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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

- Publicized

- Online ISSN

- DOI

- 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 -