Thresholding Based Image Segmentation Aided by Kleene Algebra

Makoto ISHIKAWA; Naotake KAMIURA; Yutaka HATA

Thresholding Based Image Segmentation Aided by Kleene Algebra

Makoto ISHIKAWA, Naotake KAMIURA, Yutaka HATA

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This paper proposes a thresholding based segmentation method aided by Kleene Algebra. For a given image including some regions of interest (ROIs for short) with the coherent intensity level, assume that we can segment each ROI on applying thresholding technique. Three segmented states are then derived for every ROI: Shortage denoted by logic value 0, Correct denoted by 1 and Excess denoted by 2. The segmented states for every ROI in the image can be then expressed on a ternary logic system. Our goal is then set to find "Correct (1)" state for every ROI. First, unate function, which is a model of Kleene Algebra, based procedure is proposed. However, this method is not complete for some cases, that is, correctly segmented ratio is about 70% for three and four ROI segmentation. For the failed cases, Brzozowski operations, which are defined on De Morgan algebra, can accommodate to completely find all "Correct" states. Finally, we apply these procedures to segmentation problems of a human brain MR image and a foot CT image. As the result, we can find all "1" states for the ROIs, i. e. , we can correctly segment the ROIs.

Publication: IEICE TRANSACTIONS on Information Vol.E82-D No.5 pp.962-967

Publication Date: 1999/05/25

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Type of Manuscript: Special Section PAPER (Special Issue on Multiple-Valued Logic and Its Applications)

Category: Probability and Kleene Algebra

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Makoto ISHIKAWA, Naotake KAMIURA, Yutaka HATA, "Thresholding Based Image Segmentation Aided by Kleene Algebra" in IEICE TRANSACTIONS on Information, vol. E82-D, no. 5, pp. 962-967, May 1999, doi: .
Abstract: This paper proposes a thresholding based segmentation method aided by Kleene Algebra. For a given image including some regions of interest (ROIs for short) with the coherent intensity level, assume that we can segment each ROI on applying thresholding technique. Three segmented states are then derived for every ROI: Shortage denoted by logic value 0, Correct denoted by 1 and Excess denoted by 2. The segmented states for every ROI in the image can be then expressed on a ternary logic system. Our goal is then set to find "Correct (1)" state for every ROI. First, unate function, which is a model of Kleene Algebra, based procedure is proposed. However, this method is not complete for some cases, that is, correctly segmented ratio is about 70% for three and four ROI segmentation. For the failed cases, Brzozowski operations, which are defined on De Morgan algebra, can accommodate to completely find all "Correct" states. Finally, we apply these procedures to segmentation problems of a human brain MR image and a foot CT image. As the result, we can find all "1" states for the ROIs, i. e. , we can correctly segment the ROIs.
URL: https://global.ieice.org/en_transactions/information/10.1587/e82-d_5_962/_p

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@ARTICLE{e82-d_5_962,
author={Makoto ISHIKAWA, Naotake KAMIURA, Yutaka HATA, },
journal={IEICE TRANSACTIONS on Information},
title={Thresholding Based Image Segmentation Aided by Kleene Algebra},
year={1999},
volume={E82-D},
number={5},
pages={962-967},
abstract={This paper proposes a thresholding based segmentation method aided by Kleene Algebra. For a given image including some regions of interest (ROIs for short) with the coherent intensity level, assume that we can segment each ROI on applying thresholding technique. Three segmented states are then derived for every ROI: Shortage denoted by logic value 0, Correct denoted by 1 and Excess denoted by 2. The segmented states for every ROI in the image can be then expressed on a ternary logic system. Our goal is then set to find "Correct (1)" state for every ROI. First, unate function, which is a model of Kleene Algebra, based procedure is proposed. However, this method is not complete for some cases, that is, correctly segmented ratio is about 70% for three and four ROI segmentation. For the failed cases, Brzozowski operations, which are defined on De Morgan algebra, can accommodate to completely find all "Correct" states. Finally, we apply these procedures to segmentation problems of a human brain MR image and a foot CT image. As the result, we can find all "1" states for the ROIs, i. e. , we can correctly segment the ROIs.},
keywords={},
doi={},
ISSN={},
month={May},}

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TY - JOUR
TI - Thresholding Based Image Segmentation Aided by Kleene Algebra
T2 - IEICE TRANSACTIONS on Information
SP - 962
EP - 967
AU - Makoto ISHIKAWA
AU - Naotake KAMIURA
AU - Yutaka HATA
PY - 1999
DO -
JO - IEICE TRANSACTIONS on Information
SN -
VL - E82-D
IS - 5
JA - IEICE TRANSACTIONS on Information
Y1 - May 1999
AB - This paper proposes a thresholding based segmentation method aided by Kleene Algebra. For a given image including some regions of interest (ROIs for short) with the coherent intensity level, assume that we can segment each ROI on applying thresholding technique. Three segmented states are then derived for every ROI: Shortage denoted by logic value 0, Correct denoted by 1 and Excess denoted by 2. The segmented states for every ROI in the image can be then expressed on a ternary logic system. Our goal is then set to find "Correct (1)" state for every ROI. First, unate function, which is a model of Kleene Algebra, based procedure is proposed. However, this method is not complete for some cases, that is, correctly segmented ratio is about 70% for three and four ROI segmentation. For the failed cases, Brzozowski operations, which are defined on De Morgan algebra, can accommodate to completely find all "Correct" states. Finally, we apply these procedures to segmentation problems of a human brain MR image and a foot CT image. As the result, we can find all "1" states for the ROIs, i. e. , we can correctly segment the ROIs.
ER -