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. 2021 Jan 19;12:458. doi: 10.1038/s41467-020-20730-y

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© The Author(s) 2021

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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Fig. 3 — The distances between visibility graphs based on the spectra of their Laplacians can be used in multivariate analyses and visualizations to distinguish different groups of similar shapes. We show the principal component analyses of shapes from three different domains: a sand grains, b fish shapes, and c leaf shapes^13,31,32. Source data are provided as a Source Data file.