Extraction of the Intercellular Skeleton from 2D Images of Embryogenesis Using Eikonal Equation and Advective Subjective Surface Method

Authors:
Paul Bourgine;Peter Frolkovič;Karol Mikula;Nadine Peyriéras;Mariana Remešíková
Affiliations:
CREA, Ecole Polytechnique-CNRS, Paris, France 75005;Department of Mathematics, Slovak University of Technology, Bratislava, 81368;Department of Mathematics, Slovak University of Technology, Bratislava, 81368;CNRS-DEPSN, Gif-sur-Yvette, France 91198;Department of Mathematics, Slovak University of Technology, Bratislava, 81368
Venue:
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Year:
2009

Citing 2
Cited 2

A viscosity solutions approach to shape-from-shading

SIAM Journal on Numerical Analysis
Fast Surface Reconstruction Using the Level Set Method

VLSM '01 Proceedings of the IEEE Workshop on Variational and Level Set Methods (VLSM'01)

Segmentation of 3D cell membrane images by PDE methods and its applications

Computers in Biology and Medicine
3D curve evolution algorithm with tangential redistribution for a fully automatic finding of an ideal camera path in virtual colonoscopy

SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision

Quantified Score

Hi-index	0.00

Visualization

Abstract

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 skeleton extracted from a 2D image of a zebrafish embryo.