Statistical estimation for exterior orientation from line-to-line correspondences
This paper presents a statistical estimation from which a new objective function for exterior orientation from line correspondences is derived. The objective function is based on the assumption that the underlying noise model for the line correspondences is the Fisher distribution. The assumption is appropriate for 3D orientation, is different from the underlying noise models for k pixels positions, and allows us to do a consistent estimation of the unknown parameters. The objective function gives two important facts: its formulation and concept is different for that of previous work, and it automatically estimates six unknown parameters simultaneously. As a result, it provides an optimal solution and better accuracy. We design an experimental protocol to evaluate the performance of the new algorithm. The results of each experiment shows that the new algorithm produces answers whose errors are 10%–20% less than the competing decoupled least squares algorithm.
KeywordsTranslation Vector Fisher Distribution World Coordinate System Exterior Orientation Line Correspondence
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- 1.Haralick, R. M., C. N. Lee, K. Ottenberg, and M. Nölle, “Analysis of The Three Point Perspective Pose Estimation Problem and Solutions”, IEEE conference on Computer Vision and Pattern Recognition, Maui, Hawaii, June, 1991.Google Scholar
- 2.Linnainmaa, S., D. Harwood, and L.S. Davis, “Pose Estimation of a Three-Dimensional Object Using Triangle Pairs,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 10, No.5, 1988, pp. 634–647.Google Scholar
- 3.Pope, J.A., “An Advantageous, Alternative Parameterization of Rotations for Analytical Photogrammetry,” ESSA Tech. Rep., C and GS 39.Google Scholar
- 4.Thompson, E.H. “On Exact Linear Solution of the Problem of Absolute Orientation,” Photogrammetria, Vol. 13, No. 4, 1958, pp. 163–178.Google Scholar
- 5.Lowe, D. G. Perceptual Organization and Visual Recognition, Boston: Kluwer, 1985Google Scholar
- 6.Kumar, R., and R. Hanson, “Analysis of Different Robust Methods for Pose Estimation,” IEEE Workshop on Robust Computer Vision, Seattle, WA, Oct. 1–3, 1990.Google Scholar
- 7.Liu, Yuncai, Thomas S. Huang, and O. D. Faugeras, “Determination of Camera Location from 2-D to 3-D Line and Point Correspondences,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 12, No.1, 1990, pp. 28–37.Google Scholar
- 8.Barnard S. T., “Interpreting Perspective Images,” Artificial Intelligence, Vol. 21, 1983, pp. 435–462.Google Scholar
- 9.Fisher, R. A., “Dispersion on a Sphere,” Proceedings Royal Society of London, Vol. 217, A., 1953.Google Scholar
- 10.Mardia, K.V., “Statistics of directional data,” New York: Academic Press, 1972.Google Scholar
- 11.Papoulis, A., “Probability, Random Variables, and Stochastic Process,” 1984.Google Scholar