A Locally Adaptive Peano Scanning Algorithm

This paper describes an algorithm which builds a ``Peano scanning,'' i.e., the reciprocal mapping, from [0, 1]n to [0, 1], of the well-known ``Peano curve.'' This Peano scanning is applied to a set of points in [0, 1]n and gives a one-dimensional image of it. Several applications of this technique have already been developed and are presented in this paper.

[1]  Arthur R. Butz,et al.  Convergence with Hilbert's Space Filling Curve , 1969, J. Comput. Syst. Sci..

[2]  Philippe Flajolet,et al.  A Note on Gray Code and Odd-Even Merge , 1980, SIAM J. Comput..

[3]  Arthur R. Butz,et al.  Space Filling Curves and Mathematical Programming , 1968, Inf. Control..

[4]  John Hawkes,et al.  Hausdorff Measure, Entropy, and the Independence of Small Sets , 1974 .

[5]  R. Fisher.  THE USE OF MULTIPLE MEASUREMENTS IN TAXONOMIC PROBLEMS , 1936 .

[6]  D. Hilbert.  Ueber die stetige Abbildung einer Line auf ein Flächenstück , 1891 .

[7]  Arthur R. Butz,et al.  Alternative Algorithm for Hilbert's Space-Filling Curve , 1971, IEEE Transactions on Computers.

[8]  Theodore Bially,et al.  Space-filling curves: Their generation and their application to bandwidth reduction , 1969, IEEE Trans. Inf. Theory.

[9]  J. Koenderink,et al.  New type of raster scan preserves the topology of the image , 1979, Proceedings of the IEEE.

[10]  G. H. H.,et al.  The Theory of Functions of a Real Variable and the Theory of Fourier's Series , 1907, Nature.

[11]  D. Hilbert.  Über die stetige Abbildung einer Linie auf ein Flächenstück , 1935 .

[12]  G. Peano.  Sur une courbe, qui remplit toute une aire plane , 1890 .

[13]  F. K. Bechtel,et al.  Mapping Multidimensional Space to One Dimension for Computer Output Display , 1968, IEEE Transactions on Computers.

[14]  Laveen N. Kanal,et al.  Classification of binary random patterns , 1965, IEEE Trans. Inf. Theory.