Endpoint regularity for 2d Mumford-Shah minimizers: On a theorem of Andersson and Mikayelyan

@article{Lellis2020EndpointRF,
  title={Endpoint regularity for 2d Mumford-Shah minimizers: On a theorem of Andersson and Mikayelyan},
  author={Camillo De Lellis and Matteo Focardi and Silvia Ghinassi},
  journal={Journal de Math{\'e}matiques Pures et Appliqu{\'e}es},
  year={2020}
}

Figures from this paper

A Machine-Learning-Based Medical Imaging Fast Recognition of Injury Mechanism for Athletes of Winter Sports
TLDR
A C-support vector machine (SVM) medical image segmentation method combining the Chan-Vese (CV) model and SVM is proposed in this paper, which has higher segmentation accuracy above 80% and less registration time below 40 ms, which can provide a reference for doctors to quickly identify the injury and shorten the time.
A monotonicity formula for minimizers of the Mumford-Shah functional in 2d and a sharp lower bound on the energy density
. We establish a new monotonicity formula for minimizers of the Mumford-Shah functional in planar domains. Our formula follows the spirit of Bucur–Luckhaus, but works with the David-L´eger entropy

References

SHOWING 1-10 OF 31 REFERENCES
Monotonicity and separation for the Mumford–Shah problem
Endpoint regularity of $2$d Mumford-Shah minimizers
We prove an $\varepsilon$-regularity theorem at the endpoint of connected arcs for $2$-dimensional Mumford-Shah minimizers. In particular we show that, if in a given ball $B_r (x)$ the jump set of a
Singular Sets of Minimizers for the Mumford-Shah Functional
Presentation of the Mumford-Shah Functional.- Functions in the Sobolev Spaces W1,p.- Regularity Properties for Quasiminimizers.- Limits of Almost-Minimizers.- Pieces of C1 Curves for
Regularity of the singular set for Mumford-Shah minimizers in R^3 near a minimal cone
We show that if (u;K) is a minimizer of the Mumford-Shah functional in an open set of R^3, and if x, K and r > 0 are such that K is close enough to a minimal cone of type P (a plane), Y (three half
Regularity properties of free discontinuity sets
Higher integrability of the gradient and dimension of the singular set for minimisers of the Mumford–Shah functional
Abstract. The paper is concerned with the higher regularity properties of the minimizers of the Mumford–Shah functional. It is shown that, near to singular points where the scaled Dirichlet integral
Existence theorem for a minimum problem with free discontinuity set
We study the variational problem Where Ω is an open set in ℝn,n≧2g∈Lq(Ω) ∩L∞(Ω), 1≦q<+∞, O<λ, μ<+∞ andHn−1 is the (n−1)-dimensional Hausdorff Measure.
A note on the Hausdorff dimension of the singular set for minimizers of the Mumford–Shah energy
Abstract We give a more elementary proof of a result by Ambrosio, Fusco and Hutchinson to estimate the Hausdorff dimension of the singular set of minimizers of the Mumford–Shah energy (see [Calc.
FUNCTIONS OF BOUNDED VARIATION AND FREE DISCONTINUITY PROBLEMS (Oxford Mathematical Monographs)
By Luigi Ambrosio, Nicolo Fucso and Diego Pallara: 434 pp., £55.00, isbn 0-19-850254-1 (Clarendon Press, Oxford, 2000).
...
1
2
3
4
...