A variant of the level set method and applications to image segmentation
In this paper we propose a variant of the level set formulation for identifying curves separating regions into different phases. In classical level set approaches, the sign of level set functions are utilized to identify up to 2n phases. The novelty in our approach is to introduce a piecewise const...
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| Format: | Journal Article |
| Language: | English |
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2009
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| Online Access: | https://hdl.handle.net/10356/91401 http://hdl.handle.net/10220/4604 http://sfxna09.hosted.exlibrisgroup.com:3410/ntu/sfxlcl3?sid=metalib:ISI_WOS_XML&id=doi:&genre=&isbn=&issn=0025-5718&date=2006&volume=75&issue=255&spage=1155&epage=1174&aulast=Lie&aufirst=%20J&auinit=J&title=MATHEMATICS%20OF%20COMPUTATION&atitle=A%20variant%20of%20the%20level%20set%20method%20and%20applications%20to%20image%20segmentation |
| _version_ | 1811692916187332608 |
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| author | Lie, Johan Lysaker, Marius Tai, Xue Cheng |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Lie, Johan Lysaker, Marius Tai, Xue Cheng |
| author_sort | Lie, Johan |
| collection | NTU |
| description | In this paper we propose a variant of the level set formulation for identifying curves separating regions into different phases. In classical level set approaches, the sign of level set functions are utilized to identify up to 2n phases. The novelty in our approach is to introduce a piecewise constant level set function and use each constant value to represent a unique phase. If phases should be identified, the level set function must approach 2n predetermined constants. We just need one level set function to represent 2n unique phases, and this gains in storage capacity. Further, the reinitializing procedure requested in classical level set methods is superfluous using our approach. The minimization functional for our approach is locally convex and differentiable and thus avoids some of the problems with the nondifferentiability of the Delta and Heaviside functions. Numerical examples are given, and we also compare our method with related approaches. |
| first_indexed | 2024-10-01T06:43:23Z |
| format | Journal Article |
| id | ntu-10356/91401 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T06:43:23Z |
| publishDate | 2009 |
| record_format | dspace |
| spelling | ntu-10356/914012023-02-28T19:37:17Z A variant of the level set method and applications to image segmentation Lie, Johan Lysaker, Marius Tai, Xue Cheng School of Physical and Mathematical Sciences Norwegian Research Council DRNTU::Science::Mathematics::Analysis In this paper we propose a variant of the level set formulation for identifying curves separating regions into different phases. In classical level set approaches, the sign of level set functions are utilized to identify up to 2n phases. The novelty in our approach is to introduce a piecewise constant level set function and use each constant value to represent a unique phase. If phases should be identified, the level set function must approach 2n predetermined constants. We just need one level set function to represent 2n unique phases, and this gains in storage capacity. Further, the reinitializing procedure requested in classical level set methods is superfluous using our approach. The minimization functional for our approach is locally convex and differentiable and thus avoids some of the problems with the nondifferentiability of the Delta and Heaviside functions. Numerical examples are given, and we also compare our method with related approaches. Published version 2009-05-12T08:44:23Z 2019-12-06T18:05:01Z 2009-05-12T08:44:23Z 2019-12-06T18:05:01Z 2006 2006 Journal Article Lie, J., Lysaker, M., & Tai, X. C. (2006). A variant of the level set method and applications to image segmentation. Mathematics of Computation, 75(255), 1155-1174. 0025-5718 https://hdl.handle.net/10356/91401 http://hdl.handle.net/10220/4604 http://sfxna09.hosted.exlibrisgroup.com:3410/ntu/sfxlcl3?sid=metalib:ISI_WOS_XML&id=doi:&genre=&isbn=&issn=0025-5718&date=2006&volume=75&issue=255&spage=1155&epage=1174&aulast=Lie&aufirst=%20J&auinit=J&title=MATHEMATICS%20OF%20COMPUTATION&atitle=A%20variant%20of%20the%20level%20set%20method%20and%20applications%20to%20image%20segmentation 10.1090/S0025-5718-06-01835-7 en Mathematics of Computation. Mathematics of Computation @ copyright 2006 American Mathematical Society. The journal's website is located at http://www.ams.org/mcom/2006-75-255/S0025-5718-06-01835-7/home.html. 20 p. application/pdf |
| spellingShingle | DRNTU::Science::Mathematics::Analysis Lie, Johan Lysaker, Marius Tai, Xue Cheng A variant of the level set method and applications to image segmentation |
| title | A variant of the level set method and applications to image segmentation |
| title_full | A variant of the level set method and applications to image segmentation |
| title_fullStr | A variant of the level set method and applications to image segmentation |
| title_full_unstemmed | A variant of the level set method and applications to image segmentation |
| title_short | A variant of the level set method and applications to image segmentation |
| title_sort | variant of the level set method and applications to image segmentation |
| topic | DRNTU::Science::Mathematics::Analysis |
| url | https://hdl.handle.net/10356/91401 http://hdl.handle.net/10220/4604 http://sfxna09.hosted.exlibrisgroup.com:3410/ntu/sfxlcl3?sid=metalib:ISI_WOS_XML&id=doi:&genre=&isbn=&issn=0025-5718&date=2006&volume=75&issue=255&spage=1155&epage=1174&aulast=Lie&aufirst=%20J&auinit=J&title=MATHEMATICS%20OF%20COMPUTATION&atitle=A%20variant%20of%20the%20level%20set%20method%20and%20applications%20to%20image%20segmentation |
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