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. 2019 Jun 19;9:8764. doi: 10.1038/s41598-019-45283-z

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© The Author(s) 2019

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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(a) A gray-scale image. (b) Filtration of binary images (h, threshold gray-scale value). A sequence of binary images is obtained by changing the threshold. The area surrounded by the blue line represents an example of the birth of a connected component. The area surrounded by the red line represents the death of the connected component. (c) Persistence diagram (degree 0). The point in the circle corresponds to the birth–death described above a pair of the connected component.