Thresholding Based Image Segmentation Aided by Kleene Algebra

摘要

This paper proposes a thresholding based seg- mentation method aided by Kleene Algebra. For a given image including some regions of interest (ROIs for short) with the coher- ent intensity level, assume that we can segment each ROI on ap- plying 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 com- Plete 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. Fi- nally, 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.