Abstract
We give approximation algorithms for matching two sets of line segments in constant dimension. We consider several versions of the problem: Hausdorff distance, bottleneck distance and largest common point set. We study these similarity measures under several sets of transformations: translations, rotations about a fixed point and rigid motions. As opposed to previous theoretical work on this problem, we match segments individually, in other words we regard our two input sets as sets of segments rather than unions of segments.
This work was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2017R1D1A1B04036529).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Ahn, H., Cheong, O., Park, C., Shin, C., Vigneron, A.: Maximizing the overlap of two planar convex sets under rigid motions. Comput. Geom. 37(1), 3–15 (2007)
Alt, H., Behrends, B., Blömer, J.: Approximate matching of polygonal shapes. Ann. Math. Artif. Intell. 13(3), 251–265 (1995)
Alt, H., Guibas, L.J.: Discrete geometric shapes: matching, interpolation, and approximation. In: Sack, J.R., Urrutia, J. (eds.) Handbook of Computational Geometry, pp. 121–153. B.V. North-Holland, Amsterdam (2000). Chapter 3
Alt, H., Mehlhorn, K., Wagener, H., Welzl, E.: Congruence, similarity, and symmetries of geometric objects. Discrete Comput. Geom. 3(3), 237–256 (1988)
Arya, S., Mount, D.M., Netanyahu, N.S., Silverman, R., Wu, A.Y.: An optimal algorithm for approximate nearest neighbor searching fixed dimensions. J. ACM 45(6), 891–923 (1998)
Cabello, S., de Berg, M., Giannopoulos, P., Knauer, C., van Oostrum, R., Veltkamp, R.C.: Maximizing the area of overlap of two unions of disks under rigid motion. Int. J. Comput. Geom. Appl. 19(6), 533–556 (2009)
Chen, H.H., Huang, T.S.: Matching 3-D line segments with applications to multiple-object motion estimation. IEEE Trans. Pattern Anal. Mach. Intell. 12(10), 1002–1008 (1990)
Chew, L., Goodrich, M.T., Huttenlocher, D.P., Kedem, K., Kleinberg, J.M., Kravets, D.: Geometric pattern matching under Euclidean motion. Comput. Geom. 7(1), 113–124 (1997)
Efrat, A., Itai, A., Katz, M.J.: Geometry helps in bottleneck matching and related problems. Algorithmica 31(1), 1–28 (2001)
Gao, M., Skolnick, J.: iAlign: a method for the structural comparison of protein-protein interfaces. Bioinformatics 26(18), 2259–2265 (2010)
Har-Peled, S., Roy, S.: Approximating the maximum overlap of polygons under translation. Algorithmica 78(1), 147–165 (2017)
Heffernan, P.J., Schirra, S.: Approximate decision algorithms for point set congruence. Comput. Geom. 4(3), 137–156 (1994)
Medioni, G.G., Nevatia, R.: Matching images using linear features. IEEE Trans. Pattern Anal. Mach. Intell. 6(6), 675–685 (1984)
Vigneron, A.: Geometric optimization and sums of algebraic functions. ACM Trans. Algorithms 10(1), 4:1–4:20 (2014)
Yon, J., Cheng, S., Cheong, O., Vigneron, A.: Finding largest common point sets. Int. J. Comput. Geom. Appl. 27(3), 177–186 (2017)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Yang, H., Vigneron, A. (2019). Matching Sets of Line Segments. In: Das, G., Mandal, P., Mukhopadhyaya, K., Nakano, Si. (eds) WALCOM: Algorithms and Computation. WALCOM 2019. Lecture Notes in Computer Science(), vol 11355. Springer, Cham. https://doi.org/10.1007/978-3-030-10564-8_21
Download citation
DOI: https://doi.org/10.1007/978-3-030-10564-8_21
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-10563-1
Online ISBN: 978-3-030-10564-8
eBook Packages: Computer ScienceComputer Science (R0)