Extraction of the intercellular skeleton from 2D images of embryogenesis using eikonal equation and advective subjective surface method

Paul Bourgine (1, 2) , Peter Frolkovic (3) , Karol Mikula (3) , Nadine Peyriéras (4, 5, 6) , Mariana Remesikova (3)

1 CREA - Centre de recherche en épistémologie appliquée
2 RNSC - Réseau National des Systèmes Complexes
3 STUBA - Department of Mathematics
4 N&eD - Neurobiologie et Développement
5 ISC-PIF - Institut des Systèmes Complexes - Paris Ile-de-France
6 INAF - Institut de Neurobiologie Alfred Fessard

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.

Domaines: Neurosciences [q-bio.NC]

Paul Bourgine, Peter Frolkovic, Karol Mikula, Nadine Peyriéras, Mariana Remesikova. Extraction of the intercellular skeleton from 2D images of embryogenesis using eikonal equation and advective subjective surface method. 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⟩. ⟨hal-00723370⟩