• Journal of Korea Multimedia Society
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• v.22 no.1
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• pp.18-26
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• 2019

In this paper we propose how to detect circular objects in the gray scale image and segment them using the discrete Morse theory, which makes it possible to analyze the topology of a digital image, when it is transformed into the data structure of some combinatorial complex. It is possible to get meaningful information about how many connected components and topologically circular shapes are in the image by computing the persistent homology of the filtration using the Morse complex. We obtain a Morse complex by modeling an image as a cubical cellular complex. Each cell in the Morse complex is the critical point at which the topological structure changes in the filtration consisting of the level sets of the image. In this paper, we implement the proposed algorithm of segmenting the circularly shaped objects with a long persistence of homology as well as computing persistent homology along the filtration of the input image and displaying in the form of a persistence diagram.