Combinatorial and experimental methods for approximate point pattern matching

Algorithmica (New York)

Volumn 38, Issue 1, 2003, Pages 59-90

  Gavrilov, Martin ^a   Indyk, Piotr ^a   Motwani, Rajeev ^a   Venkatasubramanian, Suresh ^b  

^a Stanford University   (United States)

^b AT&T Lab Research   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL GEOMETRY; COMPUTER VISION; IMAGE PROCESSING; OBJECT RECOGNITION; POLYNOMIALS;

IMAGE REGISTRATION; MOLECULAR MODELING; POINT COORDINATES; POINT PATTERN MATCHING;

PATTERN MATCHING;

EID: 21144432140     PISSN: 01784617     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00453-003-1043-4     Document Type: Article

References (42)

1. Agarwal, P., Aronov, B., Sharir, M., and Suri, S. Selecting distances in the plane. Algorithmica 9(5) (1993), 495-514.
2. Akutsu, T., Tamaki, H., and Tokuyama, T. Distribution of distances and triangles in a point set and algorithms for computing the largest common point set. In Proc. 13th Annuul ACM Symposium on Computational Geometry (1997), pp. 314-323.
3. Alt, H., and Guibas, L. Discrete geometric shapes: matching, interpolation, and approximation. A survey. In Handbook of Computational Geometry, J.-R. Sack and J. Urrutia, Eds. Elsevier, North-Holland, 1999, pp. 121-153.
4. Baird, H. S. Model-Based Image Matching Using Location. Distinguised Dissertation Series. MIT Press. Cambridge, MA, 1985.
5. Ballard, D. Generalizing the Hough Transform to detect arbitrary shapes. Pattern Recognition 13(2) (1981), 111-122.
6. Boxer, L. Point set pattern matching in 3-D. Pattern Recognition Letters 17(12) (1996), 1293-1297.
7. Braß, P. Exact point pattern matching and the number of congruent triangles in a three dimensional point set. In ESA 2000 - European Symposium on Algorithms (2000), M. Paterson, Ed. Vol. 1879 of Lecture Notes in Computer Science. Springer-Verlag, Berlin, pp. 112-119.
8. Cardoze, D., and Schulman, L. Pattern matching for spatial point sets. In Proc. 39th IEEE Symposium on the Foundations of Computer Science (November 1998), pp. 156-165.
9. Chew, L., Goodrich, M., Huttenlocher, D., Kedem, K., Kleinberg, J., and Kravets, D. Geometric pattern matching under euclidean motion. In Proc. Fifth Canadian Conference on Computational Geometry (1993). pp. 151-156.
10. Clarkson, K., Edelsbrunner, H., Guibas. L., Sharir, M., and Welzl, E. Combinatorial complexity bounds for arrangements of curves and spheres. Discrete &. Computational Geometry 5 (1990), 99-160.
11. 3 m) time. In Proc. 29th Annual ACM Symposium on Theory of Computing (1997), pp. 66-75.
12. 3 m) Time. In Proc. 10th Annual ACM-SIAM Symposium on Discrete Algorithms (1999), pp. 245-254.
13. Dobkin, D., and Lipton, R. Multidimensional search problems. SIAM Journal on Computing 5 (1976), 181-186.
14. Edelsbrunner, H., Valtr, P., and Welzl. E. Cutting dense point sets in half. Discrete & Compuational Geometry 17 (1997), 243-255.
15. Efrat, A. The dog in the field problem. Personal communication, 1998.
16. Efrat, A. The complexity of the union of (alpha, beta)-covered objects. In Proc. 15th ACM Symposium on Computational Geometry (1999), pp. 134-142.
17. Efrat, A., Indyk. P., and Venkatasubramanian. S. Pattern matching for sets of segments. In Proc. 12th ACM-SIAM Symposium on Discrete Algorithms (2001). pp. 295-304.
18. Erdos, P. On sets of distances of n points. American Mathematical Monthly 53 (1946). 248-250.
19. Erdos. P. On some applications of graph theory to geometry. Canadian Journal of Mathematics 19 (1967), 968-971.
20. Erdos, P., Makai. E., Pach, J., and Spencer. J. Gaps in difference sets, and the graph of nearly equal distances. Applied Geometry and Discrete Mathematics: The Victor Klee Festschrift (P. Gritzmann and B. Sturmfels, Eds.) 4 (1991). 265-273.
21. Eric, W., and Crimson. L. Object Recognition by Computer. The Rote of Geometric Constraints. MIT Press, Cambridge, MA. 1990.
22. Erickson,J. Dense point sels have sparse delaunay triangulations. In Proc. 13th ACM-SIAM Symposium on Discrete Algorithms (2002), pp. 96-105.
23. Gavrilov, M., Indyk, P., Motwani, R., and Venkatasubramanian, S. Geometric pattern matching: a performance study. In Proc. 15th ACM Symposium on Computational Geometry (1999), pp. 79-85.
24. Goodrich, M., Mitchell, J., and Orletsky, M. Practical methods for approximate geometric pattern matching under rigid motions. In Proc. 10th Annual ACM Symposium on Computational Geometry (1994), pp. 103-113.
25. Hagedoorn, M., and Veltkamp, R. C. Reliable and efficient pattern matching using an affine invariant metric. International Journal of Computer Vision 31(2/3) (1999), 203-225.
26. Heffernan, P. J., and Schirra, S. Approximate decision algorithms for point set congruence. Computational Geometry: Theory and Applications 4(3) (1994), 137-156.
27. Holm, L., and Sander, C. Mapping the protein universe. Science 273(5275) (August 1996), 595-602.
28. Huttenlocher, D. P., Kedem, K., and Sharir, M. The upper envelope of Voronoi surfaces and its applications. Discrete & Computational Geometry 9 (1993), 267-291.
29. Huttenlocher, D. P., and Rucklidge, W. T. A multi-resolution technique for comparing images using the hausdorff distance. In Proc. IEEE Conference on Computer Vision and Pattern Recognition (June 1993), pp. 705-706.
30. Indyk, P. Faster algorithms for string matching problems: matching the convolution bound. In Proc. 38th IEEE Symposium on Foundations of Computer Science (1998), pp. 166-173.
31. Indyk, P., Motwani, R., and Venkatasubramanian, S. Geometric matching under noise: combinatorial bounds and algorithms. In Proc. 10th Annual SIAM-ACM Symposium on Discrete Algorithms (1999), pp. 457-465.
32. Indyk, P., and Venkatasubramanian, S. Approximate congruence in near-linear time. International Journal of Computational Geometry and Applications (to appear).
33. Mount, D., Netanyahu, N., and LeMoigne, J. Improved algorithms for robust point pattern matching and applications to image registration. In Proc. 14th ACM Symposium on Computational Geometry (June 1998), pp. 155-164.
34. Preparata, F. P., and Shamos, M. I. Computational Geometry: An Introduction. Springer-Verlag, New York., 1985.
35. Rosenfeld, A. Image analysis and computer vision: 1998. Computer Vision and Image Understanding 74(1) (1998), 36-95.
36. Shoup, V. NTL: a library for doing number theory, http://www.cs.wisc.edu/ shoup/ntl/.
37. Székely, L. Crossing numbers and hard Erdos problems in discrete geometry. Combinatorics, Probability and Computing 6(3) (1997), 353-358.
38. Szemeredi, E., and Trotter, W. T. Extremal problems in discrete geometry. Combinatorica 3 (1983), 381-392.
39. Valtr, P. Planar point sets with bounded ratios of distances. Ph.D. thesis, Fachbereich Mathematik, Freie Universität Berlin, Berlin, 1994.
40. Valtr, P. Lines, line-point incidences and crossing families in dense sets. Combinatorica 16 (1996), 269-294.
41. Verbarg, K. Approximate center points in dense sets. In Abstracts 13th European Workshop on Computational Geometry (1997), pp. 55-56.
42. Zhou, Y., and Suri, S. Analysis of a bounding box heuristic for object intersection. Journal of the Association for Computing Machinery 46 (1999), 833-857.