Euclidean Distance-Based Skeletons: A Few Notes on Average Outward Flux and Ridgeness
| Autor: | Aurélie Leborgne, Julien Mille, Laure Tougne |
|---|---|
| Přispěvatelé: | Laboratoire d'Informatique Fondamentale et Appliquée de Tours (LIFAT), Université de Tours (UT)-Institut National des Sciences Appliquées - Centre Val de Loire (INSA CVL), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Institut Pascal (IP), SIGMA Clermont (SIGMA Clermont)-Université Clermont Auvergne [2017-2020] (UCA [2017-2020])-Centre National de la Recherche Scientifique (CNRS), Extraction de Caractéristiques et Identification (imagine), Laboratoire d'InfoRmatique en Image et Systèmes d'information (LIRIS), Université Lumière - Lyon 2 (UL2)-École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Université Lumière - Lyon 2 (UL2)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université de Tours-Institut National des Sciences Appliquées - Centre Val de Loire (INSA CVL), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA), Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-École Centrale de Lyon (ECL), Université de Lyon-Université Lumière - Lyon 2 (UL2)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Université Lumière - Lyon 2 (UL2), Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL) |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
geography geography.geographical_feature_category Applied Mathematics [INFO.INFO-CV]Computer Science [cs]/Computer Vision and Pattern Recognition [cs.CV] Geometry Context (language use) 02 engineering and technology Skeleton (category theory) Condensed Matter Physics Measure (mathematics) Euclidean distance Maxima and minima Ridge Modeling and Simulation [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV] 0202 electrical engineering electronic engineering information engineering 020201 artificial intelligence & image processing Geometry and Topology Computer Vision and Pattern Recognition Focus (optics) Distance transform Mathematics |
| Zdroj: | International Journal of Mathematical Imaging and Vision International Journal of Mathematical Imaging and Vision, 2019, 61 (3), pp.310-330. ⟨10.1007/s10851-018-0836-7⟩ International Journal of Mathematical Imaging and Vision, Springer Verlag, 2019, 61 (3), pp.310-330. ⟨10.1007/s10851-018-0836-7⟩ |
| ISSN: | 0924-9907 |
| DOI: | 10.1007/s10851-018-0836-7⟩ |
| Popis: | International audience; Among the various existing and mathematically equivalent definitions of the skeleton, we consider the set of critical points of the Euclidean distance transform of the shape. The problem of detecting these points and using them to generate a skeleton that is stable , thin and homotopic to the shape has been the focus of numerous papers. Skeleton branches correspond to ridges of the distance map, i.e. continuous lines of points that are local maxima of the distance in at least one direction. Extracting these ridges is a non-trivial task on a discrete grid. In this context, the average outward flux, used in the Hamilton-Jacobi skeleton [43], and the ridgeness measure [28] have been proposed as ridge detectors. We establish the mathematical relation between these detectors and, extending the work in [18], we study various local shape configurations, on which closed-form expressions or approximations of the average outward flux and ridgeness can be derived. In addition , we conduct experiments to assess the accuracy of skeletons generated using these measures, and study the influence of their respective parameters. |
| Databáze: | OpenAIRE |
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