Image segmentation based on Kleene algebra

This paper proposes a segmentation method based on Kleene Algebra. For an input image including some regions of interests (ROIs for short), consider three segmented states: Shortage, Correct, Excess for the target region on applying segmentation method based on standard intensity thresholding. For the target image, we do thresholding to each of ROIs, then to derive all “Correct” for ROIs, unate function (one model of Kleene Algebra) based approach proposes to find all “Correct” states. However, the 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, it is proved that Brzozowski operations are provided to completely find all “Correct” states. The experimental results on a human brain MR image and a foot CT image show that our method can correctly segment the ROI