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Topological Fidelity and Image Thresholding: A Persistent Homology Approach

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Abstract

We develop a method based on persistent homology to analyze topological structure in noisy digital images. The method returns threshold(s) for image segmentation to represent inherent topological structure as well as estimates of topological quantities in the form of Betti numbers. Two motivating data sets are scans of binary alloys and firn, the intermediate stage between snow and ice.

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Acknowledgements

The authors would like to thank Stéphane Gorsse (Bordeaux INP & ICMCB-CNRS), and Kaitlin Keegan (University of Copenhagen) for their generous sharing of data (Figs. 12, 13, respectively). This work was supported by NSF DMS 0955604.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of North Carolina at Greensboro, PO Box 26170, Greensboro, NC, 27402-6170, USA

    Yu-Min Chung

  2. Department of Mathematics, College of William and Mary, Williamsburg, USA

    Sarah Day

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Correspondence to Yu-Min Chung.

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Chung, YM., Day, S. Topological Fidelity and Image Thresholding: A Persistent Homology Approach. J Math Imaging Vis 60, 1167–1179 (2018). https://doi.org/10.1007/s10851-018-0802-4

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