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. 2018 Mar 9;8:4311. doi: 10.1038/s41598-018-22489-1

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© The Author(s) 2018

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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Intensify3D restores distorted artificial 3D data and facilitates quantification (a). 3D rendering of undistorted artificial 3D image stack of ~500 Gaussian spheres. Image stack dimensions – X Y Z: 600 × 600 × 500 pixels (b). Representative image (Z = 50) of undistorted image stack (left bottom) and distorted image stacks before and after correction with Intensify3D or CIDRE. All images are presented at the same minimum/maximum brightness levels. Outline of intensity histogram for the undistorted image (red curve) is overlaid on top of black filled intensity histograms for each of the individual images (left bottom corner) (c). ROC space for true/false positive detection rates by 3D object counter plugin (FIJI) on distorted data (crosses), Intensify3D (filled circles) or CIDRE (empty circles) corrected. Performance is in comparison to undistorted data (d). Relative mean absolute error for measured statistics of true positive spheres for distorted data, Intensify3D or CIDRE corrected. Performance is in comparison to undistorted data. Each row was corrected so that the minimal error is 1.