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Application of the Level-Set Model with Constraints in Image Segmentation

Part of: Equilibrium (steady-state) problems Parabolic equations and systems Global differential geometry Numerical methods

Published online by Cambridge University Press:  15 February 2016

Vladimír Klement ,
Tomáš Oberhuber  and
Daniel Ševčovič
Vladimír Klement
Affiliation:
Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Trojanova 13, Praha 2, 120 00, Czech Republic
Tomáš Oberhuber
Affiliation:
Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Trojanova 13, Praha 2, 120 00, Czech Republic
Daniel Ševčovič*
Affiliation:
Department of Applied Mathematics and Statistics, Comenius University, 842 48 Bratislava, Slovakia
*
*Corresponding author. Email addresses: tomas.oberhuber@fjfi.cvut.cz (T. Oberhuber), vladimir.klement@fjfi.cvut.cz (V. Klement), sevcovic@fmph.uniba.sk (D. Ševčovič)
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Abstract

We propose and analyze a constrained level-set method for semi-automatic image segmentation. Our level-set model with constraints on the level-set function enables us to specify which parts of the image lie inside respectively outside the segmented objects. Such a-priori information can be expressed in terms of upper and lower constraints prescribed for the level-set function. Constraints have the same conceptual meaning as initial seeds of the popular graph-cuts based methods for image segmentation. A numerical approximation scheme is based on the complementary-finite volumes method combined with the Projected successive over-relaxation method adopted for solving constrained linear complementarity problems. The advantage of the constrained level-set method is demonstrated on several artificial images as well as on cardiac MRI data.

Keywords

linear complementarityimage processingsegmentationlevel-set methodprojected successive over-relaxation method

MSC classification

Secondary: 90C33: Complementarity and equilibrium problems and variational inequalities (finite dimensions) 35K55: Nonlinear parabolic equations 35K52: Initial-boundary value problems for higher-order parabolic systems 53C44: Geometric evolution equations (mean curvature flow, Ricci flow, etc.) 74S10: Finite volume methods 74G15: Numerical approximation of solutions
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 9 , Issue 1 , February 2016 , pp. 147 - 168
Copyright
Copyright © Global-Science Press 2016 

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