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

Mohamed Mokbel, Walid G. Aref

Research output: Contribution to conferencePaper

15 Citations (Scopus)

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 in the area of multimedia databases is illustrated with a discussion of the problems that arise.

Original languageEnglish
Pages512-519
Number of pages8
Publication statusPublished - 1 Dec 2001
Externally publishedYes
EventProceedings of the 2001 ACM CIKM: 10th International Conference on Information and Knowledge Management - Atlanta, GA, United States
Duration: 5 Nov 200110 Nov 2001

Other

OtherProceedings of the 2001 ACM CIKM: 10th International Conference on Information and Knowledge Management
CountryUnited States
CityAtlanta, GA
Period5/11/0110/11/01

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ASJC Scopus subject areas

  • Decision Sciences(all)
  • Business, Management and Accounting(all)

Cite this

Mokbel, M., & Aref, W. G. (2001). Irregularity in multi-dimensional space-filling curves with applications in multimedia databases. 512-519. Paper presented at Proceedings of the 2001 ACM CIKM: 10th International Conference on Information and Knowledge Management, Atlanta, GA, United States.