Volume 9, Issue 1
Application of the Level-Set Model with Constraints in Image Segmentation

Vladimír Klement, Tomáš Oberhuber & Daniel Ševčovič

Numer. Math. Theor. Meth. Appl., 9 (2016), pp. 147-168.

Published online: 2016-09

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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 overrelaxation 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.

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@Article{NMTMA-9-147, author = {}, title = {Application of the Level-Set Model with Constraints in Image Segmentation}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2016}, volume = {9}, number = {1}, pages = {147--168}, 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 overrelaxation 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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2015.m1418}, url = {http://global-sci.org/intro/article_detail/nmtma/12371.html} }
TY - JOUR T1 - Application of the Level-Set Model with Constraints in Image Segmentation JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 147 EP - 168 PY - 2016 DA - 2016/09 SN - 9 DO - http://doi.org/10.4208/nmtma.2015.m1418 UR - https://global-sci.org/intro/article_detail/nmtma/12371.html KW - AB -

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 overrelaxation 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.

Vladimír Klement, Tomáš Oberhuber & Daniel Ševčovič. (2020). Application of the Level-Set Model with Constraints in Image Segmentation. Numerical Mathematics: Theory, Methods and Applications. 9 (1). 147-168. doi:10.4208/nmtma.2015.m1418
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