{"paper_id":"3812eb31-8ff3-4d90-8e69-c1d8e56f5d6e","body_text":"Inferring Object Boundaries and their Roughness with Uncertainty Quantification | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Inferring Object Boundaries and their Roughness with Uncertainty Quantification Babak Maboudi Afkham, Nicolai Andre Brogaard Riis, Yiqiu Dong, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3894410/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 13 Aug, 2024 Read the published version in Journal of Mathematical Imaging and Vision → Version 1 posted 9 You are reading this latest preprint version Abstract This work describes a Bayesian framework for reconstructing the boundaries that represent targeted features in an image, as well as the regularity (i.e., roughness vs. smoothness) of these boundaries. This regularity often carries crucial information in many inverse problem applications, e.g., for identifying malignant tissues in medical imaging. We represent the boundary as a radial function and characterize the regularity of this function by means of its fractional differentiability. We propose a hierarchical Bayesian formulation which, simultaneously, estimates the function and its regularity, and in addition we quantify the uncertainties in the estimates. Numerical results suggest that the proposed method is a reliable approach for estimating and characterizing object boundaries in imaging applications, as illustrated with examples from X-ray CT and image inpainting. We also show that our method is robust under various noise types, noise levels, and incomplete data. Bayesian inversion goal-oriented uncertainty quantification boundary roughness Whittle-Mat´ern prior data fitting computed tomography image inpainting Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 13 Aug, 2024 Read the published version in Journal of Mathematical Imaging and Vision → Version 1 posted Editorial decision: Revision requested 30 Apr, 2024 Reviews received at journal 27 Apr, 2024 Reviewers agreed at journal 10 Mar, 2024 Reviews received at journal 04 Mar, 2024 Reviewers agreed at journal 04 Feb, 2024 Reviewers invited by journal 01 Feb, 2024 Editor assigned by journal 26 Jan, 2024 Submission checks completed at journal 25 Jan, 2024 First submitted to journal 24 Jan, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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