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. 2023 Oct 19;24:235. doi: 10.1186/s13059-023-03054-0

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© The Author(s) 2023

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 licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence 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 licence, visit http://creativecommons.org/licenses/by/4.0/. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated in a credit line to the data.

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Fig. 2 — a Overview of GeneSegNet framework. GeneSegNet makes a joint use of gene spatial coordinates and imaging information for cell segmentation, and is recursively learned by alternating between the optimization of network parameters and estimation of training labels for noise-tolerant training. The outputs of GeneSegNet include a confidence map $\hat{M} \in {[0, 1]}^{w \times h}$ that stores the probability of each pixel being inside cell regions, a center map $\hat{C} \in {[0, 1]}^{w \times h}$ that gives the likelihood of each pixel being a cell center, and a two-channel offset map $\hat{V} \in R^{2 \times w \times h}$ indicating the offset vector of each pixel to the center of its corresponding cell instance. Combining the outputs together, GeneSegNet can recover the precise boundary of each individual cell. b GeneSegNet is built upon the general U-Net network architecture, where an encoder progressive downsamples the inputs for more expressive feature extraction, and a decoder upsamples the feature maps in a mirror-symmetric fashion for fine-grained cell segmentation