New robust algorithm for tracking cells in videos of drosophila morphogenesis based on finding an ideal path in segmented spatio-temporal cellular structures

Abstract

In this paper, we present a novel algorithm for tracking cells in time lapse confocal microscopy movie of a Drosophila epithelial tissue during pupal morphogenesis. We consider a 2D + time video as a 3D static image, where frames are stacked atop each other, and using a spatio-temporal segmentation algorithm we obtain information about spatio-temporal 3D tubes representing evolutions of cells. The main idea for tracking is the usage of two distance functions--first one from the cells in the initial frame and second one from segmented boundaries. We track the cells backwards in time. The first distance function attracts the subsequently constructed cell trajectories to the cells in the initial frame and the second one forces them to be close to centerlines of the segmented tubular structures. This makes our tracking algorithm robust against noise and missing spatio-temporal boundaries. This approach can be generalized to a 3D + time video analysis, where spatio-temporal tubes are 4D objects.

Nonlinear PDE based numerical methods for cell tracking in zebrafish embryogenesis

“…In this paper we suggest new PDE based cell tracking method for such complex stages of zebrafish embryogenesis. In the present work we continue the effort started in [1,17] devoted to 2D+time and 3D+time cells tracking. In contrast to [13], in our approach we first extract all possible cell trajectories inside the 3D+time data and then the cell lineage tree is reconstructed by finding merging trajectories going backward in time.…”

“…The usage of membrane images for the cell tracking would be very natural, cf. [1], but the quality of currently produced 3D membrane images is not sufficient for our purposes. In Fig.…”

“…From a mathematical point of view, the 3D+time image sequence is understood as a function u( 1], where Λ is a bounded spatio-temporal (rectangular) subdomain of R 4 . When we consider processing of 3D images, in Sections 2 and 3, we consider u at a corresponding time step θ , but for simplicity we denote it as u(x) = u(x 1 , x 2 , x 3 ) omitting the θ variable.…”

“…cell nuclei, and spurious inner structures which still remain after GMCF filtering. For cell nuclei, the diameter d is relatively large, 0 c 1 ≤ d ≤ c 2 , while the diameter of the spurious inner structures is much smaller, 0 < d c 1 . If the level sets are moving (advected) at a constant speed in the direction of the inner normal, the encompassed volume is decreasing and finally the hump disappears.…”

“…Such construction of the combined distance function D will help us to get all, also partial, cell trajectories contained in our 4D spatio-temporal tree structures. Its utilization represents a main important novelty with respect to [1,17] where just D = D 1 was used so only cell trajectories starting in the first frame could be detected. In order to construct the combined distance function D, first we define a set of values…”