IMAGE SEGMENTATION BY PIECEWISE CONSTANT MUMFORD-SHAH MODEL WITHOUT ESTIMATING THE CONSTANTS  

作　　者：Xue-cheng Tai Chang-hui Yao 

机构地区：[1]CIPR,Department of Mathematics, University of Bergen, Norway [2]Department of Mathematics, University of Bergen, Norway

出　　处：《Journal of Computational Mathematics》2006年第3期435-443,共9页计算数学（英文）

摘　　要：In this work, we try to use the so-called Piecewise Constant Level Set Method （PCLSM） for the Mumford-Shah segmentation model. For image segmentation, the Mumford-Shah model needs to find the regions and the constant values inside the regions for the segmen- tation. In order to use PCLSM for this purpose, we need to solve a minimization problem using the level set function and the constant values as minimization variables. In this work, we test on a model such that we only need to minimize with respect to the level set function, i.e., we do not need to minimize with respect to the constant values. Gradient descent method and Newton method are used to solve the Euler-Lagrange equation for the minimization problem. Numerical experiments are given to show the efficiency and advantages of the new model and algorithms.In this work, we try to use the so-called Piecewise Constant Level Set Method （PCLSM） for the Mumford-Shah segmentation model. For image segmentation, the Mumford-Shah model needs to find the regions and the constant values inside the regions for the segmen- tation. In order to use PCLSM for this purpose, we need to solve a minimization problem using the level set function and the constant values as minimization variables. In this work, we test on a model such that we only need to minimize with respect to the level set function, i.e., we do not need to minimize with respect to the constant values. Gradient descent method and Newton method are used to solve the Euler-Lagrange equation for the minimization problem. Numerical experiments are given to show the efficiency and advantages of the new model and algorithms.

关 键 词：PCLSM Image Segmentation Mumford-Shah model. 

分 类 号：O157.5[理学—数学]