Homography Estimation from Ellipse Correspondences Based on the Common Self-polar Triangle
Tóm tắt
This paper presents new implementation algorithms for estimating the homography from ellipse correspondences based on the common self-polar triangle. Firstly, we propose an analytical solution with a fourfold ambiguity to homography based on converting two ellipse correspondences to three common pole correspondences. Secondly, after exploring the position information of the common poles, we propose the analytical algorithms for estimating the homography from only two ellipse correspondences. We also propose an analytical linear algorithm for estimating the homography by using the common pole correspondences with the known projective scale factors when given three or more ellipse correspondences. Unlike the previous methods, our algorithms are very easy to implement and furthermore may usually provide a unique solution (at most two solutions). Experimental results in synthetic data and real images show the accuracy advantage and the usefulness of our proposed algorithms.
Tài liệu tham khảo
Sturm, P.F., Maybank, S.J.: On plane-based camera calibration: a general algorithm, singularities, applications. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp. 432–437 (1999)
Zhang, Z.Y.: A flexible new technique for camera calibration. IEEE Trans. Pattern Anal. Mach. Intell. 22(11), 1330–1334 (2000)
Tsai, R.Y., Huang, T.S., Zhu, W.L.: Estimating three-dimensional motion parameters of a rigid planar patch, II: singular value decomposition. IEEE Trans. Acoust. Speech Signal Process. 30(4), 525–534 (1982)
Longuet-Higgins, H.C.: The reconstruction of a plane surface from two perspective projections. Proc. R. Soc. Lond. Ser. B 227, 399–410 (1986)
Faugeras, O., Lustman, F.: Motion and structure from motion in a piecewise planar environment. Int. J. Pattern Recognit. Artif. Intell. 2(3), 485–508 (1988)
Liebowitz, D., Zisserman, A.: Metric rectification for perspective images of planes. In: Proceedings of the Conference on Computer Vision and Pattern Recognition, pp. 482–488 (1998)
Criminisi, I.R., Zisserman, A.: Single view metrology. Int. J. Comput. Vis. 40(2), 123–148 (2000)
Szeliski, R.: Image mosaicing for tele-reality applications. In: Proceedings of the Second IEEE Workshop on Applications of Computer Vision, pp. 44–53 (1994)
Rothwell, C., Zisserman, A., Marinos, C., Forsyth, D.A., Mundy, J.L.: Relative motion and pose from arbitrary plane curves. Image Vis. Comput. 104, 250–262 (1992)
Ma, S.D.: Conics-based stereo, motion estimation, and pose determination. Int. J. Comput. Vis. 10(1), 7–25 (1993)
Sugimoto, A.: A linear algorithm for computing the homography from conics in correspondence. J. Math. Imaging Vis. 13(2), 115–130 (2000)
Mudigonda, P.K., Jawahar, C.V., Narayanan, P.J.: Geometric structure computation from conics. In: ICVGIP, pp. 9–14 (2004)
Agarwal, A., Jawahar, C.V., Narayanan, P.J.: A survey of planar homography estimation techniques. Centre for Visual Information Technology, Tech. Rep. (2005)
Kannala, J., Salo, M., Heikkila, J.: Algorithms for computing a planar homography from conics in correspondence. In: British Machine Vision Conference, pp. 77–86 (2006)
Conomis, C.: Conics-based homography estimation from invariant points and pole–polar relationships. In: International Symposium on 3D Data Processing, Visualization, and Transmission, pp. 908–915 (2006)
Chum, O., Matas, J.: Homography estimation from correspondences of local elliptical features. In: International Conference on Pattern Recognition, pp. 3236–3239 (2012)
Huang, H.F., Zhang, H., Cheung, Y.M.: Homography estimation from the common self-polar triangle of separate ellipses. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 1737–1744 (2016)
Wright, J., Wagner, A., Rao, S., Ma, Y.: Homography from coplanar ellipses with application to forensic blood splatter reconstruction. In: IEEE Conference on Computer Vision and Pattern Recognition, vol. 1, pp. 1250–1257 (2006)
Hartley, R.I., Zisserman, A.: Multiple View Geometry in Computer Vision, 2nd edn. Cambridge University Press, Cambridge (2004)
Woods, F.S.: Higher Geometry. An Introduction to Advanced Methods in Analytic Geometry. Ginn and Company, Boston (1922)
Semple, J., Kneebone, G.: Algebraic Projective Geometry. Oxford University Press, Oxford (1952)
Barreto, J.P.: General Central Projection Systems: Modeling, Calibration and Visual Servoing. Ph.D. thesis, University of Coimbra (2004)
Gibson, C.G.: Elementary Geometry of Algebraic Curves: An Undergraduate Introduction. Cambridge University Press, Cambridge (1998)
Forsyth, D., Mundy, J.L., Zisserman, A.: Invariant descriptors for 3-D object recognition and pose. IEEE Trans. Pattern Anal. Mach. Intell. 13(10), 971–991 (1991)
Fitzgibbon, A.W., Pilu, M., Fisher, R.B.: Direct least square fitting of ellipses. IEEE Trans. Pattern Anal. Mach. Intell. 21(5), 476–480 (1999)