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

  • Authors:

  • Mohamed F. Mokbel;Walid G. Aref

  • Affiliations:

  • Purdue University, West Lafayette, IN;Purdue University, West Lafayette, IN

  • Venue:
  • Proceedings of the tenth international conference on Information and knowledge management
  • Year:
  • 2001

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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.