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Pose Determination from Line-to-Plane Correspondences: Existence Condition and Closed-Form Solutions
June 1991 (vol. 13 no. 6)
pp. 530-541

A class of pose determination problems in which the sensory data are lines and the corresponding reference data are planes is discussed. The lines considered are different from edge lines in that they are not the intersection of boundary faces of the object. The author describes a polynomial approach that does not require a priori knowledge about the object location. Closed-form solutions for orthogonal, parallel, and coplanar feature configurations of critical importance in real applications are derived. Findings concerning the necessary and sufficient conditions under which the line-to-plane pose determination problem can be solved are described.

[1] J. K. Aggarwal and N. Nandhakumar, "On the computation of motion from sequences of images--A review,"Proc. IEEE, vol. 76, no. 8, pp. 917-935, 1988.
[2] L. Brand,Vector and Tensor Analysis. New York: Wiley, 1947.
[3] H. H. Chen, "Sensing object location with dextrous hand," AT&T Bell Lab., Tech. Memo., 1988.
[4] H. H. Chen and T. S. Huang, "Matching 3-D line segments with applications to multiple-object motion estimation,"IEEE Trans. Pattern Anal. Machine Intell., vol. 12, no. 9, pp. 1002-1008, 1990.
[5] H. H. Chen, "Pose determination from line-to-plane correspondences: Existence condition and closed-form solutions," inProc. 3rd Int. Conf. Computer Vision, Tokyo, Japan, 1990, pp. 374-378.
[6] I. J. Cox and J. B. Kruskal, "On the congruence of noisy images to line segment models," inProc. Second Int. Conf. Computer Vision, Tampa, FL, 1988, pp. 252-258.
[7] M. Dhome, M. Richetic, J.-T. Lapreste, and G. Rives, "Determination of the attitude of 3-D objects from a single perspective view,"IEEE Trans. Pattern Anal. Machine Intell., vol. 11, no. 12, pp. 1265-1278, 1989.
[8] O. D. Faugeras and M. Hebert, "The representation, recognition, and locating of 3-D objects,"Int. J. Robotics Res., vol. 5, no. 3, Fall 1986, pp. 27-52.
[9] O. D. Faugeras and S. J. Maybank, "Motion from point matches: Multiplicity of solutions," inProc. Workshop Visual Motion, Irvine, CA, 1989, pp. 248-255.
[10] M. A. Fischler and R. C. Bolles, "Random sample consensus: A paradigm for model fitting with applications to image analysis and automated cartography,"Commun. ACM, vol. 24, no. 6, pp. 381-395, 1981.
[11] J.D. Foley and A. Van Dam,Fundamentals of Interactive Computer Graphics(The System Programming Series). Reading, MA: Addison-Wesley, 1982.
[12] W. Förstner, "Reliability analysis of parameter estimation in linear models with applications to mensuration problems in computer vision,"Comput. vision, Graphics, Image Processing, vol. 40, pp. 273-310, 1987.
[13] S. J. Gordon and W. P. Seering, "Real-time part position sensing,"IEEE Trans. Pattern Anal. Machine Intell., vol. 10, no. 3, pp. 374-386, 1988.
[14] W. E. L. Grimson and T. Lozano-Pérez, "Model-based recognition and localization from sparse range or tactile data,"Int. J. Robotics Res., vol. 3, no. 3, pp. 3-35, 1984.
[15] W. R. Hamilton,Elements of Quaternions, vols. 1 and 2. New York: Chelsea, 1899.
[16] R. M. Haralick,et al., "Pose estimation from corresponding point data,"IEEE Trans. Syst., Man, Cybern., vol. 19, no. 6, pp. 1426-1446, 1989.
[17] B. K. P. Horn,Robot Vision. New York: McGraw-Hill, 1986.
[18] B. K. P. Horn, "Motion fields are hardly ever ambiguous,"Int. J. Comput. Vision, vol. 1, pp. 259-274, 1987.
[19] T. S. Huang, "Motion analysis," inEncyclopedia of Artificial Intelligence. New York: Wiley, 1987.
[20] T. S. Huang, A. N. Netravali, and H. H. Chen, "Motion and pose determination using algebraic methods," inTime-Varying Image Processing and Moving Object Recognition, vol. 2, V. Cappellini, Ed. Amsterdam, The Netherlands: Elsevier, 1990, pp. 243-249.
[21] Y. Hung, P. Yeh, and D. Harwood, "Passive ranging to known planar point sets," presented at the IEEE Int. Conf. Robotics and Automation, St. Louis, MO, Mar. 25-28, 1985.
[22] M. A. Jenkins and J. F. Traub, "A three-stage algorithm for real polynomials using quadratic iteration,"SIAM J. Numer. Anal., vol. 7, no. 4, pp. 545-566, 1970.
[23] G. Korn and T. Korn,Mathematical Handbook for Scientists and Engineers. New York: McGraw-Hill, 1961.
[24] R. Kumar and A. R. Hanson, "Robust estimation of camera location and orientation from noisy data having outliers," inProc. Workshop Interpretation of 3D Scene, Austin, TX, 1989, pp. 52-60.
[25] J. Z. Levin, "Mathematical models for determining the intersections of quadric surfaces,"Comput. Graphics Image Processing, vol. 11, pp. 73-87, 1979.
[26] Y. Liu, T. S. Huang, and O. D. Faugeras, "Determination of camera location from 2-D to 3-D line and point correspondences,"IEEE Trans. Pattern Anal. Machine Intell., vol. 12, no. 1, pp. 28-37, 1990.
[27] H. C. Longuet-Higgins, "A computer algorithm for reconstructing a scene from two projections,"Nature, vol. 293, pp. 133-135, 1981.
[28] M. J. Maron,Numerical Analysis. New York: Macmillan, 1982.
[29] A. Morgan,Solving Polynomial Systems Using Continuation for Engineering and Scientific Problems. Englewood Cliffs, NJ: Prentice-Hall, 1987.
[30] S. Negahdaripour, "Critical surface pairs and triplets,"Int. J. Comput. Vision, vol. 3, pp. 293-312, 1989.
[31] G. Silverman, R. Y. Tsai, and M. Lavin, "Locating polyhedral objects from edge point," inProc. 1987 Workshop Spatial Reasoning and Multi-Sensor Fusion, St. Charles, IL, 1987, pp. 282-292.
[32] D. M. Y. Sommerville,An Introduction to the Geometry of N Dimension. New York, Dover, 1958.
[33] T. H. Speeter, "A tactile sensing system for robotic manipulation,"Int. J. Robotics Res., vol. 9, no. 6, pp. 25-36, 1990.
[34] R. Y. Tsai, "Uniqueness and estimation of three-dimensional motion parameters of rigid object with curves surfaces,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-6, no. 1, pp. 13-26, 1984.
[35] R.Y. Tsai, "A Versatile Camera Calibration Technique for High-Accuracy 3D Machine Vision Metrology Using Off-the-Shelf TV Cameras and Lenses,"IEEE J. of Robotics and Automation, Vol. RA-3, No. 4, Aug. 1987, pp. 323-344.
[36] J.S.-C Yuan, "A General Photogrammic Method for Determining Object Position and Orientation," IEEE Trans. Robotics and Automation, Vol. RA-5, No. 2, Apr. 1989, pp. 129-142.
[37] Z. Zhang, O. D. Faugeras, and N. Ayache, "Analysis of a sequence of stereo scenes containing multiple moving objects using rigidity constraints," inProc. Second Int. Conf. Computer Vision, Tampa, FL, 1988, pp. 177-187.

Index Terms:
dextrous manipulation; pattern recognition; machine vision; motion analysis; line-to-plane correspondences; closed-form solutions; pose determination; sensory data; boundary faces; polynomial; object location; coplanar feature; pattern recognition; polynomials; robots
H.H. Chen, "Pose Determination from Line-to-Plane Correspondences: Existence Condition and Closed-Form Solutions," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 13, no. 6, pp. 530-541, June 1991, doi:10.1109/34.87340
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