http://dx.doi.org/10.1137/090753887">
 

Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Variational fuzzy Mumford–Shah model for image segmentation

Language

English

Abstract

In this paper, we propose a variational fuzzy Mumford-Shah model for image segmentation. The model is based on the assumption that an image can be approximated by the product of a smooth function and a piecewise constant function. Image segmentation is achieved by minimizing the energy functional in terms of membership functions, which take values between 0 and 1 to accommodate the uncertainty of the membership of the pixels, and the partial volume effect inmedical images. We show the existence and symmetry of minimizers for the proposed energy minimization problem. The energy can be minimized by an efficient iterative algorithm. Our iterative method has been applied to medical images and natural images with good results. Comparisons with other segmentation methods demonstrate the advantage of our method in the presence of intensity inhomogeneities. © 2010 Society for Industrial and Applied Mathematics.

Keywords

Fuzzy membership functions, Mumford-Shah model, Operator splitting, Segmentation, Total variation

Publication Date

2010

Source Publication Title

SIAM Journal on Applied Mathematics

Volume

70

Issue

7

Start Page

2750

End Page

2770

Publisher

Society for Industrial and Applied Mathematics

ISSN (print)

00361399

ISSN (electronic)

1095712X

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