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. 2022 Oct 17;19(11):1438–1448. doi: 10.1038/s41592-022-01639-4

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© The Author(s) 2022

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. 2 — a, Comparison of distance field algorithms and corresponding flow fields on ground-truth masks. FMM produces ridges in the distance field resulting from pixelation on the cell mask boundary. Our smooth FIM algorithm minimizes these features. The difference image (FIM − FMM) highlights artifacts in the FMM method. Flow fields are calculated as the normalized gradient of the distance field. Boundary pixelation affects the FMM flow field deep into the cell, regardless of cell size. b,c, Comparison of mask reconstruction algorithms on a smooth flow field. Boundary pixel trajectories and resulting mask outlines from standard Euler integration (b). Trajectories and mask outlines under suppressed Euler integration (c). Red dots indicate the final positions of all cell pixels, not only the boundary pixels for which trajectories are displayed. Bacteria displayed are E. coli CS703-1 (a) and H. pylori (b,c) both treated with aztreonam. Scale bars, 1 μm. Images are representative of 1,299 E. coli and 701 H. pylori cells in the total ground-truth dataset, respectively.