2015, 8(5): 953-967. doi: 10.3934/dcdss.2015.8.953

Numerical algorithm for tracking cell dynamics in 4D biomedical images

1. 

Department of Mathematics, Slovak University of Technology, Radlinskeho 11, 813 68 Bratislava, Slovak Republic

2. 

Institut de Neurobiologie Alfred Fessard, CNRS UPR 3294, Av. de la Terrasse, 91198 Gif-sur-Yvette, France

Received  January 2014 Revised  July 2014 Published  July 2015

The paper presents new numerical algorithm for an automated cell tracking 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 steepest descent direction of a potential field based on these distance functions combination. The naturally parallelizable discretization of the eikonal equation which is used for computing distance functions is given and results of the tracking method for real 4D image data are presented and discussed.
Citation: Karol Mikula, Róbert Špir, Nadine Peyriéras. Numerical algorithm for tracking cell dynamics in 4D biomedical images. Discrete & Continuous Dynamical Systems - S, 2015, 8 (5) : 953-967. doi: 10.3934/dcdss.2015.8.953
References:
[1]

Y. Bellaīche, F. Bosveld, F. Graner, K. Mikula, M. Remešíková and M. Smíšek, New Robust Algorithm for Tracking Cells in Videos of Drosophila Morphogenesis Based on Finding an Ideal Path in Segmented Spatio-Temporal Cellular Structures,, Proceeding of the 33rd Annual International IEEE EMBS Conference, (2011).

[2]

P. Bourgine, R. Čunderlík, O. Drblíková, K. Mikula, N. Peyriéras, M. Remešíková, B. Rizzi and A. Sarti, 4D embryogenesis image analysis using PDE methods of image processing,, Kybernetika, 46 (2010), 226.

[3]

P. Bourgine, P. Frolkovič, K. Mikula, N. Peyriéras and M. Remešíková, Extraction of the intercellular skeleton from 2D microscope images of early embryogenesis,, Lecture Notes in Computer Science 5567 (Proceeding of the 2nd International Conference on Scale Space and Variational Methods in Computer Vision, (2009), 1.

[4]

V. Caselles, R. Kimmel and G. Sapiro, Geodesic active contours,, Computer Vision, (1995), 694. doi: 10.1109/ICCV.1995.466871.

[5]

Y. Chen, B. C. Vemuri and L. Wang, Image denoising and segmentation via nonlinear diffusion,, Comput. Math. Appl., 39 (2000), 131. doi: 10.1016/S0898-1221(00)00050-X.

[6]

P. Frolkovič, K. Mikula, N. Peyriéras and A. Sarti, A counting number of cells and cell segmentation using advection-diffusion equations,, Kybernetika, 43 (2007), 817.

[7]

S. Kichenassamy, A. Kumar, P. Olver, A. Tannenbaum and A. Yezzi, Conformal curvature flows: From phase transitions to active vision,, Arch. Rational Mech. Anal., 134 (1996), 275. doi: 10.1007/BF00379537.

[8]

Z. Krivá, K. Mikula, N. Peyriéras, B. Rizzi, A. Sarti and O. Stašová, 3D early embryogenesis image filtering by nonlinear partial differential equations,, Medical Image Analysis, 14 (2010), 510.

[9]

C. Melani, Algoritmos de Procesamiento de Imagenes Para la Reconstruccion Del Desarrollo Embrionario Del Pez Cebra,, Computer Science PhD Thesis, (2013).

[10]

K. Mikula, N. Peyriéras, M. Remešíková and M. Smíšek, 4D numerical schemes for cell image segmentation and tracking,, Finite Volumes in Complex Applications VI, 4 (2011), 6. doi: 10.1007/978-3-642-20671-9_73.

[11]

K. Mikula, N. Peyriéras, M. Remešíková and O. Stašová, Segmentation of 3D cell membrane images by PDE methods and its applications,, Computers in Biology and Medicine, 41 (2011), 326. doi: 10.1016/j.compbiomed.2011.03.010.

[12]

K. Mikula and J. Urbán, 3D curve evolution algorithm with tangential redistribution for a fully automatic finding of an ideal camera path in virtual colonoscopy,, Proceedings of the Third International Conference on Scale Space Methods and Variational Methods in ComputerVision, 6667 (2012), 640. doi: 10.1007/978-3-642-24785-9_54.

[13]

R. Mikut, T. Dickmeis, W. Driever, P. Geurts, F. A. Hamprecht, B. X. Kausler, M. J. Ledesma-Carbayo, R. Marée, K. Mikula, P. Pantazis, O. Ronneberger, A. Santos, R. Stotzka, U. Strähle and N. Peyriéras, Automated processing of zebrafish imaging data: A survey,, Zebrafish, 10 (2013), 401. doi: 10.1089/zeb.2013.0886.

[14]

E. Rouy and A. Tourin, Viscosity solutions approach to shape-from-shading,, SIAM Journal on Numerical Analysis, 29 (1992), 867. doi: 10.1137/0729053.

[15]

A. Sarti, R. Malladi and J. A. Sethian, Subjective surfaces: A method for completing missing boundaries,, Proceedings of the National Academy of Sciences of the UnitedStates of America, 97 (2000), 6258. doi: 10.1073/pnas.110135797.

[16]

C. Zanella, M. Campana, B. Rizzi, C. Melani, G. Sanguinetti, P. Bourgine, K. Mikula, N. Peyrieras and A. Sarti, Cells segmentation from 3-D confocal images of early zebrafish embryogenesis,, IEEE Transactions on Image Processing, 19 (2010), 770. doi: 10.1109/TIP.2009.2033629.

show all references

References:
[1]

Y. Bellaīche, F. Bosveld, F. Graner, K. Mikula, M. Remešíková and M. Smíšek, New Robust Algorithm for Tracking Cells in Videos of Drosophila Morphogenesis Based on Finding an Ideal Path in Segmented Spatio-Temporal Cellular Structures,, Proceeding of the 33rd Annual International IEEE EMBS Conference, (2011).

[2]

P. Bourgine, R. Čunderlík, O. Drblíková, K. Mikula, N. Peyriéras, M. Remešíková, B. Rizzi and A. Sarti, 4D embryogenesis image analysis using PDE methods of image processing,, Kybernetika, 46 (2010), 226.

[3]

P. Bourgine, P. Frolkovič, K. Mikula, N. Peyriéras and M. Remešíková, Extraction of the intercellular skeleton from 2D microscope images of early embryogenesis,, Lecture Notes in Computer Science 5567 (Proceeding of the 2nd International Conference on Scale Space and Variational Methods in Computer Vision, (2009), 1.

[4]

V. Caselles, R. Kimmel and G. Sapiro, Geodesic active contours,, Computer Vision, (1995), 694. doi: 10.1109/ICCV.1995.466871.

[5]

Y. Chen, B. C. Vemuri and L. Wang, Image denoising and segmentation via nonlinear diffusion,, Comput. Math. Appl., 39 (2000), 131. doi: 10.1016/S0898-1221(00)00050-X.

[6]

P. Frolkovič, K. Mikula, N. Peyriéras and A. Sarti, A counting number of cells and cell segmentation using advection-diffusion equations,, Kybernetika, 43 (2007), 817.

[7]

S. Kichenassamy, A. Kumar, P. Olver, A. Tannenbaum and A. Yezzi, Conformal curvature flows: From phase transitions to active vision,, Arch. Rational Mech. Anal., 134 (1996), 275. doi: 10.1007/BF00379537.

[8]

Z. Krivá, K. Mikula, N. Peyriéras, B. Rizzi, A. Sarti and O. Stašová, 3D early embryogenesis image filtering by nonlinear partial differential equations,, Medical Image Analysis, 14 (2010), 510.

[9]

C. Melani, Algoritmos de Procesamiento de Imagenes Para la Reconstruccion Del Desarrollo Embrionario Del Pez Cebra,, Computer Science PhD Thesis, (2013).

[10]

K. Mikula, N. Peyriéras, M. Remešíková and M. Smíšek, 4D numerical schemes for cell image segmentation and tracking,, Finite Volumes in Complex Applications VI, 4 (2011), 6. doi: 10.1007/978-3-642-20671-9_73.

[11]

K. Mikula, N. Peyriéras, M. Remešíková and O. Stašová, Segmentation of 3D cell membrane images by PDE methods and its applications,, Computers in Biology and Medicine, 41 (2011), 326. doi: 10.1016/j.compbiomed.2011.03.010.

[12]

K. Mikula and J. Urbán, 3D curve evolution algorithm with tangential redistribution for a fully automatic finding of an ideal camera path in virtual colonoscopy,, Proceedings of the Third International Conference on Scale Space Methods and Variational Methods in ComputerVision, 6667 (2012), 640. doi: 10.1007/978-3-642-24785-9_54.

[13]

R. Mikut, T. Dickmeis, W. Driever, P. Geurts, F. A. Hamprecht, B. X. Kausler, M. J. Ledesma-Carbayo, R. Marée, K. Mikula, P. Pantazis, O. Ronneberger, A. Santos, R. Stotzka, U. Strähle and N. Peyriéras, Automated processing of zebrafish imaging data: A survey,, Zebrafish, 10 (2013), 401. doi: 10.1089/zeb.2013.0886.

[14]

E. Rouy and A. Tourin, Viscosity solutions approach to shape-from-shading,, SIAM Journal on Numerical Analysis, 29 (1992), 867. doi: 10.1137/0729053.

[15]

A. Sarti, R. Malladi and J. A. Sethian, Subjective surfaces: A method for completing missing boundaries,, Proceedings of the National Academy of Sciences of the UnitedStates of America, 97 (2000), 6258. doi: 10.1073/pnas.110135797.

[16]

C. Zanella, M. Campana, B. Rizzi, C. Melani, G. Sanguinetti, P. Bourgine, K. Mikula, N. Peyrieras and A. Sarti, Cells segmentation from 3-D confocal images of early zebrafish embryogenesis,, IEEE Transactions on Image Processing, 19 (2010), 770. doi: 10.1109/TIP.2009.2033629.

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