A binary level set model and some applications to Mumford-Shah image segmentation

被引:252
作者
Lie, J
Lysaker, M
Tai, XC
机构
[1] Univ Bergen, Dept Math, N-5008 Bergen, Norway
[2] Simula Res Lab, N-1325 Lysaker, Norway
关键词
image processing; image segmentation; level set; PDE; piecewise constant level set functions; variational;
D O I
10.1109/TIP.2005.863956
中图分类号
TP18 [人工智能理论];
学科分类号
081104 ; 0812 ; 0835 ; 1405 ;
摘要
In this paper, we propose a PDE-based level set method. Traditionally, interfaces are represented by the zero level set of continuous level set functions. Instead, we let the interfaces be represented by discontinuities of piecewise constant level set functions. Each level set function can at convergence only take two values, i.e., it can only be 1 or - 1; thus, our method is related to phase-field methods. Some of the properties of standard level set methods are preserved in the proposed method, while others are not. Using this new method for interface problems, we need to minimize a smooth convex functional under a quadratic constraint. The level set functions are discontinuous at convergence, but the minimization functional is smooth. We show numerical results using the method for segmentation of digital images.
引用
收藏
页码:1171 / 1181
页数:11
相关论文
共 46 条
[31]   FRONTS PROPAGATING WITH CURVATURE-DEPENDENT SPEED - ALGORITHMS BASED ON HAMILTON-JACOBI FORMULATIONS [J].
OSHER, S ;
SETHIAN, JA .
JOURNAL OF COMPUTATIONAL PHYSICS, 1988, 79 (01) :12-49
[32]  
Osher S, 2003, APPL MATH SCI, V153, DOI DOI 10.1007/B98879
[33]   A variational model for image classification and restoration [J].
Samson, C ;
Blanc-Féraud, L ;
Aubert, G ;
Zerubia, J .
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, 2000, 22 (05) :460-472
[34]  
Sethian J.A., 1999, LEVEL SET METHODS FA
[35]  
Sethian JA, 2002, NATO SCI SER II-MATH, V75, P365
[36]   On the topological derivative in shape optimization [J].
Sokolowski, J ;
Zochowski, A .
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1999, 37 (04) :1251-1272
[37]  
SONG B, 2002, 0268 U CAL COMP APPL
[38]   A LEVEL SET APPROACH FOR COMPUTING SOLUTIONS TO INCOMPRESSIBLE 2-PHASE FLOW [J].
SUSSMAN, M ;
SMEREKA, P ;
OSHER, S .
JOURNAL OF COMPUTATIONAL PHYSICS, 1994, 114 (01) :146-159
[39]  
Tai X.-C., 2004, INT J NUMER ANAL MOD, V1, P25
[40]   Curve evolution implementation of the Mumford-Shah functional for image segmentation, denoising, interpolation, and magnification [J].
Tsai, A ;
Yezzi, A ;
Willsky, AS .
IEEE TRANSACTIONS ON IMAGE PROCESSING, 2001, 10 (08) :1169-1186