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Michael T. Goodrich, Joseph S.B. Mitchell, Mark W. Orletsky, "Approximate Geometric Pattern Matching Under Rigid Motions," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 21, no. 4, pp. 371379, April, 1999.  
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@article{ 10.1109/34.761267, author = {Michael T. Goodrich and Joseph S.B. Mitchell and Mark W. Orletsky}, title = {Approximate Geometric Pattern Matching Under Rigid Motions}, journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence}, volume = {21}, number = {4}, issn = {01628828}, year = {1999}, pages = {371379}, doi = {http://doi.ieeecomputersociety.org/10.1109/34.761267}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Pattern Analysis and Machine Intelligence TI  Approximate Geometric Pattern Matching Under Rigid Motions IS  4 SN  01628828 SP371 EP379 EPD  371379 A1  Michael T. Goodrich, A1  Joseph S.B. Mitchell, A1  Mark W. Orletsky, PY  1999 KW  Hausdorff distance KW  pattern matching KW  registration. VL  21 JA  IEEE Transactions on Pattern Analysis and Machine Intelligence ER   
Abstract—We present techniques for matching pointsets in two and three dimensions under rigidbody transformations. We prove bounds on the worstcase performance of these algorithms to be within a small constant factor of optimal and conduct experiments to show that the average performance of these matching algorithms is often better than that predicted by the worstcase bounds.
[1] P.K. Agarwal, B. Aronov, M. Sharir, and S. Suri, "Selecting Distances in the Plane," Algorithmica, vol. 9, pp. 495514, 1993.
[2] N. Ahuja, "Dot Pattern Processing Using Voronoi Neighborhoods," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 4, no. 3, pp. 336343, May 1982.
[3] H. Alt, B. Behrends, and J. Blömer, "Approximate Matching of Polygonal Shapes," Annals of Math. and Artificial Intelligence, vol. 13, pp. 251266, 1995.
[4] H. Alt, L. Knipping, and G. Weber, "An Application of Point Pattern Matching in Astronautics," Technical Report B9316, Institut für Informatik, Fachbereich Mathematik und Informatic, Freie Universität Berlin, 1993.
[5] H. Alt, K. Mehlhorn, H. Wagener, and E. Welzl, "Congruence, Similarity and Symmetries of Geometric Objects," Discrete Computing in Geometry, vol. 3, pp. 237256, 1988.
[6] E. M. Arkin, K. Kedem, J.S.B. Mitchell, J. Sprinzak, and M. Werman, "Matching Points into PairwiseDisjoint Noise Regions: Combinatorial Bounds and Algorithms," ORSA J. Computing, vol. 4, no. 4, pp. 375386, 1992.
[7] K.S. Arun, T.S. Huang, and S.D. Blostein, "Least Squares Fitting of Two 3(D) Point Sets," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 9, pp. 698700, 1987.
[8] S. Arya, D.M. Mount, N.S. Netanyahu, R. Silverman, and A.Y. Wu, “An Optimal Algorithm for Approximate Nearest Neighborhood Searching,” Proc. Symp. Discrete Algorithms, pp. 573582, 1994.
[9] L.P. Chew, M.T. Goodrich, D.P. Huttenlocher, K. Kedem, J.M. Kleinberg, and D. Kravets, "Geometric Pattern Matching Under Euclidean Motion," Computing Geometric Theory Applications, vol. 7, pp. 113124, 1997.
[10] L.P. Chew and K. Kedem, "Improvements on Geometric Pattern Matching Problems," Proc. Third Scandinavian Workshop Algorithm Theory, pp. 318325. SpringerVerlag, 1992.
[11] R. Cole, "Slowing Down Sorting Networks to Obtain Faster Sorting Algorithms," J. ACM, vol. 34, pp. 200208, 1987.
[12] R. Cole, "Parallel Merge Sort," SIAM J. Computing, vol. 17, pp. 770785, 1988.
[13] R. Cole, J. Salowe, W. Steiger, and E. Szemerédi, "An OptimalTime Algorithm for Slope Selection," SIAM J. Computing, vol. 18, pp. 792810, 1989.
[14] T.H. Cormen,C.E. Leiserson, and R.L. Rivest,Introduction to Algorithms.Cambridge, Mass.: MIT Press/McGrawHill, 1990.
[15] H. Edelsbrunner, Algorithms in Combinatorical Geometry. EATCS Monographs in Computer Science, Berlin: Springer, 1987.
[16] D. Forsyth, J.L. Mundy, A. Zisserman, C. Coelho, A. Heller, and C. Rothwell, "Invariant descriptors for 3D object recognition and pose," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 13, no. 10, pp. 971991, 1991.
[17] J.W. Foster, G.K. Bennett, and P.M. Griffin, "Automated Visual Inspection: Quality Control Techniques for the Modern Manufacturing Environment," Proc. 1987 IIE Integrated Systems Conf., pp. 135140, Dec. 1987.
[18] M.T. Goodrich and R. Tamassia, "Dynamic Trees and Dynamic Point Location," SIAM J. Computing, vol. 28, no. 2, pp. 612636, 1999.
[19] P.M. Griffin, J.W. Foster, and M.H. Han, "Automated Dimension Verification by Point Pattern Matching," Proc. 1988 Int'l Industrial Eng. Conf., pp. 451455, 1988.
[20] R.M. Haralick, H. Joo, C.N. Lee, X. Zhuang, and M.B. Kim, “Pose Estimation from Corresponding Point Data,” IEEE Trans. Systems, Man, and Cybernetics, vol. 19, no. 6, p. 1426, 1989.
[21] P.J. Heffernan, "Generalized Approximate Algorithms for Point Set Congruence," Proc. Third Workshop Algorithms Data Structure, pp. 373384, 1993.
[22] P.J. Heffernan and S. Schirra, "Approximate Decision Algorithms for Point Set Congruence," Computing Geometric Theory Applications, vol. 4, pp. 137156, 1994.
[23] B.K.P. Horn, "ClosedForm Solution of Absolute Orientation Using Unit Quaternions," J. Optical Soc. of Am. A, vol. 4, no. 4, pp. 629642, Apr. 1987.
[24] B.K.P. Horn, H.M. Hilden, and S. Negahdaripour, "ClosedForm Solution of Absolute Orientation Using Orthonormal Matrices," J. Optical Soc. of Am. A, vol. 5, no. 7, pp. 1,1271,135, July 1988.
[25] D.P. Huttenlocher, K. Kedem, and J.M. Kleinberg, "On Dynamic Voronoi Diagrams and the Minimum Hausdorff Distance for Point Sets Under Euclidean Motion in the Plane," Proc. Eighth Ann. ACM Symp. Computer Geometry, pp. 110120, 1992.
[26] D.P. Huttenlocher, K. Kedem, and M. Sharir, "The Upper Envelope of Voronoi Surfaces and Its Applications," Discrete Computing Geometry, vol. 9, pp. 267291, 1993.
[27] K. Imai, S. Sumino, and H. Imai, "Minimax Geometric Fitting of Two Corresponding Sets of Points," Proc. Fifth Ann. ACM Symp. Computing Geometry, pp. 266275, 1989.
[28] D.J. Kahl, A. Rosenfeld, and A. Danker, "Some Experiments in Point Pattern Matching," IEEE Trans. Systems, Man, and Cybernetics, vol. 10, no. 2, pp. 105116, 1980.
[29] L.J. Kitchen, "Relaxation for PointPattern Matching: What It Really Computes," Proc. IEEE Conf. Visualization and Pattern Recognition, pp. 405407, 1985.
[30] N. Megiddo, "Applying Parallel Computation Algorithms in the Design of Serial Algorithms," J. ACM, vol. 30, pp. 852865, 1983.
[31] H. Ogawa, "Labeled Point Pattern Matching by Fuzzy Relaxation," Pattern Recognition, vol. 17, no. 5, pp. 569573, 1984.
[32] H. Ogawa, "Labeled Point Pattern Matching by Delaunay Triangulation and Maximal Cliques," Pattern Recognition, vol. 19, no. 1, pp. 3540, 1986.
[33] F.P. Preparata and M.I. Shamos, Computational Geometry. SpringerVerlag, 1985.
[34] S. Ranade and A. Rosenfeld, "Point Pattern Matching by Relaxation," Pattern Recognition, vol. 12, pp. 269275, 1980.
[35] W. Rucklidge, "Lower Bounds for the Complexity of the Hausdorff Distance," Proc. Fifth Canadian Conf. Computer Geometry, pp. 145150, 1993.
[36] G. Stockman, S. Kopstein, and S. Benett, "Matching Images to Models for Registration and Object Detection via Clustering," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 4, no. 3, pp. 229241, May 1982.
[37] S. Umeyama, "LeastSquares Estimation of Transformation Parameters Between Two Point Patterns," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 13, no. 4, pp. 376380, Apr. 1991.
[38] C. Wang, H. Sun, S. Yada, and A. Rosenfeld, "Some Experiments in Relaxation Image Matching Using Corner Features," Pattern Recognition, vol. 16, no. 2, pp.167182, 1983.