An Overview of the Topological Gradient Approach in Image Processing: Advantages and Inconveniences
Image analysis by topological gradient approach is a technique based upon the historic application of the topological asymptotic expansion to crack localization problem from boundary measurements. This paper aims at reviewing this methodology through various applications in image processing; in part...
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2010/761783 |
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| author | Lamia Jaafar Belaid |
| author_facet | Lamia Jaafar Belaid |
| author_sort | Lamia Jaafar Belaid |
| collection | DOAJ |
| description | Image analysis by topological gradient approach is a technique based upon the historic application of the topological asymptotic expansion to crack localization problem from boundary measurements. This paper aims at reviewing this methodology through various applications in image processing; in particular image restoration with edge detection, classification and segmentation problems for both grey level and color images is presented in this work. The numerical experiments show the efficiency of the topological gradient approach for modelling and solving different image analysis problems. However, the topological gradient approach presents a major drawback: the identified edges are not connected and then the results obtained particularly for the segmentation problem can be degraded. To overcome this inconvenience, we propose an alternative solution by combining the topological gradient approach with the watershed technique. The numerical results obtained using the coupled method are very interesting. |
| format | Article |
| id | doaj-art-2200937840d2408b96282b649a2dbc7f |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-2200937840d2408b96282b649a2dbc7f2025-02-03T05:57:45ZengWileyJournal of Applied Mathematics1110-757X1687-00422010-01-01201010.1155/2010/761783761783An Overview of the Topological Gradient Approach in Image Processing: Advantages and InconveniencesLamia Jaafar Belaid0Dammam University, Faculty of Sciences, PO Box 838, 31113 Dammam, Saudi ArabiaImage analysis by topological gradient approach is a technique based upon the historic application of the topological asymptotic expansion to crack localization problem from boundary measurements. This paper aims at reviewing this methodology through various applications in image processing; in particular image restoration with edge detection, classification and segmentation problems for both grey level and color images is presented in this work. The numerical experiments show the efficiency of the topological gradient approach for modelling and solving different image analysis problems. However, the topological gradient approach presents a major drawback: the identified edges are not connected and then the results obtained particularly for the segmentation problem can be degraded. To overcome this inconvenience, we propose an alternative solution by combining the topological gradient approach with the watershed technique. The numerical results obtained using the coupled method are very interesting.http://dx.doi.org/10.1155/2010/761783 |
| spellingShingle | Lamia Jaafar Belaid An Overview of the Topological Gradient Approach in Image Processing: Advantages and Inconveniences Journal of Applied Mathematics |
| title | An Overview of the Topological Gradient Approach in Image Processing: Advantages and Inconveniences |
| title_full | An Overview of the Topological Gradient Approach in Image Processing: Advantages and Inconveniences |
| title_fullStr | An Overview of the Topological Gradient Approach in Image Processing: Advantages and Inconveniences |
| title_full_unstemmed | An Overview of the Topological Gradient Approach in Image Processing: Advantages and Inconveniences |
| title_short | An Overview of the Topological Gradient Approach in Image Processing: Advantages and Inconveniences |
| title_sort | overview of the topological gradient approach in image processing advantages and inconveniences |
| url | http://dx.doi.org/10.1155/2010/761783 |
| work_keys_str_mv | AT lamiajaafarbelaid anoverviewofthetopologicalgradientapproachinimageprocessingadvantagesandinconveniences AT lamiajaafarbelaid overviewofthetopologicalgradientapproachinimageprocessingadvantagesandinconveniences |