ON OPTIMAL 2-D DOMAIN SEGMENTATION PROBLEM VIA PIECEWISE SMOOTH APPROXIMATION OF A SELECTIVE TARGET MAPPING
In this paper we propose a new technique for the solution of the image segmentation problem which is based on the concept of a piecewise smooth approximation of some target functional. We discuss in details the consistency of the new statement of segmentation problem and its solvability. We focus ou...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Oles Honchar Dnipro National University
2019-10-01
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| Series: | Journal of Optimization, Differential Equations and Their Applications |
| Subjects: | |
| Online Access: | https://model-dnu.dp.ua/index.php/SM/article/view/139 |
| _version_ | 1818313290821926912 |
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| author | Volodymyr V. Hnatushenko Peter I. Kogut Mykola V. Uvarov |
| author_facet | Volodymyr V. Hnatushenko Peter I. Kogut Mykola V. Uvarov |
| author_sort | Volodymyr V. Hnatushenko |
| collection | DOAJ |
| description | In this paper we propose a new technique for the solution of the image segmentation problem which is based on the concept of a piecewise smooth approximation of some target functional. We discuss in details the consistency of the new statement of segmentation problem and its solvability. We focus our main intension on the rigor mathematical substantiation of the proposed approach, deriving the corresponding optimality conditions, and show that the new optimization problem is rather flexible and powerful model to the study of variational image segmentation problems. We illustrate the accuracy and efficiency of the proposed algorithm by numerical experiences. |
| first_indexed | 2024-12-13T08:31:24Z |
| format | Article |
| id | doaj.art-641e56287a99422990d22de138121b87 |
| institution | Directory Open Access Journal |
| issn | 2617-0108 2663-6824 |
| language | English |
| last_indexed | 2024-12-13T08:31:24Z |
| publishDate | 2019-10-01 |
| publisher | Oles Honchar Dnipro National University |
| record_format | Article |
| series | Journal of Optimization, Differential Equations and Their Applications |
| spelling | doaj.art-641e56287a99422990d22de138121b872022-12-21T23:53:46ZengOles Honchar Dnipro National UniversityJournal of Optimization, Differential Equations and Their Applications2617-01082663-68242019-10-01272609510.15421/141908131ON OPTIMAL 2-D DOMAIN SEGMENTATION PROBLEM VIA PIECEWISE SMOOTH APPROXIMATION OF A SELECTIVE TARGET MAPPINGVolodymyr V. Hnatushenko0Peter I. Kogut1Mykola V. Uvarov2Department of Information Systems and Technologies, Dnipro University of TechnologyDepartment of Differential Equations, Oles Honchar Dnipro National UniversityEOS Data Analytics UkraineIn this paper we propose a new technique for the solution of the image segmentation problem which is based on the concept of a piecewise smooth approximation of some target functional. We discuss in details the consistency of the new statement of segmentation problem and its solvability. We focus our main intension on the rigor mathematical substantiation of the proposed approach, deriving the corresponding optimality conditions, and show that the new optimization problem is rather flexible and powerful model to the study of variational image segmentation problems. We illustrate the accuracy and efficiency of the proposed algorithm by numerical experiences.https://model-dnu.dp.ua/index.php/SM/article/view/139optimal segmentation problempiecewise constant approximationoptimality conditionsvariational problem |
| spellingShingle | Volodymyr V. Hnatushenko Peter I. Kogut Mykola V. Uvarov ON OPTIMAL 2-D DOMAIN SEGMENTATION PROBLEM VIA PIECEWISE SMOOTH APPROXIMATION OF A SELECTIVE TARGET MAPPING Journal of Optimization, Differential Equations and Their Applications optimal segmentation problem piecewise constant approximation optimality conditions variational problem |
| title | ON OPTIMAL 2-D DOMAIN SEGMENTATION PROBLEM VIA PIECEWISE SMOOTH APPROXIMATION OF A SELECTIVE TARGET MAPPING |
| title_full | ON OPTIMAL 2-D DOMAIN SEGMENTATION PROBLEM VIA PIECEWISE SMOOTH APPROXIMATION OF A SELECTIVE TARGET MAPPING |
| title_fullStr | ON OPTIMAL 2-D DOMAIN SEGMENTATION PROBLEM VIA PIECEWISE SMOOTH APPROXIMATION OF A SELECTIVE TARGET MAPPING |
| title_full_unstemmed | ON OPTIMAL 2-D DOMAIN SEGMENTATION PROBLEM VIA PIECEWISE SMOOTH APPROXIMATION OF A SELECTIVE TARGET MAPPING |
| title_short | ON OPTIMAL 2-D DOMAIN SEGMENTATION PROBLEM VIA PIECEWISE SMOOTH APPROXIMATION OF A SELECTIVE TARGET MAPPING |
| title_sort | on optimal 2 d domain segmentation problem via piecewise smooth approximation of a selective target mapping |
| topic | optimal segmentation problem piecewise constant approximation optimality conditions variational problem |
| url | https://model-dnu.dp.ua/index.php/SM/article/view/139 |
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