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. 2018 Jan 26;8:1711. doi: 10.1038/s41598-018-19440-9

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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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Reconstruction of CA lumen surface from its XRA projections. (a) Parametric centreline curve C(t) and Frenet–Serret trihedron defined at the centreline point C. (b) Reconstruction of two points (A_i and B_i) on the lumen border. (c) Detecting A_n and B_n from n-th view. (d) Combining points A and B for fitting circle (black) or ellipse (blue) when two XRA views are acquired and polygonal approximation (red) from multiple XRA views. (e) Obtained vessel cross-sections oriented along their centreline C(t).