Using state diagrams for hilbert curve mappings

Abstract

The Hilbert Curve describes a method of mapping between one and n dimensions. Such mappings are of interest in a number of application domains including image processing and, more recently, in the indexing of multi-dimensional data. Relatively little work, however, has been devoted to techniques for mapping in more that 2 dimensions. This paper presents a technique for constructing state diagrams to facilitate mappings and is a specialization of an incomplete generic process described by Bially. Although the storage requirements for state diagrams increase exponentially with the number of dimensions, they are useful in up to about 9 dimensions.

Keywords:

• Space-filling curves
• Hilbert Curve
• State diagrams
• Dimension reduction
• Multidimensional indexing

C.R. Categories:

• F.1.1
• E.2
• E.1
• H.3.1

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Notes

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