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The substantial increase of accessible highly resolved 3D samples at the optic nerve head and the macula is directly linked to medical advancements in early detection of eye diseases. To resolve decisive information from extracted OCT volumes and to make it applicable for further diagnostic analysis, the exact measurement of retinal layer thicknesses serves as an essential task be done for each patient separately. However, manual examination of OCT scans is a demanding and time consuming task, which is typically made difficult by the presence of tissue-dependent speckle noise. Therefore, the elaboration of automated segmentation models has become an important task in the field of medical image processing. We propose a novel, purely data driven <jats:italic>geometric approach to order-constrained<\/jats:italic> 3<jats:italic>D OCT retinal cell layer segmentation<\/jats:italic> which takes as input data in any metric space and can be implemented using only simple, highly parallelizable operations. As opposed to many established retinal layer segmentation methods, we use only locally extracted features as input and do not employ any global shape prior. The physiological order of retinal cell layers and membranes is achieved through the introduction of a smoothed energy term. This is combined with additional regularization of local smoothness to yield highly accurate 3D segmentations. The approach thereby systematically avoid bias pertaining to global shape and is hence suited for the detection of anatomical changes of retinal tissue structure. To demonstrate its robustness, we compare two different choices of features on a data set of manually annotated 3D OCT volumes of healthy human retina. The quality of computed segmentations is compared to the state of the art in automatic retinal layer segmention as well as to manually annotated ground truth data in terms of mean absolute error and Dice similarity coefficient. Visualizations of segmented volumes are also provided.<\/jats:p>","DOI":"10.1007\/s11263-021-01520-5","type":"journal-article","created":{"date-parts":[[2021,9,3]],"date-time":"2021-09-03T21:30:27Z","timestamp":1630704627000},"page":"3088-3118","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Assignment Flow for Order-Constrained OCT Segmentation"],"prefix":"10.1007","volume":"129","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0022-3891","authenticated-orcid":false,"given":"Dmitrij","family":"Sitenko","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3490-3350","authenticated-orcid":false,"given":"Bastian","family":"Boll","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8999-2338","authenticated-orcid":false,"given":"Christoph","family":"Schn\u00f6rr","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,9,3]]},"reference":[{"key":"1520_CR1","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1109\/RBME.2010.2084567","volume":"3","author":"MD Abr\u00e0moff","year":"2010","unstructured":"Abr\u00e0moff, M. 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