Generalized Peano Scans for Arbitrarily-Sized Arrays

Takeshi AGUI  Takanori NAGAE  Masayuki NAKAJIMA  

IEICE TRANSACTIONS on Information and Systems   Vol.E74-D   No.5   pp.1337-1342
Publication Date: 1991/05/25
Online ISSN: 
Print ISSN: 0916-8532
Type of Manuscript: PAPER
Category: Image Processing, Computer Graphics and Pattern Recognition

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The mappings from multidimension to one-dimension, or the inverse mappings, are theoretically discussed as space-filling curves, i.e., Peano curves. The Peano scan is an application of a Peano curve to the scanning of images, and it is used for analyzing, clustering, or compressing an image, and for limiting the number of the colors used in an image. The horizontal and vertical sizes of the scanned array, however, must be a power of two. To avoid such a case, we generalize the Peano scan for scanning an arbitrarily-sized array, whose horizontal and vertical sizes are possible to be different. First we propose a binary scan which is made of binarily recursive divisions of an image. As the Peano scan is characterized by the statistical property of Brownian motion, further we describe that binary scan can be also optimized to have such statistical property.