Nonlinear PDE based numerical methods for cell tracking in zebrafish embryogenesis

Mikula, Karol; Špir, Róbert; Smíšek, Michal; Faure, Emmanuel; Peyriéras, Nadine

doi:10.1016/j.apnum.2014.09.002

Cited by 8 publications

(4 citation statements)

References 18 publications

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“…which yield equation (22). Hence, the numerical scheme given by equation ( 20) is unconditionally stable.…”

Section: Stability Of the Numerical Schemementioning

confidence: 96%

“…Next, we show that the scheme is unconditionally stable. For this, it is enough to show that equation (20) satisfies (22). Clearly, equation ( 20) is same as…”

Section: Stability Of the Numerical Schemementioning

confidence: 99%

“…In this section, the results of cell tracking based on the 4D segmentation method are presented. The cell tracking procedure is briefly described below, and details of the algorithm are given in [32]; for previous works on cell tracking, see [21,22,23,39].…”

Section: Cell Tracking Based On 4d Segmentationmentioning

confidence: 99%

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4D Segmentation Algorithm with application to 3D+time Image Segmentation

Uba¹,

Mikula²,

Park³

2021

Preprint

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“…which yield equation (22). Hence, the numerical scheme given by equation ( 20) is unconditionally stable.…”

Section: Stability Of the Numerical Schemementioning

confidence: 96%

“…Next, we show that the scheme is unconditionally stable. For this, it is enough to show that equation (20) satisfies (22). Clearly, equation ( 20) is same as…”

Section: Stability Of the Numerical Schemementioning

confidence: 99%

See 1 more Smart Citation

4D Segmentation Algorithm with application to 3D+time Image Segmentation

Uba¹,

Mikula²,

Park³

2021

Preprint

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“…To improve the results, the next step was considering 4D ellipsoids constructed also in the time dimension. Using such time overlapping we were able to achieve connected trajectories (close gaps) even in cases when the cell nuclei are missing in single time step [7,8]. We improved the approximation of cell nuclei by using the diameters of 4D ellipsoid from performed segmentations of each single cell in the whole dataset so each 4D ellipsoid is unique and is approximating the corresponding cell.…”

Section: Image Processing Workflowmentioning

confidence: 99%

Parallelization and Validation of Algorithms for Zebrafish Cell Lineage Tree Reconstruction from Big 4D Image Data

Špir¹,

Mikula²,

Peyriéras³

2017

ACTA POLYTECH HUNG

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The paper presents numerical algorithms, post processing and validation steps for an automated cell tracking and cell lineage tree reconstruction from large-scale 3D+time two-photon laser scanning microscopy images of early stages of Zebrafish (Danio rerio) embryo development. The cell trajectories are extracted as centered paths inside segmented spatio-temporal tree structures representing cell movements and divisions. Such paths are found by using a suitably designed and computed constrained distance functions and by a backtracking in the steepest descent direction of a potential field based on a combination of these distance functions combination. Since the calculations are performed on big data, parallelization is required to speed up the processing. By careful choice and tuning of algorithm parameters we can adapt the calculations to the microscope images of vertebrae species. Then we can compare the results with ground truth data obtained by manual checking of cell links by biologists and measure the accuracy of our algorithm. Using an automatic validation process and visualization tool that can display ground truth data and our result simultaneously, along with the original 3D data, we can easily verify the correctness of the tracking.

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