Image Processing by Topological Asymptotic Expansion
Journal of Mathematical Imaging and Vision
Crack reconstruction using a level-set strategy
Journal of Computational Physics
Asymptotic Imaging of Perfectly Conducting Cracks
SIAM Journal on Scientific Computing
Control of the Effects of Regularization on Variational Optic Flow Computations
Journal of Mathematical Imaging and Vision
From restoration by topological gradient to medical image segmentation via an asymptotic expansion
Mathematical and Computer Modelling: An International Journal
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This paper deals with the identifiability of nonsmooth defects by boundary measurements, and the stability of their detection. We introduce and analyze a new pointwise regularity concept at the boundary of an open set which turns out to play a crucial role in the identifiability of defects by two boundary measurements. As a consequence, we prove the unique identifiability for a large class of closed sets, including sets with an infinite number of connected components of positive capacity and totally disconnected sets. In order to rigorously justify numerical approximation results of defects by optimal design methods, we prove a geometric stability result of the defect identification process, without any a priori smoothness assumptions.