The planar Mumford-Shah conjecture predicts that the reduced edge set of an absolute minimizer of the Mumford-Shah functional consists locally of regular arcs, with only crack endpoints and triple junctions as singularities. An absolute minimizer here is compared with every admissible compact modification of both the function and its edge set, without a topological restriction on competitors.
Mumford-Shah Conjecture
See also
Mumford-Shah Functional, Partial Differential EquationExplore with Wolfram|Alpha
References
Focardi, M. "Fine Regularity Results for Mumford-Shah Minimizers: Porosity, Higher Integrability and the Mumford-Shah Conjecture." In Free Discontinuity Problems (Ed. N. Fusco and A. Pratelli). Pisa, Italy: Edizioni della Normale, pp. 1-68, 2016. https://doi.org/10.1007/978-88-7642-593-6_1.Cite this as:
Weisstein, Eric W. "Mumford-Shah Conjecture." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Mumford-ShahConjecture.html