Polyline approach for approximating Hausdorff distance between planar free-form curves

CAD Computer Aided Design

Volumn 43, Issue 6, 2011, Pages 687-698

  Bai, Yan Bing ^a,b,c   Yong, Jun Hai ^a,b,c   Liu, Chang Yuan ^a,b,c   Liu, Xiao Ming ^a,b,c,d   Meng, Yu ^a,b,c  

^a TSINGHUA UNIVERSITY   (China)

^b BEIJING UNIVERSITY OF POSTS AND TELECOMMUNICATIONS   (China)

^c TSINGHUA NATIONAL LABORATORY FOR INFORMATION SCIENCE AND TECHNOLOGY   (China)

^d RESEARCH INSTITUTE OF CHEMICAL DEFENSE   (China)

Author keywords

Free form curves; Hausdorff distance; Polylines; Pruning; Voronoi diagram

Indexed keywords

FREE FORM CURVE; HAUSDORFF DISTANCE; POLYLINES; PRUNING; VORONOI DIAGRAMS;

ALGORITHMS; COMPUTATIONAL GEOMETRY; CURVE FITTING; DECISION TREES; GRAPHIC METHODS; TREES (MATHEMATICS);

SPLINES;

EID: 79953044483     PISSN: 00104485     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cad.2011.02.008     Document Type: Article

References (38)

1. Veltkamp RC. Shape matching: similarity measures and algorithms. In: Proceedings of international conference on shape modelling and applications. 2001. p. 18897.
2. S.G. Xu, Y.X. Zhang, and J.H. Yong A fast sweeping method for computing geodesics on triangular manifolds IEEE Transactions on Pattern Analysis and Machine Intelligence 32 2 2008 231 241
3. Alt H, Godau M. Measuring the resemblance of polygonal curves. In: Proceedings of the eighth annual symposium on computational geometry. 1992. p. 1029. (Pubitemid 23624482)
4. H. Alt, C. Knauer, and C. Wenk Comparison of distance measures for planar curves Algorithmica 38 1 2003 45 58 (Pubitemid 40877160)
5. R 3 Lecture Notes in Computer Science 4975 2008 191 204
6. Alt H, Guibas LJ. Discrete geometric shapes: matching, interpolation, and approximation: a survey. tech. Rep. B 96-11, EVL-1996-142. Berlin. Institute of Computer Science. Freie Universitàt.
7. D.P. Huttenlocher, G.A. Klanderman, and W.J. Rucklidge Comparing images using the Hausdorff distance IEEE Transactions on Pattern Analysis and Machine Intelligence 15 9 1993 850 863
8. H.J. Son, S.H. Kim, and J.S. Kim Text image matching without language model using a Hausdorff distance Information Processing & Management 44 3 2008 1189 1200
9. Tan HC, Zhang YJ. Computing eigenface from edge images for face recognition based on Hausdorff distance. In: Proceedings of the 4th international conference on image and graphics. 2007. p. 63944.
10. Y.H. Lee, and J.C. Shim Curvature based human face recognition using depth weighted Hausdorff distance Proceedings on International Conference of Image Processing 3 2004 1429 1432
11. C. Du, and G.D. Su Improved line segment Hausdorff distance for face recognition Journal of Optoelectronics Laser 16 1 2005 89 93 (Pubitemid 40409378)
12. Y.S. Gao, and M.K. Leung Face recognition using line edge map IEEE Transactions on Pattern Analysis and Machine Intelligence 24 6 2002 764 779 (Pubitemid 34669590)
13. Natarajan S, Wong Y. Hausdorff distance for iris recognition. In: IEEE 22nd international symposium on intelligent control. 2007. p. 6149. (Pubitemid 351424881)
14. Li F, Leung MK. Palmprint identification using Hausdorff distance. In: IEEE international workshop on biomedical circuits and systems. 2004. p. S3.3.5S3.3.8.
15. Dubuisson MP, Jain AK. A modified Hausdorff distance for object matching. In: Proceedings of 12th IAPR international conference on pattern recognition. 1994. p. 5668.
16. X.L. Yi, and O.I. Camps Line-based recognition using a multidimensional Hausdorff distance IEEE Transactions on Pattern Analysis and Machine Intelligence 21 9 1999 901 916
17. Agarwal PK, Sariel HP, Sharir M, Wang YS. Hausdorff distance under translation for points, disks and balls. In: Proceedings of 19th annual ACM symposium on computer geometry. 2003. p. 28291.
18. H. Alt, P. Braß, M. Godau, C. Knauer, and C. Wenk Computing the Hausdorff distance of geometric patterns and shapes Discrete & Computational Geometry 25 2003 65 76 (Pubitemid 36795469)
19. W.J. Rucklidge Lower bounds for the complexity of the graph of the Hausdorff distance as a function of transformation Discrete & Computational Geometry 16 1996 135 153 (Pubitemid 126317746)
20. H. Alt, B. Beherends, and J. Blmer Approximate matching of polygonal shapes Annals of Mathematics and Artificial Intelligence 13 1995 251 266
21. Karavelas MI. A robust and efficient implementation for the segment Voronoi diagram. In: International symposium on Voronoi diagrams in science and engineering. 2004. p. 5162.
22. Hangout JF. Computation of the Hausdorff distance between plane vector polylines. In: AUTO-CARTO 12. 1995. p. 110.
23. M.J. Atallah A linear time algorithm for computing the Hausdorff distance between convex polygons Information Processing Letters 17 4 1983 207 209
24. M. Tang, M. Lee, and Y.J. Kim Interactive Hausdorff distance computation for general polygonal models ACM Transactions on Graphics 28 3 2009 1 9
25. Barto M, Hanniel I, Elber G, Kim M-S. Precise Hausdorff distance computation between polygonal meshes. Computer Aided Geometric Design.
26. B. Eugene, and C. Carlos Calculating the Hausdorff distance between curves Information Processing Letters 64 1 1997 17 22
27. Jttler B. Bounding the Hausdorff distance of implicitly defined and/or parametric curves. In: Mathematical methods for curves and surfaces. 2000. p. 22332.
28. Scharf L. Computing the Hausdorff distance between sets of curves. Master's thesis. Institut fr Informatik. Freie Universitàt Berlin; January 2004.
29. H. Alt, and L. Scharf Computing the Hausdorff distance between curved objects International Journal of Computational Geometry and Applications 18 4 2008 307 320
30. Elber G. IRIT. http://www.cs.technion.ac.il/~irit/.
31. Y.-J. Kim, Y.-T. Oh, S.-H. Yoon, M.-S. Kim, and G. Elber Precise Hausdorff distance computation for planar freeform curves using biarcs and depth buffer The Visual Computer 26 68 2010 1007 1016
32. X.D. Chen, W.Y. Ma, G. Xu, and J.-C. Paul Computing the Hausdorff distance between two B-spline curves Computer Aided Design 42 12 2010 1197 1206
33. P.D. Casteljau Shape mathematics and CAD 1986 Kogan Page London
34. W. Boehm Inserting new knots into B-Spline curves Computer Aided Design 12 1980 199 201 (Pubitemid 11445726)
35. Y.J. Yang, C. Song, J.H. Yong, H. Zhang, J.C. Paul, J.G. Sun, and H.J. Gu Approximate computation of curves on B-Spline surfaces Computer-Aided Design 40 2 2008 223 234 (Pubitemid 351199660)
36. J. Henrikson Completeness and total boundedness of the Hausdorff metric MIT Undergraduate Journal of Mathemetics 1 1999 69 79
37. Guttman A. R-trees: a dynamic index structure for spatial searching. In: SIGMOD '84: proceedings of the 1984 ACM SIGMOD international conference on management of data. vol. 14. 1984. p. 4757. (Pubitemid 15469534)
38. Cgal, computational geometry algorithms library http://www.cgal.org