Multiphase Image Segmentation and Modulation Recovery Based on Shape and Topological Sensitivity

被引：52
作者：
Hintermueller, M. [1 ,2 ]
Laurain, A.
机构：
[1] Humboldt Univ, D-10099 Berlin, Germany
[2] Graz Univ, Dept Math & Sci Comp, Special Res Ctr Control & Optimizat, Graz, Austria
来源：
JOURNAL OF MATHEMATICAL IMAGING AND VISION | 2009年 / 35卷 / 01期
基金：
奥地利科学基金会;
关键词：
Image processing; k-means clustering; Modulation recovery; Mumford-Shah functional; Piecewise constant reconstruction; Segmentation; Shape and topological sensitivity;
D O I：
10.1007/s10851-009-0150-5
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
Topological sensitivity analysis is performed for the piecewise constant Mumford-Shah functional. Topological and shape derivatives are combined in order to derive an algorithm for image segmentation with fully automatized initialization. Segmentation of 2D and 3D data is presented. Further, a generalized Mumford-Shah functional is proposed and numerically investigated for the segmentation of images modulated due to, e.g., coil sensitivities.
引用
收藏
页码：1 / 22
页数：22
相关论文
共 22 条
[1]   A level set algorithm for minimizing the Mumford-Shah functional in image processing [J].
Chan, TF ;
Vese, LA .
IEEE WORKSHOP ON VARIATIONAL AND LEVEL SET METHODS IN COMPUTER VISION, PROCEEDINGS, 2001, :161-168
[2]  
DELFOUR M, 2001, SIAM ADV DESIGN CONT
[3]  
Giaquinta M., 1993, Introduction to Regularity Theory for Nonlinear Elliptic Systems
[4]  
Hartigan J. A., 1979, Applied Statistics, V28, P100, DOI 10.2307/2346830
[5]  
Hartigan J.A., 1975, Clustering Algorithms
[6]  
He L, 2007, LECT NOTES COMPUT SC, V4485, P777
[7]  
Henrot A, 2005, MATH APPL-BERLIN, V48, P1
[8]   A second order shape optimization approach for image segmentation [J].
Hintermüller, M ;
Ring, W .
SIAM JOURNAL ON APPLIED MATHEMATICS, 2003, 64 (02) :442-467
[9]   A variational approach to magnetic resonance coil sensitivity estimation [J].
Keeling, SL ;
Bammer, R .
APPLIED MATHEMATICS AND COMPUTATION, 2004, 158 (02) :359-388
[10]  
MacQueen J., 1967, 5 BERK S MATH STAT P, P281
123