Reverse Distance Transformation and Skeletons Based upon the Euclidean Metric for <I>n</I>-Dimensional Digital Binary Pictures

Toyofumi SAITO; Jun-ichiro TORIWAKI

Reverse Distance Transformation and Skeletons Based upon the Euclidean Metric for n-Dimensional Digital Binary Pictures

Toyofumi SAITO, Jun-ichiro TORIWAKI

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In this paper, we present new algorithms to calculate the reverse distance transformation and to extract the skeleton based upon the Euclidean metric for an arbitrary binary picture. The presented algorithms are applicable to an arbitrary picture in all of n-dimensional spaces (n2) and a digitized picture sampled with the different sampling interval in each coordinate axis. The reconstruction algorithm presented in this paper is resolved to serial one-dimensional operations and efficiently executed by general purpose computer. The memory requirement is very small including only one picture array and single one-dimensional work space array for n-dimensional pictures. We introduce two different definitions of skeletons, both of them allow us to reconstruct the original binary picture exactly, and present algorithms to extract those skeltons from the result of the squared Euclidean distance transformation.

Publication: IEICE TRANSACTIONS on Information Vol.E77-D No.9 pp.1005-1016

Publication Date: 1994/09/25

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Type of Manuscript: Special Section PAPER (Special Issue on 3D Image Processing)

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Toyofumi SAITO, Jun-ichiro TORIWAKI, "Reverse Distance Transformation and Skeletons Based upon the Euclidean Metric for n-Dimensional Digital Binary Pictures" in IEICE TRANSACTIONS on Information, vol. E77-D, no. 9, pp. 1005-1016, September 1994, doi: .
Abstract: In this paper, we present new algorithms to calculate the reverse distance transformation and to extract the skeleton based upon the Euclidean metric for an arbitrary binary picture. The presented algorithms are applicable to an arbitrary picture in all of n-dimensional spaces (n2) and a digitized picture sampled with the different sampling interval in each coordinate axis. The reconstruction algorithm presented in this paper is resolved to serial one-dimensional operations and efficiently executed by general purpose computer. The memory requirement is very small including only one picture array and single one-dimensional work space array for n-dimensional pictures. We introduce two different definitions of skeletons, both of them allow us to reconstruct the original binary picture exactly, and present algorithms to extract those skeltons from the result of the squared Euclidean distance transformation.
URL: https://global.ieice.org/en_transactions/information/10.1587/e77-d_9_1005/_p

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@ARTICLE{e77-d_9_1005,
author={Toyofumi SAITO, Jun-ichiro TORIWAKI, },
journal={IEICE TRANSACTIONS on Information},
title={Reverse Distance Transformation and Skeletons Based upon the Euclidean Metric for n-Dimensional Digital Binary Pictures},
year={1994},
volume={E77-D},
number={9},
pages={1005-1016},
abstract={In this paper, we present new algorithms to calculate the reverse distance transformation and to extract the skeleton based upon the Euclidean metric for an arbitrary binary picture. The presented algorithms are applicable to an arbitrary picture in all of n-dimensional spaces (n2) and a digitized picture sampled with the different sampling interval in each coordinate axis. The reconstruction algorithm presented in this paper is resolved to serial one-dimensional operations and efficiently executed by general purpose computer. The memory requirement is very small including only one picture array and single one-dimensional work space array for n-dimensional pictures. We introduce two different definitions of skeletons, both of them allow us to reconstruct the original binary picture exactly, and present algorithms to extract those skeltons from the result of the squared Euclidean distance transformation.},
keywords={},
doi={},
ISSN={},
month={September},}

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TY - JOUR
TI - Reverse Distance Transformation and Skeletons Based upon the Euclidean Metric for n-Dimensional Digital Binary Pictures
T2 - IEICE TRANSACTIONS on Information
SP - 1005
EP - 1016
AU - Toyofumi SAITO
AU - Jun-ichiro TORIWAKI
PY - 1994
DO -
JO - IEICE TRANSACTIONS on Information
SN -
VL - E77-D
IS - 9
JA - IEICE TRANSACTIONS on Information
Y1 - September 1994
AB - In this paper, we present new algorithms to calculate the reverse distance transformation and to extract the skeleton based upon the Euclidean metric for an arbitrary binary picture. The presented algorithms are applicable to an arbitrary picture in all of n-dimensional spaces (n2) and a digitized picture sampled with the different sampling interval in each coordinate axis. The reconstruction algorithm presented in this paper is resolved to serial one-dimensional operations and efficiently executed by general purpose computer. The memory requirement is very small including only one picture array and single one-dimensional work space array for n-dimensional pictures. We introduce two different definitions of skeletons, both of them allow us to reconstruct the original binary picture exactly, and present algorithms to extract those skeltons from the result of the squared Euclidean distance transformation.
ER -