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We consider adaptations of the Mumford-Shah functional to graphs.
On a modification of Chebyshev’s inequality and of the error formula of Laplace
S. Bernstein · 1924
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Décomposition polaire et réarrangement monotone des champs de vecteurs
Y. Brenier · 1987
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A compactness theorem for a new class of functions of bounded variation
L. Ambrosio · 1989
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Optimal approximations by piecewise smooth functions and associated variational problems
D. Mumford and J. Shah · 1989
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Constrained restoration and the recovery of discontinuities
D. Geman and G. Reynolds · 1992
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Nonlinear Total Variation Based Noise Removal Algorithms
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Iterative methods for total variation denoising
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The geometry of optimal transportation
W. Gangbo and R. J. McCann · 1996
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Non-local approximation of the Mumford-Shah functional
A. Braides and G. Dal Maso · 1997
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Locally adaptive regression splines
E. Mammen and S. van de Geer · 1997
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Finite difference approximation of the Mumford-Shah functional
M. Gobbino · 1998
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Finite-differences discretizations of the Mumford-Shah functional
A. Chambolle · 1999
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A density result in sbv with respect to non-isotropic energies
G. Cortesani and R. Toader · 1999
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Functions of bounded variation and free discontinuity problems
L. Ambrosio, N. Fusco, and D. Pallara · 2000
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Active contours without edges
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Finite-difference approximation of free-discontinuity problems
M. Gobbino and M. G. Mora · 2001
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A multiphase level set framework for image segmentation using the Mumford and Shah model
L. A. Vese and T. F. Chan · 2002
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Sparsity and smoothness via the fused lasso
R. Tibshirani, M. Saunders, S. Rosset, J. Zhu, and K. Knight · 2005
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Optimal rates for total variation denoising
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Trend filtering on graphs
Y.-X. Wang, J. Sharpnack, A. J. Smola, and R. J. Tibshirani · 2016
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Partial regularity and smooth topology-preserving approximations of rough domains
J. M. Ball and A. Zarnescu · 2017
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A new analytical approach to consistency and overfitting in regularized empirical risk minimization
N. García Trillos and R. Murray · 2017
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