HS | 200.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | −23.908 |

2 | 2_{MM}-0°-1/99-HS | 199.987 | 0.000 | 0.007 | 0.000 | 0.000 | 0.000 | −33.978 |

3 | 2_{MM}-0°-10/90-HS | 199.782 | −0.019 | 0.616 | −0.001 | 0.000 | 0.000 | −33.878 |

4 | 2_{MM}-0°-20/80-HS | 199.586 | −0.039 | 1.288 | −0.004 | 0.004 | 0.000 | −33.758 |

5 | 2_{MM}-0°-30/70-HS | 199.441 | −0.056 | 2.092 | −0.006 | 0.007 | 0.000 | −33.630 |

6 | 2_{MM}-0°-40/60-HS | 199.345 | −0.028 | 2.187 | −0.003 | 0.011 | 0.000 | −33.496 |

7 | 2_{MM}-0°-50/50-HS | 199.287 | −0.028 | 2.254 | −0.001 | 0.013 | 0.000 | −33.362 |

**Table 9.**Major correlations between selected interior and relative orientation parameters for dataset 2

_{MM}-0°-50/50-Cube and 2

_{MM}-0°-50/50-HS. Only correlations bigger than |0.5| are listed. Grey cells indicate correlations less than |0.5|.

Parameter | Dataset | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

Cube | HS | Cube | HS | Cube | HS | Cube | HS | Cube | HS | |

X | ||||||||||

Y | ||||||||||

Z | −0.54 | −0.58 | ||||||||

ω | 0.55 | 0.63 | 0.54 | 0.63 | ||||||

φ | −0.64 | −0.64 | −0.64 | −0.62 | ||||||

κ | ||||||||||

c | Xh | Yh | B1 | B2 |

**Table 10.**Relative orientation as a result of the multimedia bundle adjustment for the most critical datasets.

No. | Dataset | Relative Orientation | |||||
---|---|---|---|---|---|---|---|

X0 [mm] | Y0 mm] | Z0 [mm] | ω [°] | φ [°] | κ [°] | ||

0 | nominal | 200.000 | 0.000 | 0.000 | 0.000 | 0–25 | 0.000 |

1 | 2_{MM}-25°-1/99-Cube | 200.000 | 0.000 | 0.000 | 0.000 | 25.000 | 0.000 |

2 | 2_{MM}-0°-50/50-Cube | 200.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |

3 | 2_{MM}-25°-50/50-Cube | 200.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |

**Table 11.**Interior orientation parameters and their standard deviation of the left camera of the bundle adjustment using standard software in the air and in the underwater configuration (exemplary for the parallel setup, 3D calibration fixture used).

Data | c | xh | yh | A1 | A2 | A3 | B1 | B2 | C1 | C2 |
---|---|---|---|---|---|---|---|---|---|---|

[mm] | [mm] | [mm] | ||||||||

σ_{c} | σ_{xh} | σ_{yh} | σ_{A1} | σ_{A2} | σ_{A3} | σ_{B1} | σ_{B2} | σ_{C1} | σ_{C2} | |

IO^{AIR} | −10.52 | −6.84E-02 | −4.24E-02 | −1.13E-03 | 1.04E-05 | −4.45E-08 | −4.08E-05 | −3.79E-05 | −1.83E-04 | −6.51E-05 |

1.08E-03 | 7.43E-04 | 7.96E-04 | 4.88E-06 | 2.25E-07 | 3.18E-09 | 2.50E-06 | 2.02E-06 | 1.16E-05 | 1.15E-05 | |

IO^{Water} | −14.49 | −4.41E-02 | −3.01E-02 | 6.35E-04 | 2.64E-06 | 6.87E-08 | 4.62E-05 | −1.34E-05 | −1.30E-04 | −2.02E-04 |

3.07E-03 | 2.73E-03 | 2.85E-03 | 9.32E-06 | 4.41E-07 | 6.31E-09 | 8.22E-06 | 8.39E-06 | 2.53E-05 | 3.09E-05 |

**Table 12.**The relative orientation of the bundle adjustment using standard software (implicit modelling) and own implementation (explicit modelling). The ending 2D/3D indicates which calibration fixture is used. The ending “ex” indicates the explicitly modelled data.

No. | Dataset | Relative Orientation | c [mm] | |||||
---|---|---|---|---|---|---|---|---|

X0 [mm] | Y0 [mm] | Z0 [mm] | ω [°] | Φ [°] | κ [°] | |||

0 | air, parallel | −37.914 | 0.886 | 0.214 | 0.120 | −0.022 | −0.180 | −10.520 |

1 | parallel-2D | −37.817 | 0.916 | 0.251 | 0.197 | 0.040 | −0.194 | −14.547 |

2 | parallel-3D | −37.814 | 0.939 | 0.510 | 0.139 | 0.022 | −0.180 | −14.492 |

3 | parallel-2D_{ex} | −37.544 | 0.838 | 0.940 | 0.079 | −0.053 | −0.197 | −10.520 |

4 | parallel-3D_{ex} | −37.744 | 0.935 | 0.450 | 0.080 | 0.069 | −0.193 | −10.520 |

5 | convergent-2D | −75.961 | −2.683 | −17.026 | 2.461 | −27.792 | −2.859 | −14.555 |

6 | convergent-3D | −75.611 | −2.735 | −16.769 | 2.452 | −27.556 | −2.862 | −14.501 |

7 | convergent-2D_{ex} | −72.735 | −2.602 | −15.273 | 2.446 | −27.334 | −2.846 | −10.520 |

8 | convergent-3D_{ex} | −74.194 | −4.169 | 5.248 | 3.285 | −28.640 | −2.828 | −10.520 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Kahmen, O.; Rofallski, R.; Luhmann, T. Impact of Stereo Camera Calibration to Object Accuracy in Multimedia Photogrammetry. *Remote Sens.* **2020**, *12*, 2057.
https://doi.org/10.3390/rs12122057

**AMA Style**

Kahmen O, Rofallski R, Luhmann T. Impact of Stereo Camera Calibration to Object Accuracy in Multimedia Photogrammetry. *Remote Sensing*. 2020; 12(12):2057.
https://doi.org/10.3390/rs12122057

**Chicago/Turabian Style**

Kahmen, Oliver, Robin Rofallski, and Thomas Luhmann. 2020. "Impact of Stereo Camera Calibration to Object Accuracy in Multimedia Photogrammetry" *Remote Sensing* 12, no. 12: 2057.
https://doi.org/10.3390/rs12122057