Inferring Object Boundaries and their Roughness with Uncertainty Quantification
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866929222740606976 |
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| author | Afkham, Babak Maboudi Riis, Nicolai André Brogaard Dong, Yiqiu Hansen, Per Christian |
| author_facet | Afkham, Babak Maboudi Riis, Nicolai André Brogaard Dong, Yiqiu Hansen, Per Christian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_04608 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Inferring Object Boundaries and their Roughness with Uncertainty Quantification Afkham, Babak Maboudi Riis, Nicolai André Brogaard Dong, Yiqiu Hansen, Per Christian Numerical Analysis 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. |
| title | Inferring Object Boundaries and their Roughness with Uncertainty Quantification |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2305.04608 |