Abstract
The problem of matching sets of points or sets of horizontal line segments in plane under translations is considered. For finding the exact occurrences of a point set of size m within another point set of size n we give an algorithm with running time O(mn), and for finding partial occurrences an algorithm with running time O(mnlogm). To find the largest overlap between two line segment patterns we develop an algorithm with running time O(mnlog(mn)). All algorithms are based on a simple sweepline traversal of one of the patterns in the lexicographic order. The motivation for the problems studied comes from music retrieval and analysis.
A work supported by the Academy of Finland.
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
Preview
Unable to display preview. Download preview PDF.
References
H. Alt and L. Guibas. Discrete geometric shapes: Matching, interpolation, and approximation. In J.-R. Sack and J. Urrutia, editors, Handbook of Computational Geometry, pages 121–153. Elsevier Science Publishers B.V. North-Holland, Amsterdam, 1999.
H. Alt, K. Mehlhorn, H. Wagener, and E. Welzl. Congruence, similarity and symmetries of geometric objects. Discrete Comput. Geom., 3:237–256, 1988.
M. D. Atkinson. An optimal algorithm for geometric congruence. J. Algorithms, 8:159–172, 1997.
J. L. Bentley and T. A. Ottmann. Algorithms for reporting and counting geometric intersections. IEEE Transactions on Computers, C-28:643–647, September 1979.
L. P. Chew and K. Kedem. Improvements on geometric pattern matching problems. In Proceedings of the Scandinavian Workshop Algomthm Theory (SWAT), pages 318–325, 1992.
M. Clausen, R. Engelbrecht, D. Meyer, and J. Schmitz. Proms: A web-based tool for searching in polyphonic music. In Proceedings of the International Symposium on Music Information Retrieval (ISMIR’2000), 2000.
R. Cole and R. Hariharan. Verifying candidate matches in sparse and wildcard matching. In Proceedings of the 34th ACM Symposium on Theory of Computing, pages 592–601. ACM Press, 2002.
M. J. Dovey. A technique for “regular expression” style searching in polyphonic music. In the 2nd Annual International Symposium on Music Information Retrieval (ISMIR’2001), pages 179–185, 2001.
A. Efrat and A. Itai. Improvements on bottleneck matching and related problems using geometry. In Proceedings of the twelfth annual symposium on Computational geometry, pages 301–310. ACM Press, 1996.
A. Ghias, J. Logan, D. Chamberlin, and B. C. Smith. Query by humming-musical information retrieval in an audio database. In ACM Multimedia 95 Proceedings, pages 231–236, 1995. Electronic Proceedings: http://www.cs.cornell.edu/Info/Faculty/bsmith/queryby-humming.
J. Holub, C. S. Iliopoulos, and L. Mouchard. Distributed string matching using finite automata. Journal of Automata, Languages and Combinatorics, 6(2):191–204, 2001.
D. Huttenlocher and S. Ullman. Recognizing solid objects by alignment with an image. Intern. J. Computer Vision, 5:195–212, 1990.
K. Lemström. String Matching Techniques for Music Retrieval. PhD thesis, University of Helsinki, Department of Computer Science, 2000. Report A-2000-4.
K. Lemström and S. Perttu. SEMEX-an efficient music retrieval prototype. In Proceedings of the International Symposium on Music Information Retrieval (ISMIR’2000), 2000.
K. Lemström and J. Tarhio. Detecting monophonic patterns within polyphonic sources. In ontent-Based Multimedia Information Access Conference Proceedings (RIAO’2000), pages 1261–1279, 2000.
K. Lemström and E. Ukkonen. Including interval encoding into edit distance based music comparison and retrieval. In Proceedings of the AISB’2000 Symposium on Creative & Cultural Aspects and Applications of AI & Cognitive Science, pages 53–60, 2000.
V. Mäkinen, G. Navarro, and E. Ukkonen. Algorithms for transposition invariant string matching. Technical Report TR/DCC-2002-5, Department of Computer Science, University of Chile, 2002.
R. J. McNab, L. A. Smith, D. Bainbridge, and I. H. Witten. The New Zealand digital library MELody in DEX. D-Lib Magazine, 1997. http://www.nzdl.org/musiclib.
D. Meredith, G. A. Wiggins, and K. Lemström. Pattern induction and matching in polyphonic music and other multi-dimensional data. In the 5th World Multi-Conference on Systemics, Cybernetics and Informatics (SCI’2001), volume X, pages 61–66, 2001.
M. Mongeau and D. Sankoff. Comparison of musical sequences. Computers and the Humanities, 24:161–175, 1990.
G. A. Wiggins, K. Lemström, and D. Meredith. SIA(M)-a family of efficient algorithms for translation invariant pattern matching in multidimensional datasets. Manuscript (submitted), September 2002.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Ukkonen, E., Lemström, K., Mäkinen, V. (2003). Sweepline the Music. In: Klein, R., Six, HW., Wegner, L. (eds) Computer Science in Perspective. Lecture Notes in Computer Science, vol 2598. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36477-3_25
Download citation
DOI: https://doi.org/10.1007/3-540-36477-3_25
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-00579-7
Online ISBN: 978-3-540-36477-1
eBook Packages: Springer Book Archive