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Article: Numerical methods for interactive multiple-class image segmentation problems
Title | Numerical methods for interactive multiple-class image segmentation problems |
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Authors | |
Keywords | M-matrix Image segmentation Domain decomposition Discrete maximum principle Condition numbers Boundary conditions |
Issue Date | 2010 |
Citation | International Journal of Imaging Systems and Technology, 2010, v. 20, n. 3, p. 191-201 How to Cite? |
Abstract | In this article, we consider a bilaterally constrained optimization model arising from the semisupervised multiple-class image segmentation problem. We prove that the solution of the corresponding unconstrained problem satisfies a discrete maximum principle. This implies that the bilateral constraints are satisfied automatically and that the solution is unique. Although the structure of the coefficient matrices arising from the optimality conditions of the segmentation problem is different for different input images, we show that they are M-matrices in general. Therefore, we study several numerical methods for solving such linear systems and demonstrate that domain decomposition with block relaxation methods are quite effective and outperform other tested methods. We also carry out a numerical study of condition numbers on the effect of boundary conditions on the optimization problems, which provides some insights into the specification of boundary conditions as an input knowledge in the learning context. © 2010 Wiley Periodicals, Inc. |
Persistent Identifier | http://hdl.handle.net/10722/276874 |
ISSN | 2023 Impact Factor: 3.0 2023 SCImago Journal Rankings: 0.706 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Ng, Michael K. | - |
dc.contributor.author | Qiu, Guoping | - |
dc.contributor.author | Yip, Andy M. | - |
dc.date.accessioned | 2019-09-18T08:34:55Z | - |
dc.date.available | 2019-09-18T08:34:55Z | - |
dc.date.issued | 2010 | - |
dc.identifier.citation | International Journal of Imaging Systems and Technology, 2010, v. 20, n. 3, p. 191-201 | - |
dc.identifier.issn | 0899-9457 | - |
dc.identifier.uri | http://hdl.handle.net/10722/276874 | - |
dc.description.abstract | In this article, we consider a bilaterally constrained optimization model arising from the semisupervised multiple-class image segmentation problem. We prove that the solution of the corresponding unconstrained problem satisfies a discrete maximum principle. This implies that the bilateral constraints are satisfied automatically and that the solution is unique. Although the structure of the coefficient matrices arising from the optimality conditions of the segmentation problem is different for different input images, we show that they are M-matrices in general. Therefore, we study several numerical methods for solving such linear systems and demonstrate that domain decomposition with block relaxation methods are quite effective and outperform other tested methods. We also carry out a numerical study of condition numbers on the effect of boundary conditions on the optimization problems, which provides some insights into the specification of boundary conditions as an input knowledge in the learning context. © 2010 Wiley Periodicals, Inc. | - |
dc.language | eng | - |
dc.relation.ispartof | International Journal of Imaging Systems and Technology | - |
dc.subject | M-matrix | - |
dc.subject | Image segmentation | - |
dc.subject | Domain decomposition | - |
dc.subject | Discrete maximum principle | - |
dc.subject | Condition numbers | - |
dc.subject | Boundary conditions | - |
dc.title | Numerical methods for interactive multiple-class image segmentation problems | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1002/ima.20238 | - |
dc.identifier.scopus | eid_2-s2.0-77958070485 | - |
dc.identifier.volume | 20 | - |
dc.identifier.issue | 3 | - |
dc.identifier.spage | 191 | - |
dc.identifier.epage | 201 | - |
dc.identifier.eissn | 1098-1098 | - |
dc.identifier.isi | WOS:000280966800001 | - |
dc.identifier.issnl | 0899-9457 | - |