Inferring Object Boundaries and their Roughness with Uncertainty Quantification
CoRR(2023)
摘要
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.
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关键词
roughness,features
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