Extraction of the Intercellular Skeleton from 2D Images of Embryogenesis Using Eikonal Equation and Advective Subjective Surface Method
| Autor: | Mariana Remešíková, Peter Frolkovič, Nadine Peyriéras, Paul Bourgine, Karol Mikula |
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| Přispěvatelé: | Centre de recherche en épistémologie appliquée (CREA), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), Réseau National des Systèmes Complexes (RNSC), Centre de Coopération Internationale en Recherche Agronomique pour le Développement (Cirad)-Institut National de la Recherche Agronomique (INRA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Français de Recherche pour l'Exploitation de la Mer (IFREMER)-Institut National de la Santé et de la Recherche Médicale (INSERM)-CGE-CPU-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics (STUBA), Slovak University of Technology in Bratislava, Neurobiologie et Développement (N&eD), Centre National de la Recherche Scientifique (CNRS), Institut des Systèmes Complexes - Paris Ile-de-France (ISC-PIF), École normale supérieure - Cachan (ENS Cachan)-Université Paris 1 Panthéon-Sorbonne (UP1)-Université Paris-Sud - Paris 11 (UP11)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS)-Institut Curie [Paris]-École polytechnique (X), Institut de Neurobiologie Alfred Fessard (INAF), Xue-Cheng Tai, Knut Morken, Marius Lysaker, Knut-Andreas Lie, Centre National de la Recherche Scientifique (CNRS)-CPU-CGE-Institut National de la Santé et de la Recherche Médicale (INSERM)-Institut Français de Recherche pour l'Exploitation de la Mer (IFREMER)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de la Recherche Agronomique (INRA)-Centre de Coopération Internationale en Recherche Agronomique pour le Développement (Cirad), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), École normale supérieure - Cachan (ENS Cachan)-Université Panthéon-Sorbonne (UP1)-Université Paris-Sud - Paris 11 (UP11)-Université Pierre et Marie Curie - Paris 6 (UPMC)-École polytechnique (X)-Institut Curie-Centre National de la Recherche Scientifique (CNRS), École normale supérieure - Cachan (ENS Cachan)-Université Paris 1 Panthéon-Sorbonne (UP1)-Université Paris-Sud - Paris 11 (UP11)-Université Pierre et Marie Curie - Paris 6 (UPMC)-École polytechnique (X)-Institut Curie [Paris]-Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 2009 |
| Předmět: |
Surface (mathematics)
Discretization Eikonal equation Computation Mathematical analysis Geometry Signed distance function 010103 numerical & computational mathematics 02 engineering and technology 01 natural sciences Quantitative Biology::Cell Behavior Image (mathematics) 0202 electrical engineering electronic engineering information engineering [SDV.NEU]Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC] 020201 artificial intelligence & image processing Segmentation Vector field 0101 mathematics Mathematics |
| Zdroj: | Lecture Notes in Computer Science ISBN: 9783642022555 SSVM Scale Space and Variational Methods in Computer Vision Xue-Cheng Tai, Knut Morken, Marius Lysaker, Knut-Andreas Lie. Scale Space and Variational Methods in Computer Vision, Springer Verlag, pp.38-49, 2009, Lecture Notes in Computer Science volume 5567, 9783642022555. ⟨10.1007/978-3-642-02256-2_4⟩ |
| DOI: | 10.1007/978-3-642-02256-2_4 |
| Popis: | 2nd International Conference on Scale Space and Variational Methods in Computer Vision,Voss, NORWAY, JUN 01-05, 2009; International audience; We suggest an efficient method for automatic detection of the intercellular skeleton in microscope images of early embryogenesis. The method is based on the solution of two advective PDEs. First, we solve numerically the time relaxed eikonal equation in order to obtain the signed distance function to a given set - a set of points representing cell centers or a set of closed curves representing segmented inner borders of cells. The second step is a segmentation process driven by the advective version of subjective surface equation where the velocity field is given by the gradient of the computed distance function. The first equation is discretized by Rouy-Tourin scheme and we suggest a fixing strategy that significantly improves the speed of the computation. The second equation is solved using a classical upwind strategy. We present several test examples and we show a practical application - the intercellular. |
| Databáze: | OpenAIRE |
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