Topological Optimization with the <inline-formula> <graphic file="1687-2770-2009-896813-i1.gif"/></inline-formula>-Laplacian Operator and an Application in Image Processing
<p>Abstract</p> <p>We focus in this paper on the theoretical and numerical aspect os image processing. We consider a non linear boundary value problem (the <inline-formula> <graphic file="1687-2770-2009-896813-i2.gif"/></inline-formula>-Laplacian) from w...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2009-01-01
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| Series: | Boundary Value Problems |
| Online Access: | http://www.boundaryvalueproblems.com/content/2009/896813 |
| _version_ | 1831527165984768000 |
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| author | Seck Diaraf Sy Alassane |
| author_facet | Seck Diaraf Sy Alassane |
| author_sort | Seck Diaraf |
| collection | DOAJ |
| description | <p>Abstract</p> <p>We focus in this paper on the theoretical and numerical aspect os image processing. We consider a non linear boundary value problem (the <inline-formula> <graphic file="1687-2770-2009-896813-i2.gif"/></inline-formula>-Laplacian) from which we will derive the asymptotic expansion of the Mumford-Shah functional. We give a theoretical expression of the topological gradient as well as a numerical confirmation of the result in the restoration and segmentation of images.</p> |
| first_indexed | 2024-12-16T16:24:15Z |
| format | Article |
| id | doaj.art-c0704c3296894ad1b26e54f8f483d372 |
| institution | Directory Open Access Journal |
| issn | 1687-2762 1687-2770 |
| language | English |
| last_indexed | 2024-12-16T16:24:15Z |
| publishDate | 2009-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-c0704c3296894ad1b26e54f8f483d3722022-12-21T22:24:49ZengSpringerOpenBoundary Value Problems1687-27621687-27702009-01-0120091896813Topological Optimization with the <inline-formula> <graphic file="1687-2770-2009-896813-i1.gif"/></inline-formula>-Laplacian Operator and an Application in Image ProcessingSeck DiarafSy Alassane<p>Abstract</p> <p>We focus in this paper on the theoretical and numerical aspect os image processing. We consider a non linear boundary value problem (the <inline-formula> <graphic file="1687-2770-2009-896813-i2.gif"/></inline-formula>-Laplacian) from which we will derive the asymptotic expansion of the Mumford-Shah functional. We give a theoretical expression of the topological gradient as well as a numerical confirmation of the result in the restoration and segmentation of images.</p>http://www.boundaryvalueproblems.com/content/2009/896813 |
| spellingShingle | Seck Diaraf Sy Alassane Topological Optimization with the <inline-formula> <graphic file="1687-2770-2009-896813-i1.gif"/></inline-formula>-Laplacian Operator and an Application in Image Processing Boundary Value Problems |
| title | Topological Optimization with the <inline-formula> <graphic file="1687-2770-2009-896813-i1.gif"/></inline-formula>-Laplacian Operator and an Application in Image Processing |
| title_full | Topological Optimization with the <inline-formula> <graphic file="1687-2770-2009-896813-i1.gif"/></inline-formula>-Laplacian Operator and an Application in Image Processing |
| title_fullStr | Topological Optimization with the <inline-formula> <graphic file="1687-2770-2009-896813-i1.gif"/></inline-formula>-Laplacian Operator and an Application in Image Processing |
| title_full_unstemmed | Topological Optimization with the <inline-formula> <graphic file="1687-2770-2009-896813-i1.gif"/></inline-formula>-Laplacian Operator and an Application in Image Processing |
| title_short | Topological Optimization with the <inline-formula> <graphic file="1687-2770-2009-896813-i1.gif"/></inline-formula>-Laplacian Operator and an Application in Image Processing |
| title_sort | topological optimization with the inline formula graphic file 1687 2770 2009 896813 i1 gif inline formula laplacian operator and an application in image processing |
| url | http://www.boundaryvalueproblems.com/content/2009/896813 |
| work_keys_str_mv | AT seckdiaraf topologicaloptimizationwiththeinlineformulagraphicfile168727702009896813i1gifinlineformulalaplacianoperatorandanapplicationinimageprocessing AT syalassane topologicaloptimizationwiththeinlineformulagraphicfile168727702009896813i1gifinlineformulalaplacianoperatorandanapplicationinimageprocessing |