Fast Mumford-Shah Two-Phase Image Segmentation Using Proximal Splitting Scheme
The Mumford-Shah model is extensively used in image segmentation. Its energy functional causes the content of the segments to remain homogeneous and the segment boundaries to become short. However, the problem is that optimization of the functional can be very slow. To attack this problem, we propos...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/6618505 |
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| author | Nilima Shah Dhanesh Patel Pasi Fränti |
| author_facet | Nilima Shah Dhanesh Patel Pasi Fränti |
| author_sort | Nilima Shah |
| collection | DOAJ |
| description | The Mumford-Shah model is extensively used in image segmentation. Its energy functional causes the content of the segments to remain homogeneous and the segment boundaries to become short. However, the problem is that optimization of the functional can be very slow. To attack this problem, we propose a reduced two-phase Mumford-Shah model to segment images having one prominent object. First, initial segmentation is obtained by the k-means clustering technique, further minimizing the Mumford-Shah functional by the Douglas-Rachford algorithm. Evaluation of segmentations with various error metrics shows that 70 percent of the segmentations keep the error values below 50%. Compared to the level set method to solve the Chan-Vese model, our algorithm is significantly faster. At the same time, it gives almost the same or better segmentation results. When compared to the recent k-means variant, it also gives much better segmentation with convex boundaries. The proposed algorithm balances well between time and quality of the segmentation. A crucial step in the design of machine vision systems is the extraction of discriminant features from the images, which is based on low-level segmentation which can be obtained by our approach. |
| format | Article |
| id | doaj-art-5442b87951934fac951a506023afaea9 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-5442b87951934fac951a506023afaea92025-02-03T01:32:25ZengWileyJournal of Applied Mathematics1110-757X1687-00422021-01-01202110.1155/2021/66185056618505Fast Mumford-Shah Two-Phase Image Segmentation Using Proximal Splitting SchemeNilima Shah0Dhanesh Patel1Pasi Fränti2Department of Applied Mathematics, Faculty of Technology and Engineering, The Maharaja Sayajirao University of Baroda, Vadodara, Gujarat, IndiaDepartment of Applied Mathematics, Faculty of Technology and Engineering, The Maharaja Sayajirao University of Baroda, Vadodara, Gujarat, IndiaSchool of Computing, University of Eastern Finland, Joensuu, FinlandThe Mumford-Shah model is extensively used in image segmentation. Its energy functional causes the content of the segments to remain homogeneous and the segment boundaries to become short. However, the problem is that optimization of the functional can be very slow. To attack this problem, we propose a reduced two-phase Mumford-Shah model to segment images having one prominent object. First, initial segmentation is obtained by the k-means clustering technique, further minimizing the Mumford-Shah functional by the Douglas-Rachford algorithm. Evaluation of segmentations with various error metrics shows that 70 percent of the segmentations keep the error values below 50%. Compared to the level set method to solve the Chan-Vese model, our algorithm is significantly faster. At the same time, it gives almost the same or better segmentation results. When compared to the recent k-means variant, it also gives much better segmentation with convex boundaries. The proposed algorithm balances well between time and quality of the segmentation. A crucial step in the design of machine vision systems is the extraction of discriminant features from the images, which is based on low-level segmentation which can be obtained by our approach.http://dx.doi.org/10.1155/2021/6618505 |
| spellingShingle | Nilima Shah Dhanesh Patel Pasi Fränti Fast Mumford-Shah Two-Phase Image Segmentation Using Proximal Splitting Scheme Journal of Applied Mathematics |
| title | Fast Mumford-Shah Two-Phase Image Segmentation Using Proximal Splitting Scheme |
| title_full | Fast Mumford-Shah Two-Phase Image Segmentation Using Proximal Splitting Scheme |
| title_fullStr | Fast Mumford-Shah Two-Phase Image Segmentation Using Proximal Splitting Scheme |
| title_full_unstemmed | Fast Mumford-Shah Two-Phase Image Segmentation Using Proximal Splitting Scheme |
| title_short | Fast Mumford-Shah Two-Phase Image Segmentation Using Proximal Splitting Scheme |
| title_sort | fast mumford shah two phase image segmentation using proximal splitting scheme |
| url | http://dx.doi.org/10.1155/2021/6618505 |
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