Fast and stable direct relative orientation of UAV-based stereo pair

(1) * Martinus Edwin Tjahjadi Mail (National Institute of technology (ITN) Malang, Indonesia)
(2) Fransisca Dwi Agustina Mail (National Institute of technology (ITN) Malang, Indonesia)
*corresponding author


Coplanarity-based relative orientation (RO) is one of the most crucial processes to obtain reliable 3D model and point clouds in Computer Vision and Photogrammetry community. Whilst a classical and rigorous procedure requires very close approximate values of five independent parameters, a direct method needs additional constraints to solve the parameters. This paper proposes a new approach that facilitates a very fast but stable and accurate solution from five point correspondences between two overlapping aerial images taken form unmanned aerial vehicle (UAV) flight. Furthermore, if 3D coordinates of perspective centers are available form geotagged images, rotational elements of the RO parameters can be quickly solved using three correspondences only. So it is very reliable for a provision of closed-form solutions for the rigorous methods. Our formulation regards Thompson’s parameterizations of Euler angles in composing a coplanarity condition. Nonlinear terms are subsequently added into a stereo parallax within a constant term under a linear least squares criteria. This strategy is considered new as compared with the known literatures since the proposed approach can find optimal solution. Results from real datasets confirm that our method produces a fast, stable and reliable linear solution by using at least five correspondences or even only three conjugate points of geotagged image pairs.


Relative Orientation; Closed-Form Solution; Stereoscopic Processing



Article metrics

Abstract views : 113 | PDF views : 36




Full Text



[1] G. Buffi, P. Manciola, S. Grassi, M. Barberini, and A. Gambi, “Survey of the Ridracoli Dam: UAV-based photogrammetry and traditional topographic techniques in the inspection of vertical structures,” J. Assoc. Inf. Syst., vol. 18(11), no. 11, pp. 1562–1579, 2017, doi: 10.1080/19475705.2017.1362039.

[2] J. San, J. Wanshou, H. Wei, and Y. Liang, “UAV-Based Oblique Photogrammetry for Outdoor Data Acquisition and Offsite Visual Inspection of Transmission Line,” Remote Sens., vol. 9(3), no. 3, pp. 1–25, 2017, doi: 10.3390/rs9030278.

[3] Z. Yong, L. Wenzhuo, C. Shiyu, and Y. Xiuxiao, “Automatic Power Line Inspection Using UAV Images,” Remote Sens., vol. 9(8), no. 8, pp. 1–19, 2017, doi: 10.3390/rs9080824.

[4] S. Baofeng, X. Jinru, X. Chunyu, F. Yulin, S. Yuyang, and S. Fuentes, “Digital surface model applied to unmanned aerial vehicle based photogrammetry to assess potential biotic or abiotic effects on grapevine canopies,” Int. J. Agric. Biol. Eng., vol. 9(6), no. 6, pp. 119–130, 2016, available at:

[5] A. C. Birdal, U. Avdan, and T. Türk, “Estimating tree heights with images from an unmanned aerial vehicle,” J. Assoc. Inf. Syst., vol. 18(11), no. 11, pp. 1144–1156, 2017, doi: 10.1080/19475705.2017.1300608.

[6] J. Dempewolf, J. Nagol, S. Hein, C. Thiel, and R. Zimmermann, “Measurement of Within-Season Tree Height Growth in a Mixed Forest Stand Using UAV Imagery,” Forests, vol. 8(7), no. 7, pp. 1–15, 2017, doi: 10.3390/f8070231.

[7] R. Mlambo, I. H. Woodhouse, F. Gerard, and K. Anderson, “Structure from Motion (SfM) Photogrammetry with Drone Data: A Low Cost Method for Monitoring Greenhouse Gas Emissions from Forests in Developing Countries,” Forests, vol. 8(3), no. 3, pp. 1–20, 2017, doi: 10.3390/f8030068.

[8] Q. Wang et al., “Accuracy Evaluation of 3D Geometry from Low-Attitude UAV collections A case at Zijin Mine,” Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci., vol. 40(4), no. 4, pp. 297–300, 2014, doi: 10.5194/isprsarchives-XL-4-297-2014.

[9] M. Shahbazi, G. Sohn, J. Theau, and P. Menard, “Development and Evaluation of a UAV-Photogrammetry System for Precise 3D Environmental Modeling,” Sensors, vol. 15(11), no. 11, pp. 27493–27524, 2015, doi: 10.3390/s151127493.

[10] A. Tscharf, M. Rumpler, F. Fraundorfer, G. Mayer, and H. Bischof, “On the Use of UAVs in Mining and Archaeology - Geo-Accurate 3D Reconstructions using Various Platforms and Terrestrial Views,” ISPRS Ann. Photogramm. Remote Sens. Spat. Inf. Sci., vol. II(1/W1), no. 1, pp. 15–22, 2015, doi: 10.5194/isprsannals-II-1-W1-15-2015.

[11] B. Ruzgienė, Č. Aksamitauskas, I. Daugėla, Š. Prokopimas, V. Puodžiukas, and D. Rekus, “UAV Photogrammetry for Road Surfce Modelling,” Balt. J. Road Bridg. Eng., vol. 10(2), no. 2, pp. 151–158, 2015, doi: 10.3846/bjrbe.2015.19.

[12] J. O. Kim and J. K. Lee, “UAV Application for Process Control of the Reclamation Project,” J. Coast. Res., vol. (79), pp. 309–313, 2017, doi: 10.2112/SI79-063.1.

[13] A. Ellenberg, L. Branco, A. Krick, I. Bartoli, and A. Kontsos, “Use of Unmanned Aerial Vehicle for Quantitative Infrastructure Evaluation,” J. Infrastruct. Syst., vol. 21(3), no. 3, pp. 1–8, 2015, doi: 10.1061/(ASCE)IS.1943-555X.0000246.

[14] A. Barreiro, J. M. Domínguez, A. J. C. Crespo, H. González-Jorge, D. Roca, and M. Gómez-Gesteira, “Integration of UAV Photogrammetry and SPH Modelling of Fluids to Study Runoff on Real Terrains,” PLoS One, vol. 9(11), no. 11, p. e111031, 2014, doi: 10.1371/journal.pone.0111031.

[15] F. Alidoost and H. Arefi, “An Image-Based Technique for 3D Building Reconstruction using Multi-View UAV Images,” Int. Arch. Photogramm. Remote Sens., vol. XL(1/W5), pp. 43–46, 2015, doi: 10.5194/isprsarchives-XL-1-W5-43-2015.

[16] G. Ceraudo, P. Guacci, and A. Merico, “The Use of UAV Technology in Topographical Research: Some Case Studies from Central Southern Italy,” SCIRES-IT, vol. 7(1), no. 1, pp. 29–38, 2017, doi: 10.2423/i22394303v7n1p29.

[17] X. Zhihua, W. Lixin, S. Yonglin, L. Fashuai, W. Qiuling, and W. Ran, “Tridimensional Reconstruction Applied to Cultural Heritage with the Use of Camera-Equipped UAV and Terrestrial Laser Scanner,” Remote Sens., vol. 6(11), no. 11, pp. 10413–10434, 2014, doi: 10.3390/rs61110413.

[18] C. F. Lo et al., “The Direct Georeferencing Application and Performance Analysis of UAV Helicopter in GCP-Free Area,” Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci., vol. 40(1/W4), no. 1/W4, pp. 151–157, 2015, doi: 10.5194/isprsarchives-XL-1-W4-151-2015.

[19] J. Wang, M. Garratt, A. Lambert, J. J. Wang, S. Han, and D. Sinclair, “Integration of GPS/INS/vision sensors to navigate unmanned aerial vehicles,” Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci., vol. 37(B1), no. B1, pp. 963–970, 2008, available at:

[20] M. E. Tjahjadi, F. Handoko, and S. S. Sai, “Novel Image Mosaicking of UAV’s Imagery Using Collinearity Condition,” Int. J. Electr. Comput. Eng., vol. 7(3), no. 3, pp. 1188–1196, 2017, doi: 10.11591/ijece.v7i3.pp1188-1196.

[21] M. Saadatseresht, A. H. Hashempour, and M. Hasanlou, “UAV Photogrametry: a Practical Solution for Challenging Mapping Projects,” Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci., vol. 40(1/W5), no. 1/W5, pp. 619–623, 2015, doi: 10.5194/isprsarchives-XL-1-W5-619-2015.

[22] F. Mancini, M. Dubbini, M. Gattelli, F. Stecchi, S. Fabbri, and G. Gabbianelli, “Using Unmanned Aerial Vehicles (UAV) for High-Resolution Reconstruction of Topography: The Structure from Motion Approach on Coastal Environments,” Remote Sens., vol. 5(12), no. 12, pp. 6880–6898, 2013, doi: 10.3390/rs5126880.

[23] M. E. Tjahjadi and F. Handoko, “Precise wide baseline stereo image matching for compact digital cameras,” in 2017 4th International Conference on Electrical Engineering, Computer Science and Informatics (EECSI), 2017, pp. 181–186, doi: 10.1109/EECSI.2017.8239106.

[24] L. Hyoseong, R. Huinam, O. Jae Hong, and P. Jin Ho, “Measurement of 3-D Vibrational Motion by Dynamic Photogrammetry Using Least-Square Image Matching for Sub-Pixel Targeting to Improve Accuracy,” Sensors, vol. 16(3), no. 3, pp. 359–373, 2016, doi: 10.3390%2Fs16030359.

[25] N. Ma, S. Peng-fei, M. Yu-bo, M. Chao-guang, and X. Li, “A Subpixel Matching Method for Stereovision of Narrow Baseline Remotely Sensed Imagery,” Math. Probl. Eng., p. 14 pp., 2017, doi: 10.1155/2017/7901692.

[26] A. Lucieer, S. M. de Jong, and D. Turner, “Mapping landslide displacements using Structure from Motion (SfM) and image correlation of multi-temporal UAV photography,” Prog. Phys. Geogr., vol. 38(1), no. 1, pp. 97–116, 2014, doi: 10.1177/0309133313515293.

[27] G. Caroti, I. M.-E. Zaragoza, and A. Piemonte, “Accuracy Assessment in Structure From Motion 3D Reconstruction from UAV-Born Images: The Influence of the Data Processing Methods,” Int. Arch. Photogramm. Remote Sens., vol. XL(1/W4), pp. 103–109, 2015, doi: 10.5194/isprsarchives-XL-1-W4-103-2015.

[28] M. E. Tjahjadi and F. D. Agustina, “A Relative Rotation between Two Overlapping UAV’s Images,” in 2018 5th International Conference on Electrical Engineering, Computer Science and Informatics (EECSI), 2018, p. 6.

[29] E. H. Thompson, “The Projective Theory of Relative Orientation,” Photogrammetria, vol. 23, no. 1968, pp. 67–75, 1968, doi: 10.1016/0031-8663(68)90028-8.

[30] E. H. Thompson, “A Rational Algebraic Formulation Of The Problem Of Relative Orientation,” Photogramm. Rec., vol. 3(14), no. 14, pp. 152–159, 1959, doi: 10.1111/j.1477-9730.1959.tb01267.x.

[31] P. Stefanovic, “Relative Orientation - a New Approach,” ITC J., pp. 417–448, 1973, available at : Google Scholar.

[32] C. M. A. Van Den Hout and P. Stefanovic, “Efficient Analytical Relative Orientation,” ITC J., vol. (2), no. 2, pp. 304–323, 1976, available at: Google Scholar.

[33] U. Helmke, K. Hüper, L. Pei Yean, and J. Moore, “Essential Matrix Estimation Using Gauss-Newton Iterations on a Manifold,” Int. J. Comput. Vis., vol. 74(2), no. 2, pp. 117–136, 2007, doi: 10.1007/s11263-006-0005-0.

[34] H. C. Longuet-Higgins, “A Computer Algorithm for Reconstructing a Scene from Two Projections,” Nature, vol. 293(5828), no. 5828, pp. 133–135, 1981, doi: 10.1038/293133a0.

[35] R. Y. Tsai and T. S. Huang, “Uniqueness and Estimation of Three-Dimensional Motion Parameters of Rigid Objects with Curved Surfaces,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 6(1), no. 1, pp. 13–27, 1984, doi: 10.1109/TPAMI.1984.4767471.

[36] J. Weng, T. S. Huang, and N. Ahuja, “Motion and Structure from Two Perspective Views: Algorithms, Error Analysis, and Error Estimation,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 11(5), no. 5, pp. 451–476, 1989, doi: 10.1109/34.24779.

[37] S. J. Maybank, “Properties of Essential Matrices,” Int. J. Imaging Syst. Technol., vol. 2(4), no. 4, pp. 380–384, 1990, doi: 10.1002/ima.1850020412.

[38] B. K. P. Horn, “Relative Orientation,” Int. J. Comput. Vis., vol. 4(1), no. 1, pp. 59–78, 1990, doi: 10.1007/BF00137443.

[39] R. I. Hartley, “In Defense of the Eight-Point Algorithm,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 19(6), no. 6, pp. 580–593, 1997, doi: 10.1109/34.601246.

[40] S. Agarwal, H.-L. Lee, B. Sturmfels, and R. Thomas, “On the Existence of Epipolar Matrices,” Int. J. Comput. Vis., vol. 121(3), no. 3, pp. 403–415, 2017, doi: 10.1007/s11263-016-0949-7.

[41] D. Nistér, “An Efficient Solution to the Five-Point Relative Pose Problem,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 26(6), no. 6, pp. 756–770, 2004, doi: 10.1109/TPAMI.2004.17.

[42] H. Stewénius, D. Nistér, F. Kahl, and F. Schaffalitzky, “A minimal solution for relative pose with unknown focal length,” in 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05), 2005, vol. 2, pp. 789-794, doi: 10.1109/CVPR.2005.36.

[43] J. Philip, “A Non-Iterative Algorithm for Determining All Essential Matrices Corresponding to Five Point Pairs,” Photogramm. Rec., vol. 15(88), no. 88, pp. 589–599, 1996, doi: 10.1111/0031-868X.00066.

[44] Y. Chen, Z. Xie, Z. Qiu, M. Zhang, and S. Zhong, “The model of direct relative orientation with seven constraints for geological landslides measurement and 3D reconstruction,” Earth Sci. Res. J., vol. 20(4), no. 4, pp. F1–F6, 2016, doi: 10.15446/esrj.v20n4.60211.

[45] Y. Zhang, X. Huang, X. Hu, Fangqi Wan, and L. Lin, “Direct relative orientation with four independent constraints,” ISPRS J. Photogramm. Remote Sens., vol. 66(6), no. 6, pp. 809–817, 2011, doi: 10.1016/j.isprsjprs.2011.09.006.

[46] T. Y. Shih, “RLT: A Closed Form Solution for Relative Orientation,” Int. Arch. Photogramm. Remote Sens., vol. 30(B5), no. B5, pp. 357–364, 1994, available at: Google Scholar.

[47] T.-Y. Shih, “On the Duality of Relative Orientation,” Photogramm. Eng. Remote Sensing, vol. 56(9), no. 9, pp. 1281–1283, 1990, available at:

[48] J. Wang, Z. Lin, and C. Ren, “Relative Orientation in low Altitude Photogrammetry Survey,” Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci., vol. 39(B1), no. B1, pp. 463–467, 2012, available at:

[49] T.-Y. Shih, “The Sign Permutation in the Rotation Matrix and the Formulation of the Collinearity and Coplanarity Equations,” Photogramm. Eng. Remote Sens., vol. 62(10), no. 10, pp. 1145–1149, 1996, available at:

[50] W. Förstner and B. P. Wrobel, Photogrammetric Computer Vision: Statistic, Geometry, Orientation and Reconstruction. Bonn: Springer, 2016, doi: 10.1007/978-3-319-11550-4.

[51] M. E. Tjahjadi and F. Handoko, “Single frame resection of compact digital cameras for UAV imagery,” in 2017 4th International Conference on Electrical Engineering, Computer Science and Informatics (EECSI), 2017, pp. 409–413, doi: 10.1109/EECSI.2017.8239147.

[52] M. E. Tjahjadi and F. D. Agustina, “Single image orientation of UAV’s imagery using orthogonal projection model,” in 2017 International Symposium on Geoinformatics (ISyG), 2017, pp. 18–23, doi: 10.1109/ISYG.2017.8280668.

[53] M. Benes, “Relative and Absolute Orientation Error Analysis,” Photogramm. Eng. Remote Sens., 1968, available at:

[54] M. Kedzierski and P. Delis, “Fast Orientation of Video Images of Buildings Acquired from a UAV without Stabilization,” Sensors, vol. 16, no. 7, p. 951, 2016, doi: 10.3390/s16070951.

[55] H. Hastedt and T. Luhmann, “Investigations on the quality of the interior orientation and its impact in object space for UAV photogrammetry,” Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci., vol. XL, no. 1/W4, pp. 321–328, 2015, available at:

[56] M. E. Tjahjadi, “A Fast And Stable Orientation Solution of Three Cameras-Based UAV Imageries,” ARPN J. Eng. Appl. Sci., vol. 11, no. 5, pp. 3449–3455, 2016, available at:

[57] E. M. Mikhail, J. S. Bethel, and C. J. McGlone, Introduction to Modern Photogrammetry. New York: John Wiley & Sons, Inc., 2001, available at: Google Scholar.

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

International Journal of Advances in Intelligent Informatics
ISSN 2442-6571  (print) | 2548-3161 (online)
Organized by Informatics Department - Universitas Ahmad Dahlan , and UTM Big Data Centre - Universiti Teknologi Malaysia
Published by Universitas Ahmad Dahlan
W :
E :, (paper handling issues), (publication issues)

View IJAIN Stats

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0