GEOMETRIC ANALYSIS OF PLANAR SHAPES WITH APPLICATIONS TO CELL DEFORMATIONS
Shape analysis is of great importance in many fields such as computer vision, medical imaging, and computational biology. In this paper we focus on a shape space in which shapes are represented by means of planar closed curves. In this shape space a new metric was recently introduced with the result...
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| Format: | Article |
| Language: | English |
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Slovenian Society for Stereology and Quantitative Image Analysis
2015-09-01
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| Series: | Image Analysis and Stereology |
| Subjects: | |
| Online Access: | http://www.ias-iss.org/ojs/IAS/article/view/1151 |
| _version_ | 1811322675065257984 |
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| author | Ximo Gual-Arnau Silena Herold-García Amelia Simó |
| author_facet | Ximo Gual-Arnau Silena Herold-García Amelia Simó |
| author_sort | Ximo Gual-Arnau |
| collection | DOAJ |
| description | Shape analysis is of great importance in many fields such as computer vision, medical imaging, and computational biology. In this paper we focus on a shape space in which shapes are represented by means of planar closed curves. In this shape space a new metric was recently introduced with the result that this shape space has the property of being isometric to an infinite-dimensional Grassmann manifold of 2-dimensional subspaces. Using this isometry it is possible, from Younes et al. (2008), to explicitly describe geodesics, a task that previously was not at all easy. Our aim is twofold, namely: to use this general theory in order to show some applications to the study of erythrocytes, using digital images of peripheral blood smears, in the treatment of sickle cell disease; and, since normal erythrocytes are almost circular and many Sickle cells have elliptical shape, to particularize the computation of geodesics and distances between shapes using this metric to planar objects considered as deformations of a template (circle or ellipse). The applications considered include: shape interpolation, shape classification, and shape clustering. |
| first_indexed | 2024-04-13T13:39:19Z |
| format | Article |
| id | doaj.art-7070cdc03d4a49d3ad6d0d5339046d7b |
| institution | Directory Open Access Journal |
| issn | 1580-3139 1854-5165 |
| language | English |
| last_indexed | 2024-04-13T13:39:19Z |
| publishDate | 2015-09-01 |
| publisher | Slovenian Society for Stereology and Quantitative Image Analysis |
| record_format | Article |
| series | Image Analysis and Stereology |
| spelling | doaj.art-7070cdc03d4a49d3ad6d0d5339046d7b2022-12-22T02:44:41ZengSlovenian Society for Stereology and Quantitative Image AnalysisImage Analysis and Stereology1580-31391854-51652015-09-0134317118210.5566/ias.1151938GEOMETRIC ANALYSIS OF PLANAR SHAPES WITH APPLICATIONS TO CELL DEFORMATIONSXimo Gual-Arnau0Silena Herold-García1Amelia Simó2Departament de Matemàtiques-INIT. Universitat Jaume I.Department of Computing. Universidad de Oriente.University Jaume I Castellón SpainShape analysis is of great importance in many fields such as computer vision, medical imaging, and computational biology. In this paper we focus on a shape space in which shapes are represented by means of planar closed curves. In this shape space a new metric was recently introduced with the result that this shape space has the property of being isometric to an infinite-dimensional Grassmann manifold of 2-dimensional subspaces. Using this isometry it is possible, from Younes et al. (2008), to explicitly describe geodesics, a task that previously was not at all easy. Our aim is twofold, namely: to use this general theory in order to show some applications to the study of erythrocytes, using digital images of peripheral blood smears, in the treatment of sickle cell disease; and, since normal erythrocytes are almost circular and many Sickle cells have elliptical shape, to particularize the computation of geodesics and distances between shapes using this metric to planar objects considered as deformations of a template (circle or ellipse). The applications considered include: shape interpolation, shape classification, and shape clustering.http://www.ias-iss.org/ojs/IAS/article/view/1151cell deformationgeodesicsplanar closed curvesradius-vector functionshape space |
| spellingShingle | Ximo Gual-Arnau Silena Herold-García Amelia Simó GEOMETRIC ANALYSIS OF PLANAR SHAPES WITH APPLICATIONS TO CELL DEFORMATIONS Image Analysis and Stereology cell deformation geodesics planar closed curves radius-vector function shape space |
| title | GEOMETRIC ANALYSIS OF PLANAR SHAPES WITH APPLICATIONS TO CELL DEFORMATIONS |
| title_full | GEOMETRIC ANALYSIS OF PLANAR SHAPES WITH APPLICATIONS TO CELL DEFORMATIONS |
| title_fullStr | GEOMETRIC ANALYSIS OF PLANAR SHAPES WITH APPLICATIONS TO CELL DEFORMATIONS |
| title_full_unstemmed | GEOMETRIC ANALYSIS OF PLANAR SHAPES WITH APPLICATIONS TO CELL DEFORMATIONS |
| title_short | GEOMETRIC ANALYSIS OF PLANAR SHAPES WITH APPLICATIONS TO CELL DEFORMATIONS |
| title_sort | geometric analysis of planar shapes with applications to cell deformations |
| topic | cell deformation geodesics planar closed curves radius-vector function shape space |
| url | http://www.ias-iss.org/ojs/IAS/article/view/1151 |
| work_keys_str_mv | AT ximogualarnau geometricanalysisofplanarshapeswithapplicationstocelldeformations AT silenaheroldgarcia geometricanalysisofplanarshapeswithapplicationstocelldeformations AT ameliasimo geometricanalysisofplanarshapeswithapplicationstocelldeformations |