October  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).   Google Scholar

[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.   Google Scholar

[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.   Google Scholar

[4]

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

[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.  Google Scholar

[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.   Google Scholar

[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.  Google Scholar

[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.   Google Scholar

[9]

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

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

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).   Google Scholar

[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.   Google Scholar

[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.   Google Scholar

[4]

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

[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.  Google Scholar

[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.   Google Scholar

[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.  Google Scholar

[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.   Google Scholar

[9]

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

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[1]

H. M. Srivastava, H. I. Abdel-Gawad, Khaled Mohammed Saad. Oscillatory states and patterns formation in a two-cell cubic autocatalytic reaction-diffusion model subjected to the Dirichlet conditions. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020433

[2]

Liping Tang, Ying Gao. Some properties of nonconvex oriented distance function and applications to vector optimization problems. Journal of Industrial & Management Optimization, 2021, 17 (1) : 485-500. doi: 10.3934/jimo.2020117

[3]

Mehdi Bastani, Davod Khojasteh Salkuyeh. On the GSOR iteration method for image restoration. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 27-43. doi: 10.3934/naco.2020013

[4]

Yifan Chen, Thomas Y. Hou. Function approximation via the subsampled Poincaré inequality. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 169-199. doi: 10.3934/dcds.2020296

[5]

Abdelghafour Atlas, Mostafa Bendahmane, Fahd Karami, Driss Meskine, Omar Oubbih. A nonlinear fractional reaction-diffusion system applied to image denoising and decomposition. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020321

[6]

Cheng Peng, Zhaohui Tang, Weihua Gui, Qing Chen, Jing He. A bidirectional weighted boundary distance algorithm for time series similarity computation based on optimized sliding window size. Journal of Industrial & Management Optimization, 2021, 17 (1) : 205-220. doi: 10.3934/jimo.2019107

[7]

Neng Zhu, Zhengrong Liu, Fang Wang, Kun Zhao. Asymptotic dynamics of a system of conservation laws from chemotaxis. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 813-847. doi: 10.3934/dcds.2020301

[8]

Bahaaeldin Abdalla, Thabet Abdeljawad. Oscillation criteria for kernel function dependent fractional dynamic equations. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020443

[9]

Jia Cai, Guanglong Xu, Zhensheng Hu. Sketch-based image retrieval via CAT loss with elastic net regularization. Mathematical Foundations of Computing, 2020, 3 (4) : 219-227. doi: 10.3934/mfc.2020013

[10]

Xuhui Peng, Rangrang Zhang. Approximations of stochastic 3D tamed Navier-Stokes equations. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5337-5365. doi: 10.3934/cpaa.2020241

[11]

Jiahao Qiu, Jianjie Zhao. Maximal factors of order $ d $ of dynamical cubespaces. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 601-620. doi: 10.3934/dcds.2020278

[12]

Yi An, Bo Li, Lei Wang, Chao Zhang, Xiaoli Zhou. Calibration of a 3D laser rangefinder and a camera based on optimization solution. Journal of Industrial & Management Optimization, 2021, 17 (1) : 427-445. doi: 10.3934/jimo.2019119

[13]

Weiwei Liu, Jinliang Wang, Yuming Chen. Threshold dynamics of a delayed nonlocal reaction-diffusion cholera model. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020316

[14]

Manil T. Mohan. First order necessary conditions of optimality for the two dimensional tidal dynamics system. Mathematical Control & Related Fields, 2020  doi: 10.3934/mcrf.2020045

[15]

Cuicui Li, Lin Zhou, Zhidong Teng, Buyu Wen. The threshold dynamics of a discrete-time echinococcosis transmission model. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020339

[16]

Shao-Xia Qiao, Li-Jun Du. Propagation dynamics of nonlocal dispersal equations with inhomogeneous bistable nonlinearity. Electronic Research Archive, , () : -. doi: 10.3934/era.2020116

[17]

Ebraheem O. Alzahrani, Muhammad Altaf Khan. Androgen driven evolutionary population dynamics in prostate cancer growth. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020426

[18]

Lingfeng Li, Shousheng Luo, Xue-Cheng Tai, Jiang Yang. A new variational approach based on level-set function for convex hull problem with outliers. Inverse Problems & Imaging, , () : -. doi: 10.3934/ipi.2020070

[19]

Mohammed Abdulrazaq Kahya, Suhaib Abduljabbar Altamir, Zakariya Yahya Algamal. Improving whale optimization algorithm for feature selection with a time-varying transfer function. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 87-98. doi: 10.3934/naco.2020017

[20]

Xin-Guang Yang, Lu Li, Xingjie Yan, Ling Ding. The structure and stability of pullback attractors for 3D Brinkman-Forchheimer equation with delay. Electronic Research Archive, 2020, 28 (4) : 1395-1418. doi: 10.3934/era.2020074

2019 Impact Factor: 1.233

Metrics

  • PDF downloads (56)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]