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A new algorithm for N-dimensional Hilbert scanning.

S I Kamata1, R O Eason, Y Bandou

  • 1Dept. of Intelligent Syst., Kyushu Univ., Fukuoka. kamata@is.kyushu-u.ac.jp

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|February 13, 2008
PubMed
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A new Hilbert scanning algorithm simplifies N-dimensional mapping. This fast, nonrecursive method using lookup tables is easier to implement in hardware than existing complex algorithms.

Area of Science:

  • Computer Science
  • Data Structures
  • Algorithms

Background:

  • The Hilbert curve is a space-filling curve used for mapping N-dimensional data to 1D space, preserving neighborhood properties.
  • Existing algorithms like Butz and Quinqueton for N-dimensional Hilbert scanning are computationally complex and difficult for hardware implementation.

Purpose of the Study:

  • To introduce a novel, simplified algorithm for N-dimensional Hilbert scanning.
  • To overcome the computational complexity and hardware implementation challenges of existing Hilbert curve algorithms.

Main Methods:

  • A new, nonrecursive algorithm for N-dimensional Hilbert scanning is proposed.
  • The algorithm utilizes lookup tables for efficient computation.

Main Results:

Related Experiment Videos

  • The proposed algorithm offers fast computation speeds.
  • It significantly simplifies hardware implementation compared to previous methods.

Conclusions:

  • The new Hilbert scanning algorithm provides a more efficient and practical solution for N-dimensional data mapping.
  • Its simplicity and speed make it suitable for various applications requiring Hilbert curve transformations.