Article

Irregularity in multi-dimensional space-filling curves with applications in multimedia databases

Authors:

Mohamed F. Mokbel,

Walid G. ArefAuthors Info & Claims

CIKM '01: Proceedings of the tenth international conference on Information and knowledge management

Pages 512 - 519

https://doi.org/10.1145/502585.502671

Published: 05 October 2001 Publication History

Abstract

A space-filling curve is a way of mapping the multi-dimensional space into the one-dimensional space. It acts like a thread that passes through every cell element (or pixel) in the N-dimensional space so that every cell is visited at least once. Thus, a space-filling curve imposes a linear order of the cells in the N-dimensional space. There are numerous kinds of space-filling curves. The difference between such curves is in their way of mapping to the one-dimensional space. Selecting the appropriate curve for any application requires a brief knowledge of the mapping scheme provided by each space-filling curve. Irregularity is proposed as a quantitative measure of the quality of the mapping of the space-filling curve. Closed formulas are developed to compute the irregularity for any general dimension D with N points in each dimension for different space-filling curves.A comparative study of different space-filling curves with respect to irregularity is conducted and results are presented and discussed. The applicability of this research is the area of multimedia databases is illustrated with a discussion of the problems that arise.

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cover image ACM Conferences

CIKM '01: Proceedings of the tenth international conference on Information and knowledge management

October 2001

616 pages

ISBN:1581134363

DOI:10.1145/502585

Editors:
Henrique Paques
Georgia Institute of Technology
,
Ling Liu
Georgia Institute of Technology
,
David Grossman
Illinois Institute of Technology
,
General Chair:
Calton Pu
Georgia Institute of Technology

Copyright © 2001 ACM.

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Published: 05 October 2001

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Cited By

Li JWang ZCong GLong CKiah HCui B(2023)Towards Designing and Learning Piecewise Space-Filling CurvesProceedings of the VLDB Endowment10.14778/3598581.359858916:9(2158-2171)Online publication date: 10-Jul-2023
https://dl.acm.org/doi/10.14778/3598581.3598589
El-Mahgary SVirtanen JHyyppä H(2020)A Simple Semantic-Based Data Storage Layout for Querying Point CloudsISPRS International Journal of Geo-Information10.3390/ijgi90200729:2(72)Online publication date: 22-Jan-2020
https://doi.org/10.3390/ijgi9020072
Nishimura SYokota HChirkova RYang JSuciu D(2017)QUILTSProceedings of the 2017 ACM International Conference on Management of Data10.1145/3035918.3035934(1525-1537)Online publication date: 9-May-2017
https://dl.acm.org/doi/10.1145/3035918.3035934
Li TLin YShen H(2016)A locality-aware similar information searching schemeInternational Journal on Digital Libraries10.1007/s00799-014-0128-917:2(79-93)Online publication date: 1-Jun-2016
https://dl.acm.org/doi/10.1007/s00799-014-0128-9
Kang J(2016)Space-Filling CurvesEncyclopedia of GIS10.1007/978-3-319-23519-6_1233-2(1-6)Online publication date: 31-May-2016
https://doi.org/10.1007/978-3-319-23519-6_1233-2
Mokbel MAref W(2009)Space-Filling Curves for Query ProcessingEncyclopedia of Database Systems10.1007/978-0-387-39940-9_350(2675-2680)Online publication date: 2009
https://doi.org/10.1007/978-0-387-39940-9_350
Zhang JKamata S(2008)An N-Dimensional Pseudo-Hilbert Scan for Arbitrarily-Sized HypercuboidsIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences10.1093/ietfec/e91-a.3.846E91-A:3(846-858)Online publication date: 1-Mar-2008
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Mokbel MAref W(2008)Space-Filling CurvesEncyclopedia of GIS10.1007/978-0-387-35973-1_1233(1068-1072)Online publication date: 2008
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Castro JGeorgiopoulos MDemara RGonzalez A(2005)Data-partitioning using the Hilbert space filling curvesNeural Networks10.1016/j.neunet.2005.01.00718:7(967-984)Online publication date: 1-Sep-2005
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Li CFeng Y(2005)Algorithm for analyzing n-dimensional hilbert curveProceedings of the 6th international conference on Advances in Web-Age Information Management10.1007/11563952_60(657-662)Online publication date: 11-Oct-2005
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