PARAMETRIC MAXIMUM FLOW ALGORITHMS FOR FAST TOTAL VARIATION MINIMIZATION

被引:52
作者
Goldfarb, Donald [1 ]
Yin, Wotao [2 ]
机构
[1] Columbia Univ, Dept Ind Engn & Operat Res, New York, NY 10027 USA
[2] Rice Univ, Dept Computat & Appl Math, Houston, TX 77005 USA
基金
美国国家科学基金会;
关键词
maximum flow; minimum cut; graph cut; parametric maximum flow; total variation; image denoising; MRI; IMAGE SEGMENTATION; FILTERS;
D O I
10.1137/070706318
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
This report studies the global minimization of anisotropically discretized total variation (TV) energies with an L-p (in particular, L-1 and L-2) fidelity term using parametric maximum flow algorithms to minimize s-t cut representations of these energies. The TV/L-2 model, also known as the Rudin-Osher-Fatemi (ROF) model, is suitable for restoring images contaminated by Gaussian noise, while the TV/L-1 model is able to remove impulsive noise from grayscale images and perform multiscale decompositions of them. Preliminary numerical results on large-scale two-dimensional CT and three-dimensional brain MR images are presented to illustrate the effectiveness of these approaches.
引用
收藏
页码:3712 / 3743
页数:32
相关论文
共 59 条
[1]  
Ahuja RK, 1995, NETWORK FLOWS THEORY
[2]   Total variation regularization for image denoising, I. Geometric theory [J].
Allard, William K. .
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2007, 39 (04) :1150-1190
[3]   DIGITAL-FILTERS AS ABSOLUTE NORM REGULARIZERS [J].
ALLINEY, S .
IEEE TRANSACTIONS ON SIGNAL PROCESSING, 1992, 40 (06) :1548-1562
[4]   A property of the minimum vectors of a regularizing functional defined by means of the absolute norm [J].
Alliney, S .
IEEE TRANSACTIONS ON SIGNAL PROCESSING, 1997, 45 (04) :913-917
[5]   Recursive median filters of increasing order: A variational approach [J].
Alliney, S .
IEEE TRANSACTIONS ON SIGNAL PROCESSING, 1996, 44 (06) :1346-1354
[6]   SELECTION PROBLEM [J].
BALINSKI, ML .
MANAGEMENT SCIENCE SERIES A-THEORY, 1970, 17 (03) :230-231
[7]  
Boykov Y, 2003, NINTH IEEE INTERNATIONAL CONFERENCE ON COMPUTER VISION, VOLS I AND II, PROCEEDINGS, P26
[8]   An experimental comparison of min-cut/max-flow algorithms for energy minimization in vision [J].
Boykov, Y ;
Kolmogorov, V .
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, 2004, 26 (09) :1124-1137
[9]  
BOYKOV Y, 2004, MAXFLOW V3 0
[10]   Planelike minimizers in periodic media [J].
Caffarelli, LA ;
De La Llave, R .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2001, 54 (12) :1403-1441