Hausdorff distance under translation for points and balls

Proceedings of the Annual Symposium on Computational Geometry

Volumn , Issue , 2003, Pages 282-291

  Agarwal, Pankaj K ^a   Har Peled, Sariel ^b   Sharir, Micha ^c,d   Wang, Yusu ^a  

^a Duke University   (United States)

^b University of Illinois at Urbana Champaign   (United States)

^c TEL AVIV UNIVERSITY   (Israel)

^d NEW YORK UNIVERSITY   (United States)

Author keywords

1 median; Hausdorff distance; Shape matching; Voronoi diagrams

Indexed keywords

ALGORITHMS; COMPUTER AIDED DESIGN; COMPUTER GRAPHICS; COMPUTER VISION; DATA STRUCTURES; PATTERN RECOGNITION; SET THEORY;

SHAPE MATCHING;

PROBLEM SOLVING;

EID: 0037700435     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/777833.777835     Document Type: Conference Paper

References (24)

1. P. K. Agarwal, B. Aronov, S. Har-Peled, and M. Sharir, Approximation and exact algorithms for minimum-width annuli and shells, Discrete Comput. Geom., 24 (2000), 687-705.
2. P. K. Agarwal and J. Matousek, Ray shooting and parametric search, SIAM J. Comput., 22 (1993), 540-570.
3. P. K. Agarwal, M. Sharir, and S. Toledo, Applications of parametric searching in geometric optimization, J. Algorithms, 17 (1994), 292-318.
4. O. Aichholzer, H. Alt, and G. Rote, Matching shapes with a reference point, Intl. J. Comput. Geom. and Appl., 7 (1997), 349-363.
5. H. Alt, B. Behrends, and J. Blömer, Approximate matching of polygonal shapes, Ann. Math. Artif. Intell., 13 (1995), 251-266.
6. H. Alt and L. J. Guibas, Discrete geometric shapes: Matching, interpolation, and approximation, in: Handbook of Computational Geometry (J.-R. Sack and J. Urrutia, eds.), Elsevier Science Publishers E.V. North-Holland, Amsterdam, 2000, pp. 121-153.
7. N. Amenta and R. Kolluri, The medial axis of a union of balls, Comput. Geom: Theory Appl., 20 (2001), 25-37.
8. A. Amir, E. Porat, and M. Lewenstein, Approximate subset matching with Don't Cares, Proc. 12th ACM-SIAM Symp. Discrete Algorithms, 2001, pp. 305-306.
9. S. Arya and T. Malamatos, Linear-size approximate voronoi diagrams, Proc. 13th ACM-SIAM Symp. on Discrete Algorithms, 2002, pp. 147-155.
10. M. J. Atallah, A linear time algorithm for the Hausdorff distance between convex polygons, Inform. Process. Lett., 17 (1983), 207-209.
11. L. P. Chew, D. Dor, A. Efrat, and K. Kedem, Geometric pattern matching in d-dimensional space, Discrete Comput. Geom., 21 (1999), 257-274.
12. L. P. Chew, M. T. Goodrich, D. P. Huttenlocher, K. Kedem, J. M. Kleinberg, and D. Dravets, Geometric pattern matching under euclidean motion, Comput. Geom: Theory Appl., 7 (1997), 113-124.
13. J. R. Driscoll, N. Sarnak, D. D. Sleator, and R. E. Tarjan, Making data structures persistent, J. Comput. Syst. Sci., 38 (1989), 86-124.
14. M. T. Goodrich, J. S. Mitchell, and M. W. Orletsky, Practical methods for approximate geometric pattern matching under rigid motion, Proc. 10th Annu. ACM Sympos. Comput. Geom., 1994, pp. 103-112.
15. I. Halperin, B. Ma, H. Wolfson, and R. Nussinov, Principles of docking: An overview of search algorithms and a guide to scoring functions, Proteins: Structure, Function, and Genetics, 47 (2002), 409-443.
16. S. Har-Peled, A replacement for voronoi diagrams of near linear size, Proc. 42nd Annu. IEEE Sympos. Found. Comput. Sci., 2001, pp. 94-103.
17. 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. 8th Annu. ACM Sympos. Comput. Geom., 1992, pp. 110-120.
18. D. P. Huttenlocher, K. Kedem, and M. Sharir, The upper envelope of Voronoi surfaces and its applications, Discrete Comput. Geom., 9 (1993), 267-291.
19. P. Indyk, R. Motwani, and S. Venkatasubramanian, Geometric matching under noise: Combinatorial bounds and algorithms, Proc. 10th ACM-SIAM Sympos. Discrete Algorithms, 1999, pp. 457-465.
20. K. Kedem, R. Livne, J. Pach, and M. Sharir, On the union of Jordan regions and collision-free translational motion amidst polygonal obstacles, Discrete Comput. Geom., 1 (1986), 59-71.
21. N. Megiddo, Applying parallel computation algorithms in the design of serial algorithms, J. ACM, 30 (1983), 852-865.
22. H. Samet, Spatial Data Structures: Quadtrees, Octrees, and Other Hierarchical Methods, Addison-Wesley, Reading, MA, 1989.
23. S. Seeger and X. Laboureux, Feature extraction and registration: An overview, Principles of 3D Image Analysis and Synthesis, (2002), 153-166.
24. M. Sharir and P. K. Agarwal, Davenport-Schinzel Sequences and Their Geometric Applications, Cambridge University Press, New York, 1995.