A Convex Decomposition Formula for the Mumford-Shah Functional in Dimension One

zbMath1405.49035arXiv1610.01846MaRDI QIDQ4557935

Marcello Carioni

Publication date: 27 November 2018

Full work available at URL: https://arxiv.org/abs/1610.01846

zbMATH Keywords

rectifiable currentscalibrationsMumford-Shah functionalconvex liftMumford-Shah conjecture

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Image processing (compression, reconstruction, etc.) in information and communication theory (94A08) Functional inequalities, including subadditivity, convexity, etc. (39B62)

Cites Work

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• Existence theory for a new class of variational problems
• Calibrated geometries
• Generalized coarea formula and fractal sets
• Higher integrability of the gradient and dimension of the singular set for minimisers of the Mumford-Shah functional
• Local calibrations for minimizers of the Mumford-Shah functional with rectilinear discontinuity sets
• Existence theorem for a minimum problem with free discontinuity set
• The calibration method for the Mumford-Shah functional and free-discontinuity problems
• On the regularity of edges in image segmentation
• Optimal approximations by piecewise smooth functions and associated variational problems
• Continuous limits of discrete perimeters
• $C^{1} $-Arcs for Minimizers of the Mumford-Shah Functional
• Local calibrations for minimizers of the Mumford-Shah functional with a regular discontinuity set.

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