Efficient computation of the Hausdorff distance between polytopes by exterior random covering

Computational Optimization and Applications

Volumn 30, Issue 2, 2005, Pages 161-194

  Llanas, Bernardo ^a  

^a UNIVERSIDAD POLITÉCNICA DE MADRID   (Spain)

Author keywords

Hausdorff distance; Lipschitz random covering; Maximum distance; Polyhedra; Polytopes; Projection algorithms

Indexed keywords

ALGORITHMS; COMPUTATION THEORY; COMPUTER VISION; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; PATTERN RECOGNITION; PROBLEM SOLVING;

HAUSDORFF DISTANCE; LIPSCHITZ RANDOM COVERING; MAXIMUM DISTANCE; POLYTOPES; PROJECTION ALGORITHM;

RANDOM PROCESSES;

EID: 18644381128     PISSN: 09266003     EISSN: 15732894     Source Type: Journal    
DOI: 10.1007/s10589-005-4560-z     Document Type: Article

References (33)

1. H. Alt, B. Behrends, and J. BlÖmer. "Approximate matching of polygonal shapes." In Proc. 7th Annu. ACM Sympos. Comput. Geom., 1991, pp. 186-193.
2. H. Alt, B. Behrends, and J. Blömer. "Approximate matching of polygonal shapes." Ann. Math. Artif. Intell., vol. 13. pp. 251-266, 1995.
3. H. Alt, P. Brass, M. Godau, Ch. Knauer. and C. Wenk, "Computing the Hausdorff distance of geometric patterns and shapes," Technical Report B01-07. Freie Universität. Berlin. Fachbereich Mathematik und Informatik, Nov. 2001.
4. M.J. Atallah, C. Ribeiro, and S. Lifschitz. "A linear time algorithm for the computation of some distance functions between convex polygons." KAIRO Rech. Opérǎt., vol. 25. no. 4. pp. 413-424, 1991.
5. H.H. Bauschke and J.M. Borwein. "On projection algorithms for solving convex feasibility problems." SIAM Rev., vol. 38, pp. 367-426, 1996.
6. J.D. Boissonat and M. Yvinec. Algorithmic Geometry. Cambridge University Press: Cambridge. 1998.
7. H. Brezis, Analyse Fonctionelle, Masson, 1983.
8. L.P. Chew, M.T. Goodrich, D.P. Huttenlocher, K. Kedem, J.M. Kleinberg, and D. Kravets. "Geometric pattern matching under euclidean motion." Comput. Geom. Theory Appl., vol. 7. pp. 113-124, 1997.
9. L.P. Chew, D. Dor, A. Efrat. and K. Kedem, "Geometric pattern matching in d-dimensional space," Discrete Comput. Geom., vol. 10. pp. 257-274, 1999.
10. F.H. Clarke, Optimization and Nonsmooth Analysis, John Wiley and Sons: New York. 1983.
11. L. Devroye, "Progressive global random search of continuous functions." Math. Program., vol. 15, pp. 330-342, 1978.
12. Y.G. Etvushenko, Numerical Optimization Techniques. Springer: Berlin. 1985.
13. M. Godau, "On the complexity of measuring the similarity between geometric objects in higher dimensions," Dissertation. Freien Universität, Berlin. 1998.
14. M.T. Goodrich, J.S.B. Mitchell. and M.W. Orletsky. "Approximate geometric pattern matching under rigid motions" I.E.E.E. Trans. on Pattern Analysis and Machine Intelligence, vol. 21. pp. 371-379, 1999.
15. M. Hagedorn, "Pattern matching using similarity measures." Thesis. Universiteit Utretch. 2000.
16. R. Horst and H. Tuy. Global Optimization. Deterministic Approaches. Springer: Berlin, 1993.
17. D.P. Huttenlocher, K. Kedem. and M. Sharir. "The upper envelope of Voronoi surfaces and its applications." Discrete Comput. Geom., vol. 9. pp. 267-291, 1993.
18. K.U. Jahn. "Effective evaluation of Hausdorff distances for finite unions of hyperrectangles." In Validation Numerics. Theory and Applications. R. Albrecht, G. Alefeld, and H.J. Stetter (Eds.). Springer: Berlin. 1993, pp. 93-100.
19. S.R. Lay, Convex Sets and their Applications. John Wiley and Sons: New York. 1982.
20. R. Lenz. Group Theoretical Methods in Image Processing. Lecture Notes in Computer Science 413. Springer: Berlin. 1990.
21. M. Lin, "Efficient collision detection for animation and robotics," Ph.D. Thesis. University of California at Berkeley. 1993.
22. B. Llanas and F.J. Sainz, "Hausdorff matching and Lipschitz optimization." (submitted). 2001.
23. B. Llanas and C. Moreno, "Finding the projection on a polytope: An iterative method." Comput. Math. Appl., vol. 32. pp. 33-39, 1996.
24. N," Comput. Math. Appl., vol. 40. pp. 971-983, 2000.
25. B. Lianas, M. Fernández de Sevilla. and V. Feliú. "Minimum distance between the faces of two convex polyhedra. A sufficient condition." J. Global Optim. vol. 26. pp. 361-385, 2003.
26. R. Motwani and P. Raghavan. "Randomized Algorithms." in Algorithms and Theory of Computation Hand-book, M. J. Atallah (Ed.). CRC Pess. 1999.
27. K. Mulmuley, Computational Geometry. An Introduction Through Randomized Algorithms. Prentice Hall, 1994.
28. R.T. Rockafellar, Convex Analysis. Princeton University Press: Princeton. 1983.
29. S. Schirra, "Robustness and Precision Issues in Geometric Computation." in Handbook of Computational Geometry. J.-R. Sack and J. Urrutia (Eds.). Elsevier, 2000, pp. 597-632.
30. K. Sekitani and Y. Yamamoto, "A recursive algorithm for finding the minimum norm point in a polytope and a pair of closest points in two polytopes," Math. Program., vol, 61. pp. 233-249, 1993.
31. R.C. Veltkamp and M. Hagedoom. "State-of-the-art in shape matching," Technical Report UU-CS-1999-27, Utrecht University, the Netherlands, 1999.
32. Ph. Wolfe. "Finding the nearest point in a polytope," Math. Program., vol. 11, pp. 128-149, 1976.
33. A.A. Zhigljavsky. Theory of Global Random Search, Kluwer: Dordrecht, 1991.