Browse > Article
http://dx.doi.org/10.7848/ksgpc.2019.37.3.189

Single Photo Resection Using Cosine Law and Three-dimensional Coordinate Transformation  

Hong, Song Pyo (Department of GIS Engineering, Namseoul University)
Choi, Han Seung (GIS Research Center, Geospatial Information Technology Co., Ltd)
Kim, Eui Myoung (Department of Spatial Information Engineering, Namseoul University)
Publication Information
Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography / v.37, no.3, 2019 , pp. 189-198 More about this Journal
Abstract
In photogrammetry, single photo resection is a method of determining exterior orientation parameters corresponding to a position and an attitude of a camera at the time of taking a photograph using known interior orientation parameters, ground coordinates, and image coordinates. In this study, we proposed a single photo resection algorithm that determines the exterior orientation parameters of the camera using cosine law and linear equation-based three-dimensional coordinate transformation. The proposed algorithm first calculated the scale between the ground coordinates and the corresponding normalized coordinates using the cosine law. Then, the exterior orientation parameters were determined by applying linear equation-based three-dimensional coordinate transformation using normalized coordinates and ground coordinates considering the calculated scale. The proposed algorithm was not sensitive to the initial values by using the method of dividing the longest distance among the combinations of the ground coordinates and dividing each ground coordinates, although the partial derivative was required for the nonlinear equation. In addition, since the exterior orientation parameters can be determined by using three points, there was a stable advantage in the geometrical arrangement of the control points.
Keywords
Single Photo Resection; Exterior Orientation Parameters; Cosine Law; Three-Dimensional Coordinate Transformation; Normalized Coordinate;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 Bouguet, J.Y. (2015), Camera calibration toolbox for Matlab, Caltech Vision, URL: http://www.vision.caltech.edu/bouguetj/calib_doc (last date accessed: 22 May 2019).
2 Fischler, M.A. and Bolles, R.C. (1981), Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography. Communications of the ACM. Vol. 24, No. 6, pp. 381-395.   DOI
3 Gao, X.S., Hou, X.R., Tang, J., and Cheng, H.F. (2003), Complete solution classification for the perspective-threepoint problem. IEEE transactions on pattern analysis and machine intelligence, Vol. 25, No. 8, pp. 930-943.   DOI
4 Grafarend, E.W. and Shan, J. (1997), Closed-form solution of P4P or the three-dimensional resection problem in terms of Mobius barycentric coordinates, Journal of Geodesy, Vol. 71, No. 4, pp. 217-231.   DOI
5 Guan, Y., Cheng, X., Zhan, X., and Zhou, S. (2008), Closed-form solution of space resection using unit quaternion. In Artigo apresentado no XXI ISPRS Congress, 3-11 July 2008, Beijing, China, Vol. XXXVII, Part B3b, pp. 3-11.
6 Jiang, G.W., Jiang, T., Wang, Y., and Gong, H. (2007). Space resection independent of initial value based on unit quaternions, Acta Geodaetica et Cartographica Sinica, Vol. 36, No. 2, pp. 169-175.   DOI
7 Hong, S.P. and Kim, E.M. (2019), Comparison of point-based 3d transformation methods, Proceedings of Journal of Korean Society for Geospatial Information System, Korean Society for Geospatial Information Science, 31-1 May, Busan, Korea, pp. 19-22. (in Korean)
8 Kabsch, W. (1976), A solution for the best rotation to relate two sets of vectors, Acta Crystallographica Section A: Crystal Physics, Diffraction, Theoretical and General Crystallography, Vol. 32, No. 5, pp. 922-923.   DOI
9 Kim, E.M. and Choi, H.S. (2018), Analysis of the accuracy of quaternion-based spatial resection based on the layout of control points, Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography, Vol. 36, No. 4, pp. 255-262. (in Korean with English abstract)   DOI
10 Lepetit, V., Moreno-Noguer, F., and Fua, P. (2009). EPnP: an accurate o(n) solution to the PnP problem. International Journal of Computer Vision, Vol. 81, No. 2, pp. 155-166.   DOI
11 Lim, J.H. (2018), Optimization Theory, Jang-Hwan Publishing, Goyang.
12 Luhmann, T., Robson, S., Kyle, S., and Harley, I. (2011), Close Range Photogrammetry Principles, techniques and applications, Whittles Publishing, Caithness.
13 Mazaheri, M. and Habib, A. (2015), Quaternion-based solutions for the single photo resection problem, Photogrammetric Engineering & Remote Sensing, Vol. 81, No. 3, pp. 209-217.   DOI
14 Mikhail, E.M., Bethel, J.S., and McGlone, J.C. (2001), Introduction to Modern Photogrammetry, John Wiley & Sons Inc., New York, N.Y.
15 Nielsen, A.A. (2013). Least squares adjustment: linear and nonlinear weighted regression analysis. Applied Mathematics and Computer Science/National Space Institute, Technical University of Denmark, URL: http://www2.imm.dtu.dk/pubdb/views/edoc_download.php/2804/pdf/imm2804.pdf (last date accessed: 22 May 2019).
16 Strang, G. (2016), Introduction to Linear Algebra, Wellesley-Cambridge Press, Massachusetts, M.A.
17 Torr, P.H.S. and Zisserman, A. (2000), Mlesac: a new robust estimator with application to estimating image geometry, Computer Vision and Image Understanding, Vol. 78, No. 1, pp. 138-156.   DOI