Generalized Peano Scans for Arbitrarily-Sized Arrays

Takeshi AGUI; Takanori NAGAE; Masayuki NAKAJIMA

Generalized Peano Scans for Arbitrarily-Sized Arrays

Takeshi AGUI, Takanori NAGAE, Masayuki NAKAJIMA

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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.

Publication: IEICE TRANSACTIONS on Information Vol.E74-D No.5 pp.1337-1342

Publication Date: 1991/05/25

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Type of Manuscript: PAPER

Category: Image Processing, Computer Graphics and Pattern Recognition

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Takeshi AGUI
Takanori NAGAE
Masayuki NAKAJIMA

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Takeshi AGUI, Takanori NAGAE, Masayuki NAKAJIMA, "Generalized Peano Scans for Arbitrarily-Sized Arrays" in IEICE TRANSACTIONS on Information, vol. E74-D, no. 5, pp. 1337-1342, May 1991, doi: .
Abstract: 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.
URL: https://global.ieice.org/en_transactions/information/10.1587/e74-d_5_1337/_p

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@ARTICLE{e74-d_5_1337,
author={Takeshi AGUI, Takanori NAGAE, Masayuki NAKAJIMA, },
journal={IEICE TRANSACTIONS on Information},
title={Generalized Peano Scans for Arbitrarily-Sized Arrays},
year={1991},
volume={E74-D},
number={5},
pages={1337-1342},
abstract={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.},
keywords={},
doi={},
ISSN={},
month={May},}

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TY - JOUR
TI - Generalized Peano Scans for Arbitrarily-Sized Arrays
T2 - IEICE TRANSACTIONS on Information
SP - 1337
EP - 1342
AU - Takeshi AGUI
AU - Takanori NAGAE
AU - Masayuki NAKAJIMA
PY - 1991
DO -
JO - IEICE TRANSACTIONS on Information
SN -
VL - E74-D
IS - 5
JA - IEICE TRANSACTIONS on Information
Y1 - May 1991
AB - 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.
ER -