Mumford-Shah functionals on graphs and their asymptotics

被引：10

作者：

Caroccia, Marco ^{[1
]}

Chambolle, Antonin ^{[2
]}

Slepcev, Dejan ^{[3
]}

机构：

[1] Univ Roma Tor Vergata, Dipartimento Matemat, I-00133 Rome, Italy

[2] Ecole Polytech, CMAP, F-91128 Palaiseau, France

[3] Carnegie Mellon Univ, Dept Math Sci, Pittsburgh, PA 15213 USA

来源：

NONLINEARITY | 2020年 / 33卷 / 08期

基金：

美国安德鲁·梅隆基金会;

关键词：

nonlocal variational problems; variational problems with randomness; discrete to continuum limit; asymptotic consistency; Gamma convergence; regression; FINITE-DIFFERENCE APPROXIMATION; CONSISTENCY; RECOVERY;

D O I：

10.1088/1361-6544/ab81ee

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider adaptations of the Mumford-Shah functional to graphs. These are based on discretizations of nonlocal approximations to the Mumford-Shah functional. Motivated by applications in machine learning we study the random geometric graphs associated to random samples of a measure. We establish the conditions on the graph constructions under which the minimizers of graph Mumford-Shah functionals converge to a minimizer of a continuum Mumford-Shah functional. Furthermore we explicitly identify the limiting functional. Moreover we describe an efficient algorithm for computing the approximate minimizers of the graph Mumford-Shah functional.

引用

页码：3846 / 3888

页数：43

共 50 条

[31] An extended Mumford-Shah model for shape partitioning
Nabi, Habiba
Douik, Ali
INTERNATIONAL JOURNAL OF SIGNAL AND IMAGING SYSTEMS ENGINEERING, 2016, 9 (4-5) : 226 - 232
[32] Singular Sets of Minimizers for the Mumford-Shah Functional
Radulescu, Vicentiu
REVUE ROUMAINE DE MATHEMATIQUES PURES ET APPLIQUEES, 2007, 52 (01): : 124 - 125
[33] A Convex Representation for the Vectorial Mumford-Shah Functional
Strekalovskiy, Evgeny
Chambolle, Antonin
Cremers, Daniel
2012 IEEE CONFERENCE ON COMPUTER VISION AND PATTERN RECOGNITION (CVPR), 2012, : 1712 - 1719
[34] On a notion of unilateral slope for the Mumford-Shah functional
Gianni Dal Maso
Rodica Toader
Nonlinear Differential Equations and Applications NoDEA, 2007, 13 : 713 - 734
[35] Image segmentation based on Mumford-Shah functional
Chen Xu-feng
Guan Zhi-cheng
Journal of Zhejiang University-SCIENCE A, 2004, 5 (1): : 123 - 128
[36] A note on the discrete binary Mumford-Shah model
Darbon, Jerome
COMPUTER VISION/COMPUTER GRAPHICS COLLABORATION TECHNIQUES, 2007, 4418 : 283 - 294
[37] The Mumford-Shah functional: From segmentation to stereo
Yezzi, A
Soatto, S
Tsai, A
Willsky, A
MATHEMATICAL METHODS IN COMPUTER VISION, 2003, 133 : 125 - 147
[38] Discrete stochastic approximations of the Mumford-Shah functional
Ruf, Matthias
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2019, 36 (04): : 887 - 937
[39] On the singular sets of minimizers of the Mumford-Shah functional
David, G
Semmes, S
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 1996, 75 (04): : 299 - 342
[40] Mumford-Shah model with fast algorithm on lattice
Yu, Lu
Wang, Qiao
Wu, Lenan
Xie, Jun
2006 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING, VOLS 1-13, 2006, : 1929 - 1932

← 1 2 3 4 5 →