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Author: Hintermüller, Michael × DDC: 510 × Has files: Yes × Type: article ×

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    Variable Step Mollifiers and Applications
    (Berlin ; Heidelberg : Springer, 2020) Hintermüller, Michael; Papafitsoros, Kostas; Rautenberg, Carlos N.
    We consider a mollifying operator with variable step that, in contrast to the standard mollification, is able to preserve the boundary values of functions. We prove boundedness of the operator in all basic Lebesgue, Sobolev and BV spaces as well as corresponding approximation results. The results are then applied to extend recently developed theory concerning the density of convex intersections. © 2020, The Author(s).
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    Uncertainty Quantification in Image Segmentation Using the Ambrosio–Tortorelli Approximation of the Mumford–Shah Energy
    (Dordrecht [u.a.] : Springer Science + Business Media B.V, 2021) Hintermüller, Michael; Stengl, Steven-Marian; Surowiec, Thomas M.
    The quantification of uncertainties in image segmentation based on the Mumford–Shah model is studied. The aim is to address the error propagation of noise and other error types in the original image to the restoration result and especially the reconstructed edges (sharp image contrasts). Analytically, we rely on the Ambrosio–Tortorelli approximation and discuss the existence of measurable selections of its solutions as well as sampling-based methods and the limitations of other popular methods. Numerical examples illustrate the theoretical findings.