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We tested our approach using the MESSIDOR dataset that consists of colour fundus photographs from 547 healthy individuals,\u00a0149 with mild diabetic retinopathy (DR), 239 with moderate DR, 199 pre-PDR and 53 PDR. The skeleton (centrelines) of the automatically segmented retinal vasculature was represented as an \u03b1-shape and the proposed parameters, complexity (<jats:inline-formula><jats:alternatives><jats:tex-math>$${Op\\alpha }_{min}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mrow>\n                      <mml:mi>O<\/mml:mi>\n                      <mml:mi>p<\/mml:mi>\n                      <mml:mi>\u03b1<\/mml:mi>\n                    <\/mml:mrow>\n                    <mml:mrow>\n                      <mml:mi>min<\/mml:mi>\n                    <\/mml:mrow>\n                  <\/mml:msub>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>), spread (<jats:italic>OpA<\/jats:italic>), global shape (VS) and presence of abnormal angiogenesis (<jats:italic>Grad<\/jats:italic><jats:sub><jats:italic>\u03b1<\/jats:italic><\/jats:sub>) were computed. In cross-sectional analysis, individuals with PDR had a lower <jats:inline-formula><jats:alternatives><jats:tex-math>$${Op\\alpha }_{min}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mrow>\n                      <mml:mi>O<\/mml:mi>\n                      <mml:mi>p<\/mml:mi>\n                      <mml:mi>\u03b1<\/mml:mi>\n                    <\/mml:mrow>\n                    <mml:mrow>\n                      <mml:mi>min<\/mml:mi>\n                    <\/mml:mrow>\n                  <\/mml:msub>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, OpA and <jats:italic>Grad<\/jats:italic><jats:sub><jats:italic>\u03b1<\/jats:italic><\/jats:sub> indicating a vasculature that is more complex, less spread (i.e. dense) and the presence of numerous small vessels. The results show that \u03b1-shape parameters characterise vascular abnormalities predictive of PDR (AUC 0.73; 95% CI [0.73 0.74]) and have therefore potential to reveal changes in retinal microvascular morphology.<\/jats:p>","DOI":"10.1038\/s41598-021-02329-5","type":"journal-article","created":{"date-parts":[[2021,11,24]],"date-time":"2021-11-24T11:02:33Z","timestamp":1637751753000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["2D alpha-shapes to quantify retinal microvasculature morphology and their application to proliferative diabetic retinopathy characterisation in fundus photographs"],"prefix":"10.1038","volume":"11","author":[{"given":"Emma","family":"Pead","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ylenia","family":"Giarratano","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andrew J.","family":"Tatham","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Miguel O.","family":"Bernabeu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5993-0278","authenticated-orcid":false,"given":"Baljean","family":"Dhillon","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5055-0794","authenticated-orcid":false,"given":"Emanuele","family":"Trucco","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5120-0086","authenticated-orcid":false,"given":"Tom","family":"MacGillivray","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,11,24]]},"reference":[{"key":"2329_CR1","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1186\/s40662-015-0026-2","volume":"2","author":"R Lee","year":"2015","unstructured":"Lee, R., Wong, T. 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