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David Nist?, "An Efficient Solution to the FivePoint Relative Pose Problem," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 26, no. 6, pp. 756777, June, 2004.  
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@article{ 10.1109/TPAMI.2004.17, author = {David Nist?}, title = {An Efficient Solution to the FivePoint Relative Pose Problem}, journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence}, volume = {26}, number = {6}, issn = {01628828}, year = {2004}, pages = {756777}, doi = {http://doi.ieeecomputersociety.org/10.1109/TPAMI.2004.17}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
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TY  JOUR JO  IEEE Transactions on Pattern Analysis and Machine Intelligence TI  An Efficient Solution to the FivePoint Relative Pose Problem IS  6 SN  01628828 SP756 EP777 EPD  756777 A1  David Nist?, PY  2004 KW  Imaging geometry KW  motion KW  relative orientation KW  structure from motion KW  camera calibration KW  egomotion estimation KW  scene reconstruction. VL  26 JA  IEEE Transactions on Pattern Analysis and Machine Intelligence ER   
Abstract—An efficient algorithmic solution to the classical fivepoint relative pose problem is presented. The problem is to find the possible solutions for relative camera pose between two calibrated views given five corresponding points. The algorithm consists of computing the coefficients of a tenth degree polynomial in closed form and, subsequently, finding its roots. It is the first algorithm wellsuited for numerical implementation that also corresponds to the inherent complexity of the problem. We investigate the numerical precision of the algorithm. We also study its performance under noise in minimal as well as overdetermined cases. The performance is compared to that of the wellknown 8 and 7point methods and a 6point scheme. The algorithm is used in a robust hypothesizeandtest framework to estimate structure and motion in realtime with low delay. The realtime system uses solely visual input and has been demonstrated at major conferences.
[1] P. Beardsley, A. Zisserman, and D. Murray, Sequential Updating of Projective and Affine Structure from Motion Int'l J. Computer Vision, vol. 23, no. 3, pp. 235259, 1997.
[2] O. Chum and J. Matas, Randomized RANSAC with$T_{d,d}$Test Proc. British Machine Vision Conf., pp. 448457, 2002.
[3] M. Demazure, Sur Deux Problemes de Reconstruction Technical Report No. 882, INRIA, France, 1988.
[4] O. Faugeras and S. Maybank, Motion from Point Matches: Multiplicity of Solutions Int'l J. Computer Vision, vol. 4, no. 3, pp. 225246, 1990.
[5] O. Faugeras, What Can Be Seen in Three Dimensions with an Uncalibrated Stereo Rig? Proc. European Conf. Computer Vision, pp. 563578, 1992.
[6] O. Faugeras, ThreeDimensional Computer Vision: A Geometric Viewpoint. MIT Press, 1993.
[7] A. Fitzgibbon and A. Zisserman, Automatic Camera Recovery for Closed or Open Image Sequences Proc. European Conf. Computer Vision, pp. 311326, 1998.
[8] M. Fischler and R. Bolles, Random Sample Consensus: A Paradigm for Model Fitting with Application to Image Analysis and Automated Cartography Comm. ACM, vol. 24, pp. 381395, 1981.
[9] W. Gellert, K. Küstner, M. Hellwich, and H. Kastner, The VNR Concise Encyclopedia of Mathematics. Van Nostrand Reinhold Company, 1975.
[10] A. Gruen and T. Huang, Calibration and Orientation of Cameras in Computer Vision. Springer Verlag, 2001.
[11] R. Haralick, C. Lee, K. Ottenberg, and M. Nölle, Review and Analysis of Solutions of the Three Point Perspective Pose Estimation Problem Int'l J. Computer Vision, vol. 13, no. 3, pp. 331356, 1994.
[12] R. Hartley, Estimation of Relative Camera Positions for Uncalibrated Cameras Proc. European Conf. Computer Vision, pp. 579587, 1992.
[13] R.I. Hartley, In Defense of the 8Point Algorithm IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 19, no. 6, pp. 580593, June 1997.
[14] R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision. Cambridge Univ. Press, 2000.
[15] D. Heeger and A. Jepson, Subspace Methods for Recovering Rigid Motion Int'l J. Computer Vision, vol. 7, no. 2, pp. 95117, 1992.
[16] A. Heyden and G. Sparr, Reconstruction from Calibrated Cameras A New Proof of the KruppaDemazure Theorem J. Math. Imaging&Vision, vol. 10, pp. 120, 1999.
[17] D. Hook and P. McAree, Using Sturm Sequences to Bracket Real Roots of Polynomial Equations Graphic Gems I, Academic Press, pp. 416423, 1990.
[18] B. Horn, Relative Orientation Int'l J. Computer Vision, vol. 4, pp. 5978, 1990.
[19] E. Kruppa, Zur Ermittlung eines Objektes aus Zwei Perspektiven mit Innerer Orientierung Sitz.Ber. Akad. Wiss., Wien, Math. Naturw. Kl., Abt. IIa., vol. 122, pp. 19391948, 1913.
[20] H. LonguetHiggins, A Computer Algorithm for Reconstructing a Scene from Two Projections Nature, vol. 293, no. 10, pp. 133135, 1981.
[21] H. LonguetHiggins, The Reconstruction of a Plane Surface from Two Perspective Projections Proc. Royal Soc. London B, vol. 277, pp. 399410, 1986.
[22] S. Maybank, Theory of Reconstruction from Image Motion. Springer Verlag, 1993.
[23] S. Negahdaripour, ClosedForm Relationship Between the Two Interpretations of a Moving Plane J. Optical Soc. of Am., vol. 7, no. 2, pp. 279285, 1990.
[24] D. Nistér, Reconstruction from Uncalibrated Sequences with a Hierarchy of Trifocal Tensors Proc. European Conf. Computer Vision, pp. 649663, 2000.
[25] D. Nistér, Automatic Dense Reconstruction from Uncalibrated Video Sequences PhD thesis, Royal Inst. of Technology KTH, Mar. 2001.
[26] D. Nistér, Preemptive RANSAC for Live Structure and Motion Estimation Proc. Int'l Conf. Computer Vision, pp. 199206, 2003.
[27] D. Nistér, An Efficient Solution to the FivePoint Relative Pose Problem Proc. Computer Vision and Pattern Recognition, pp. 195202, 2003.
[28] D. Nistér, Live Structure and Motion Estimation Proc. Computer Vision and Pattern Recognition, 2003.
[29] D. Nistér, Live EgoMotion Estimation Proc. Int'l Conf. Computer Vision, 2003.
[30] J. Oliensis and Y. Genc, “New Algorithms for TwoFrame Structure from Motion,” NECI technical report, 2000. Expanded version of Proc. Int'l Conf. Computer Vision, pp. 737–744, 1999.
[31] J. Oliensis, A Critique of Structure from Motion Algorithms Computer Vision and Image Understanding, vol. 80, pp. 172214, 2000.
[32] J. Philip, A NonIterative Algorithm for Determining All Essential Matrices Corresponding to Five Point Pairs Photogrammetric Record, vol. 15, no. 88, pp. 589599, 1996.
[33] J. Philip, Critical Point Configurations of the 5, 6, 7, and 8point Algorithms for Relative Orientation TRITAMAT1998MA13, Feb. 1998.
[34] M. Pollefeys, R. Koch, and L. Van Gool, SelfCalibration and Metric Reconstruction in Spite of Varying and Unknown Internal Camera Parameters, Int'l J. Computer Vision, vol. 32, no. 1, pp. 725, 1999.
[35] M. Pollefeys, F. Verbiest, and L. Van Gool, Surviving Dominant Planes in Uncalibrated Structure and Motion Recovery Proc. European Conf. Computer Vision, pp. 837851, 2002.
[36] W. Press, S. Teukolsky, W. Vetterling, and B. Flannery, Numerical Recipes in C, Cambridge Univ. Press, 1988.
[37] J. Semple and G. Kneebone, Algebraic Projective Geometry. Oxford Univ. Press, 1952.
[38] P. Stefanovic, Relative OrientationA New Approach I.T.C.J., vol. 3, pp. 417448, 1973.
[39] R. Sturm, Das Problem der Projektivität und seine Anwendung auf die Flächen Zweiten Grades Math. Annalen 1, pp. 533573, 1869.
[40] T.Y. Tian, C. Tomasi, and D.J. Heeger, “Comparison of Approaches to Egomotion Computation,” Proc. Conf. Computer Vision and Pattern Recognition, pp. 315–320, 1996.
[41] P. Torr and D. Murray, The Development and Comparison of Robust Methods for Estimating the Fundamental Matrix Int'l J. Computer Vision, vol. 24, no. 3, pp. 271300, 1997.
[42] P. Torr and A. Zisserman, Robust Parameterization and Computation of the Trifocal Tensor Image and Vision Computing, vol. 15, pp. 591605, 1997.
[43] P. Torr, A. Fitzgibbon, and A. Zisserman, The Problem of Degeneracy in Structure and Motion Recovery from Uncalibrated Image Sequences Int'l J. Computer Vision, vol. 32, no. 1, pp. 2744, 1999.
[44] B. Triggs, Routines for Relative Pose of Two Calibrated Cameras from 5 Points technical report, http://www.inrialpes.fr/ movi/peopleTriggsINRIA, France, 2000.
[45] B. Triggs, P. McLauchlan, R. Hartley, and A. Fitzgibbon, Bundle AdjustmentA Modern Synthesis Lecture Notes in Computer Science, vol. 1883, pp. 298375, 2000.
[46] R. Tsai and T. Huang, Uniqueness and Estimation of ThreeDimensional Motion Parameters of Rigid Objects with Curved Surfaces IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 6, no. 1, pp. 1327, 1984.
[47] H. von Sanden, Die Bestimmung der Kernpunkte in der Photogrammetrie PhD thesis, Univ. of Gottingen, 1908.
[48] Z. Zhang, Determining the Epipolar Geometry and Its Uncertainty: A Review Int'l J. Computer Vision, vol. 27, no. 2, pp. 161195, 1998.
[49] Z.Y. Zhang, A Flexible New Technique for Camera Calibration Proc. Int'l Conf. Computer Vision, vol. 1, pp. 666673, Sept. 1999.