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dc.contributor.authorDebroux, Nen
dc.contributor.authorAston, Johnen
dc.contributor.authorBonardi, Fen
dc.contributor.authorForbes, Aen
dc.contributor.authorLe Guyader, Cen
dc.contributor.authorRomanchikova, Men
dc.contributor.authorSchonlieb, CBen
dc.date.accessioned2020-04-21T23:30:44Z
dc.date.available2020-04-21T23:30:44Z
dc.date.issued2019-01-01en
dc.identifier.issn1936-4954
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/304601
dc.description.abstractIn medical image analysis, constructing an atlas, i.e., a mean representative of an ensemble of images, is a critical task for practitioners to estimate variability of shapes inside a population, and to characterize and understand how structural shape changes have an impact on health. This involves identifying significant shape constituents of a set of images, a process called segmentation, and mapping this group of images to an unknown mean image, a task called registration, making a statistical analysis of the image population possible. To achieve this goal, we propose treating these operations jointly to leverage their positive mutual influence, in a hyperelasticity setting, by viewing the shapes to be matched as Ogden materials. The approach is complemented by novel hard constraints on the L\infty norm of both the Jacobian and its inverse, ensuring that the deformation is a bi-Lipschitz homeomorphism. Segmentation is based on the Potts model, which allows for a partition into more than two regions, i.e., more than one shape. The connection to the registration problem is ensured by the dissimilarity measure that aims to align the segmented shapes. A representation of the deformation field in a linear space equipped with a scalar product is then computed in order to perform a geometry-driven Principal Component Analysis (PCA) and to extract the main modes of variations inside the image population. Theoretical results emphasizing the mathematical soundness of the model are provided, among which are existence of minimizers, analysis of a numerical method, asymptotic results, and a PCA analysis, as well as numerical simulations demonstrating the ability of the model to produce an atlas exhibiting sharp edges, high contrast, and a consistent shape.
dc.publisherSociety for Industrial and Applied Mathematics
dc.rightsAll rights reserved
dc.titleA variational model dedicated to joint segmentation, registration, and atlas generation for shape analysisen
dc.typeArticle
prism.endingPage380
prism.issueIdentifier1en
prism.publicationDate2019en
prism.publicationNameSIAM Journal on Imaging Sciencesen
prism.startingPage351
prism.volume13en
dc.identifier.doi10.17863/CAM.51683
dcterms.dateAccepted2019-10-25en
rioxxterms.versionofrecord10.1137/19M1271907en
rioxxterms.versionVoR
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserveden
rioxxterms.licenseref.startdate2019-01-01en
dc.identifier.eissn1936-4954
rioxxterms.typeJournal Article/Reviewen
pubs.funder-project-idLeverhulme Trust (RPG-2015-250)
pubs.funder-project-idEPSRC (EP/N014588/1)
pubs.funder-project-idEuropean Commission Horizon 2020 (H2020) Marie Sk?odowska-Curie actions (691070)
pubs.funder-project-idEuropean Commission Horizon 2020 (H2020) Marie Sk?odowska-Curie actions (777826)
pubs.funder-project-idLeverhulme Trust (PLP-2017-275)
pubs.funder-project-idNational Physical Laboratory (NPL) (Unknown)
pubs.funder-project-idAlan Turing Institute (Unknown)
pubs.funder-project-idEPSRC (EP/M00483X/1)
pubs.funder-project-idEPSRC (EP/J009539/1)
pubs.funder-project-idEPSRC (EP/S026045/1)


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