Coupling Image Restoration and Segmentation: A Generalized Linear Model/Bregman Perspective

被引:64
作者
Paul, Gregory [1 ]
Cardinale, Janick [1 ]
Sbalzarini, Ivo F. [1 ]
机构
[1] ETH, MOSAIC Grp, CH-8092 Zurich, Switzerland
关键词
Segmentation; Restoration; Generalized linear model; Shape gradient; Convex relaxation; Alternating split Bregman; ACTIVE CONTOURS; VARIATIONAL APPROACH; GLOBAL MINIMIZATION; CONVEX FORMULATION; REGION COMPETITION; SHAPE; ALGORITHMS; MODEL; RECONSTRUCTION; PARAMETER;
D O I
10.1007/s11263-013-0615-2
中图分类号
TP18 [人工智能理论];
学科分类号
081104 ; 0812 ; 0835 ; 1405 ;
摘要
We introduce a new class of data-fitting energies that couple image segmentation with image restoration. These functionals model the image intensity using the statistical framework of generalized linear models. By duality, we establish an information-theoretic interpretation using Bregman divergences. We demonstrate how this formulation couples in a principled way image restoration tasks such as denoising, deblurring (deconvolution), and inpainting with segmentation. We present an alternating minimization algorithm to solve the resulting composite photometric/geometric inverse problem. We use Fisher scoring to solve the photometric problem and to provide asymptotic uncertainty estimates. We derive the shape gradient of our data-fitting energy and investigate convex relaxation for the geometric problem. We introduce a new alternating split-Bregman strategy to solve the resulting convex problem and present experiments and comparisons on both synthetic and real-world images.
引用
收藏
页码:69 / 93
页数:25
相关论文
共 81 条
[21]   Completely Convex Formulation of the Chan-Vese Image Segmentation Model [J].
Brown, Ethan S. ;
Chan, Tony F. ;
Bresson, Xavier .
INTERNATIONAL JOURNAL OF COMPUTER VISION, 2012, 98 (01) :103-121
[22]   Colour, texture, and motion in level set based segmentation and tracking [J].
Brox, Thomas ;
Rousson, Mikael ;
Deriche, Rachid ;
Weickert, Joachim .
IMAGE AND VISION COMPUTING, 2010, 28 (03) :376-390
[23]   A survey in mathematics for industry - A survey on level set methods for inverse problems and optimal design [J].
Burger, M ;
Osher, SJ .
EUROPEAN JOURNAL OF APPLIED MATHEMATICS, 2005, 16 :263-301
[24]  
Burger M., 2005, PAMM, V5, P11
[25]   Discrete Region Competition for Unknown Numbers of Connected Regions [J].
Cardinale, Janick ;
Paul, Gregory ;
Sbalzarini, Ivo F. .
IEEE TRANSACTIONS ON IMAGE PROCESSING, 2012, 21 (08) :3531-3545
[26]   Geodesic active contours [J].
Caselles, V ;
Kimmel, R ;
Sapiro, G .
INTERNATIONAL JOURNAL OF COMPUTER VISION, 1997, 22 (01) :61-79
[27]   A GEOMETRIC MODEL FOR ACTIVE CONTOURS IN IMAGE-PROCESSING [J].
CASELLES, V ;
CATTE, F ;
COLL, T ;
DIBOS, F .
NUMERISCHE MATHEMATIK, 1993, 66 (01) :1-31
[28]  
Chambolle A, 2004, J MATH IMAGING VIS, V20, P89
[29]   A Convex Approach to Minimal Partitions [J].
Chambolle, Antonin ;
Cremers, Daniel ;
Pock, Thomas .
SIAM JOURNAL ON IMAGING SCIENCES, 2012, 5 (04) :1113-1158
[30]   A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging [J].
Chambolle, Antonin ;
Pock, Thomas .
JOURNAL OF MATHEMATICAL IMAGING AND VISION, 2011, 40 (01) :120-145