This Article 
 Bibliographic References 
 Add to: 
A Method for Registration of 3-D Shapes
February 1992 (vol. 14 no. 2)
pp. 239-256

The authors describe a general-purpose, representation-independent method for the accurate and computationally efficient registration of 3-D shapes including free-form curves and surfaces. The method handles the full six degrees of freedom and is based on the iterative closest point (ICP) algorithm, which requires only a procedure to find the closest point on a geometric entity to a given point. The ICP algorithm always converges monotonically to the nearest local minimum of a mean-square distance metric, and the rate of convergence is rapid during the first few iterations. Therefore, given an adequate set of initial rotations and translations for a particular class of objects with a certain level of 'shape complexity', one can globally minimize the mean-square distance metric over all six degrees of freedom by testing each initial registration. One important application of this method is to register sensed data from unfixtured rigid objects with an ideal geometric model, prior to shape inspection. Experimental results show the capabilities of the registration algorithm on point sets, curves, and surfaces.

[1] K. S. Arun, T. S. Huang, and S. D. Blostein, "Least-squares fitting of two 3-D point sets,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-9, no. 5, pp. 698-700, 1987.
[2] R. Bajcsy and F. Solina, "Three-dimensional object representation revisited,"Proc. 1st Int. Conf. Comput. Vision(London), June 8-11, 1989, pp. 231-240.
[3] P. J. Besl, "Geometric modeling and computer vision,"Proc. IEEE, vol. 76, no. 8, pp. 936-958, Aug. 1988.
[4] P. J. Besl, "Active optical range imaging sensors," inAdvances in Machine Vision(J. Sanz, Ed.). New York: Springer-Verlag, 1989; see alsoMachine Vision and Applications, vol. 1, pp. 127-152, 1989.
[5] P. J. Besl, "The free-form surface matching problem,"Machine Vision for Three-Dimensional Scenes(H. Freeman, Ed.). New York: Academic, 1990.
[6] P. J. Besl and R. C. Jain, "Three-dimensional object recognition,"ACM Comput. Surveys, vol. 17, no. 1, pp. 75-145, Mar. 1985.
[7] J. Blumenthal, "Polygonizing implicit surfaces," Xerox Parc Tech. Rep. EDL-88-4, 1988.
[8] B. Bhanu and C.-C. Ho, "CAD-based 3D object representation for robot vision,"Computer, vol. 20, pp. 19-35, Aug. 1987.
[9] W. Boehm, G. Farin, and J. Kahmann, "A survey of curve and surface methods in CAGD,"Comput. Aided Geometric Des., vol. 1, no. 1, pp. 1-60, July 1984.
[10] R. C. Bolles and P. Horaud, "3DPO: A three dimensional part orientation svstem,"Int. J. Robotics Res., vol. 5, no. 3, Fall 1986, pp. 3-26.
[11] P. Brou, "Using the Gaussian image to find the orientation of an object,"Int. J. Robotics Res., vol. 3, no. 4, pp. 89-125, 1983.
[12] J. Callahan and R. Weiss, "A model for describing surface shape," inProc. Conf. Comput. Vision. Patt. Recogn.(San Francisco, CA), June 1985, pp. 240-247.
[13] C. H. Chen and A. C. Kak, "3DPOLY: A robot vision system for recognizing 3-D objects in low-order polynomial time," Tech. Rep. 88-48, Elect. Eng. Dept., Purdue Univ., West Lafayette, IN, 1988.
[14] R.T. Chin and C. R. Dyer, "Model-based recognition in robot vision,"ACM Comput. Surveys, vol. 18, no. 1, pp. 67-108, Mar. 1986.
[15] C. DeBoor,A Practical Guide to Splines. New York: Springer-Verlag, 1978.
[16] C. DeBoor and K. Hollig, "B-splines without divided differences,"Geometric Modeling: Algorithms and New Trends(G. Farin, Ed.),SIAM, pp. 21-28, 1987.
[17] G. Farin,Curves and Surfaces in Computer Aided Geometric Design: A Practical Guide. New York: Academic, 1990.
[18] 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.
[19] T.-J. Fan, "Describing and recognizing 3-D objects using surface properties," Ph.D dissertation, University of Southern California, Tech. Rep. IRIS-237, Aug. 1988.
[20] P. J. Flynn and A. K. Jain, "CAD-based computer vision: From CAD models to relational graphs,"IEEE Trans. Patt. Anal. Machine Intell., vol. 13, no. 2, pp. 114-132, 1991; see also Ph.D. Thesis, Comput. Sci. Dept., Michigan State Univ., E. Lansing, MI.
[21] E. G. Gilbert and C. P. Foo, "Computing the distance between smooth objects in 3D space," RSD-TR-13-88, Univ. of Michigan, Ann Arbor, 1988.
[22] E. G. Gilbert, D. W. Johnson, S. S. Keerthi, "A fast procedure for computing the distance between complex objects in 3D space,"IEEE J. Robotics Automat., vol. 4, pp. 193-203, 1988.
[23] G. H. Golub and C. F. Van Loan,Matrix Computations. Baltimore, MD: Johns Hopkins Univ. Press, 1983.
[24] W. E. L. Grimson, "The combinatorics of local constraints in model-based recognition and localization from sparse data,"J. ACM, vol. 33, no. 4, pp. 658-686, 1986.
[25] 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, Fall 1984.
[26] K. T. Gunnarsson and F. B. Prinz, "CAD model-based localization of parts in manufacturing,"IEEE Comput., vol. 20, no. 8, pp. 66-74, Aug. 1987.
[27] E. Hall, J. Tio, C. McPherson, and F. Sadjadi, "Measuring curved surfaces for robot vision,"Comput.vol. 15, no. 12, pp. 42-54, Dec. 1982.
[28] R. M. Haralicket al., "Pose estimation from corresponding point data," inMachine Vision for Inspection and Measurement(H. Freeman, Ed.). New York: Academic, 1989.
[29] H. Hilton,Mathematical Crystallography and the Theory of Groups of Movements. Oxford: Clarendon, 1963; London: Dover, 1963.
[30] B. K. P. Horn, "Extended Gaussian images,"Proc. IEEE, vol. 72, no. 12, pp. 1656-1678, Dec. 1984.
[31] B. K. P. Horn, "Closed-form solution of absolute orientation using unit quaternions,"J. Opt. Soc. Amer. Avol. 4, no. 4, pp. 629-642, Apr. 1987.
[32] B. K. P. Horn, "Relative orientation," A.I. Memo 994, AI Lab, Mass. Inst. Technol., Cambridge, Sept. 1987.
[33] B. K. P. Horn and J. G. Harris, "Rigid body motion from range image sequences,"Comput. Vision Graphics Image Processing, 1989.
[34] K. Ikeuchi, "Generating an interpretation tree from a CAD model for 3-D object recognition in bin-picking tasks,"Int. J. Comput. Vision, vol. 1, no. 2, pp. 145-165, 1987.
[35] A. K. Jain and R. Hoffman, "Evidence-based recognition of 3-D objects,"IEEE Trans. Patt. Anal. Machine Intell, vol. 10, no. 6, pp. 793-802, 1988.
[36] B. Kamgar-Parsi, J. L. Jones, and A. Rosenfeld, "Registration of multiple overlapping range images: Scenes without distinctive features,"Proc. IEEE Comput. Vision Patt. Recogn. Conf.(San Diego, CA), June 1989.
[37] Y. Lamdan and H. J. Wolfson, "Geometric hashing: A general and efficient model-based recognition scheme," inProc. 2nd Int. Conf. Computer vision, 1988.
[38] S. Z. Li, "Inexact matching of 3D surfaces," VSSP-TR-3-90, Univ. of Surrey, England, 1990.
[39] P. Liang, "Measurement, orientation determination, and recognition of surface shapes in range images," Cent. Robotics Syst., Univ. of California, Santa Barbara, 1987.
[40] D. Luenberger,Linear and Nonlinear Programming. Reading, MA Addison-Wesley, 1984.
[41] A. P. Morgan,Solving Polynomial Systems Using Continuation for Engineering and Scientific Problems. Englewood Cliffs, NJ: Prentice Hall, 1987.
[42] M. E. Mortenson,Geometric Modeling. New York: Wiley, 1985.
[43] J. Mundyet al., "The PACE system," inProc. CVPR '88 Workshop; see alsoDARPA IUW.
[44] D. W. Murray, "Model-based recognition using 3D shape alone,"Computer Vision, Graphics and Image Process., vol. 40, pp. 250-266, 1987.
[45] W. Press, B. Flannery, S. Teukolsky, and W. Vetterling,Numeric Recipes in C-The Art of Scientific Computing.Cambridge, UR: Cambridge University Press, 1988.
[46] J.H. Rieger, "On the classification of views of piecewise smooth objects,"Image Vision Comput., vol. 5, no. 2, pp. 91-97, May 1987.
[47] Proc. IEEE Robust Methods Workshop. Univ. of Washington, Seattle.
[48] P. Sander, "On reliably inferring differential structure from 3D im ages," Ph.D. dissertation, Dept. of Elect. Eng., McGill Univ., Montreal Canada, 1988.
[49] P. H. Schonemann, "A generalized solution to the orthogonal procrustes problem,"Psychometrika, vol. 31, no. 1, 1966.
[50] J. T. Schwartz and M. Sharir, "Identification of objects in two and three dimensions by matching noisy characteristic curves,"Int. J. Robotics Res., vol. 6, no. 2, pp. 29-44, 1987.
[51] T. W. Sederberg, "Piecewise algebraic surface patches,"Comput. Aided Geometric Des., vol. 2, no. 1, pp. 53-59, 1985.
[52] B. M. Smith, "IGES: A key to CAD/CAM systems integration,"IEEE Comput. Graphics Applications, vol. 3, no. 8, pp. 78-83, 1983.
[53] G. Stockman, "Object recognition and localization via pose clustering,"Comp. Vision Graphics Image Processing, vol. 40, pp. 361-387, 1987.
[54] R. Szeliski, "Estimating motion from sparse range data without correspondence,"2nd Int. Conf. Comput. Vision(Tarpon Springs, FL), Dec. 5-8, 1988, pp. 207-216.
[55] G. Taubin, "Algebraic nonplanar curve and surface estimation in 3- space with applications to position estimation," Tech. Rep. LEMS-43, Div. Eng., Brown Univ., Providence, RI, 1988.
[56] G. Taubin, "About shape descriptors and shape matching," Tech. Rep. LEMS-57, Div. Eng., Brown Univ., Providence, RI, 1989.
[57] D. Terzopoulos, J. Platt, A. Barr, and K. Fleischer, "Elastically deformable models."Comput. Graphics, vol. 21, no. 4, pp. 205-214, July 1987.
[58] B.C. Vemuri, A. Mitiche, and J.K. Aggarwal, "Curvature-based representation of objects from range data,"Image and Vision Comput., vol. 4, no. 2, pp. 107-114, May 1986.
[59] B. C. Vemuri and J. K. Aggarwal, "Representation and recognition of objects from dense range maps,"IEEE Trans. Circuits Syst., vol. CAS-34, no. 11, pp. 1351-1363, Nov. 1987.
[60] A. K. C. Wong, S. W. Lu, and M. Rioux, "Recognition and shape synthesis of 3-D objects based on attributed hypergraphs,"IEEE Trans. Patt. Anal. Machine Intell., vol. 11, no. 3, pp. 279-290, Mar. 1989.

Index Terms:
3D shape registration; pattern recognition; point set registration; iterative closest point; geometric entity; mean-square distance metric; convergence; geometric model; computational geometry; convergence of numerical methods; iterative methods; optimisation; pattern recognition; picture processing
P.J. Besl, N.D. McKay, "A Method for Registration of 3-D Shapes," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 14, no. 2, pp. 239-256, Feb. 1992, doi:10.1109/34.121791
Usage of this product signifies your acceptance of the Terms of Use.