dynamic spatial mixture modelling and its application in cell tracking - work in progress -
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Dynamic Spatial Mixture Modelling and its Application in Cell Tracking - Work in Progress -. Chunlin Ji & Mike West Department of Statistical Sciences, Duke University SMC Mid-Program Workshop February 19, 2009. Outline. Spatial Inhomogeneous Point Process - PowerPoint PPT PresentationTRANSCRIPT
Dynamic Spatial Mixture Dynamic Spatial Mixture Modelling and its Application in Modelling and its Application in
Cell TrackingCell Tracking- Work in Progress -- Work in Progress -
Chunlin Ji & Mike WestChunlin Ji & Mike WestDepartment of Statistical Department of Statistical
Sciences, Sciences, Duke UniversityDuke University
SMC Mid-Program WorkshopSMC Mid-Program WorkshopFebruary 19, 2009February 19, 2009
OutlineOutline Spatial Inhomogeneous Point ProcessSpatial Inhomogeneous Point Process
Dynamic Spatial Mixture ModellingDynamic Spatial Mixture Modelling
Particle Filter ImplementationParticle Filter Implementation
Cell Fluorescence Imaging TrackingCell Fluorescence Imaging Tracking
Conclusion and Future WorksConclusion and Future Works
IntroductionIntroduction
Dynamic spatial inhomogeneous Dynamic spatial inhomogeneous point processpoint process
Potential application areasPotential application areas Multi-target tracking, particularly for Multi-target tracking, particularly for
extended targetextended target Cell fluorescence imaging trackingCell fluorescence imaging tracking
Existing methodsExisting methods Probability hypothesis density (PHD) Probability hypothesis density (PHD)
filter filter (Vo and Ma, 2006; Clark et al., 2007)(Vo and Ma, 2006; Clark et al., 2007)
Poisson models for extended target Poisson models for extended target tracking tracking (Gilholm et al., 2005)(Gilholm et al., 2005)
Cell fluorescence dataCell fluorescence data
Spatial Poisson point Spatial Poisson point processprocess
Point process over SPoint process over S Intensity Intensity function function (())
Density: Density: ff(()=)=(()/)/ = = zz S S (z)dz (z)dz
Realized locations ZRealized locations ZNN={z={z11,...,z,...,zNN}}
LikelihoodLikelihood
Spatial Dirichlet process Spatial Dirichlet process mixture (DPM) model mixture (DPM) model (Ji et al. (Ji et al.
2009)2009)
Flexible model for spatially varying Flexible model for spatially varying ff(())
Bivariate Gaussian mixture ff(())
Hierarchical DP prior over Hierarchical DP prior over parametersparameters
Dynamic Spatial DPM Dynamic Spatial DPM (DSDPM)(DSDPM)
DPM at each time pointDPM at each time point
Time evolution of mixture model Time evolution of mixture model parameters induces dynamic model for parameters induces dynamic model for time-varying intensity functiontime-varying intensity function
Dynamic spatial point process
Intensity function
Zt-1 Zt Zt+1
Parameters of DPMs
t-
1()t() t+1(
)
t-1
t
t+1
How points “move” in How points “move” in DSDPMDSDPM
Generalized Polya Urn scheme Generalized Polya Urn scheme (Caron et al., 2007)
(4) t
(2) t|t-1
(3) t|t-1
(1) t-1
Dynamic model for cellsDynamic model for cells
Component locations: Component locations: i,ti,t={={i,ti,t, s, si,ti,t}, }, i,ti,t ~ position of cells ~ position of cells
ssi,ti,t ~ parameters describing shape/appearance ~ parameters describing shape/appearance of cellsof cells
“Near constant” velocity model for i,t i,t and s and si,ti,t
Split process to simulate cell division:Split process to simulate cell division: - e.g. if s- e.g. if si,ti,t says cell is “large”, then cell splits says cell is “large”, then cell splits
Particle filter Particle filter implementationimplementation
At time At time tt 2 2 For each particle For each particle ii=1,...,=1,...,NN
Evolve Evolve mmtt((ii)) according to the Generalized Polya according to the Generalized Polya
UrnUrn Update i,t i,t and s and si,t i,t via near constant velocity
model Split processSplit process Sample cSample ctt
((ii)) qq(c(ctt||mmtt((ii)),,t|t-t|t-11
((ii)),Z,Ztt)) Sample Sample tt
((ii)) qq((tt||t|t-t|t-11((ii)),c,ctt
((ii)), Z, Ztt)) Compute importance weightsCompute importance weights
Resampling if neededResampling if needed
Tracking resultTracking result
Cells represented by blue color are segmented from the original movie Cells represented by blue color are segmented from the original movie Green dots are the estimation of center positions of cells from the PF.Green dots are the estimation of center positions of cells from the PF.
Trajectory of cellsTrajectory of cells
Further workFurther work
Data association and track Data association and track managementmanagement
Dynamic lineage analysisDynamic lineage analysis Observation generation methodsObservation generation methods
Result of image segmentation Result of image segmentation Original image--fluorescence imageOriginal image--fluorescence image Feature points, e.g. Harris Feature Feature points, e.g. Harris Feature
PointsPoints Performance evaluation of MTTPerformance evaluation of MTT
ReferenceReference Doucet, A., De Freitas, J. and Gordon, N. (eds.): Sequential Monte Doucet, A., De Freitas, J. and Gordon, N. (eds.): Sequential Monte
Carlo Methods in Practice. New York: Springer, (2001)Carlo Methods in Practice. New York: Springer, (2001)
F. Caron, M. Davy, and A. Doucet. Generalized poly urn for time-F. Caron, M. Davy, and A. Doucet. Generalized poly urn for time-varying dirichlet process mixtures. Proceedings of the International varying dirichlet process mixtures. Proceedings of the International Conference on Uncertainty in Artificial Intelligence(UAI),2007.Conference on Uncertainty in Artificial Intelligence(UAI),2007.
K. Gilholm, S.J. Godsill, S. Maskell, and D. Salmond. Poisson models K. Gilholm, S.J. Godsill, S. Maskell, and D. Salmond. Poisson models for extended target and group tracking. In Proc. SPIE: Signal and for extended target and group tracking. In Proc. SPIE: Signal and Data Processing of Small Targets, 2005.Data Processing of Small Targets, 2005.
B. Vo, and W. K. Ma. The Gaussian mixture Probability Hypothesis B. Vo, and W. K. Ma. The Gaussian mixture Probability Hypothesis Density filter. IEEE Transactions on Signal Processing, 2006.Density filter. IEEE Transactions on Signal Processing, 2006.
Chunlin Ji, Daniel Merl, Thomas Kepler and Mike West. "Spatial Chunlin Ji, Daniel Merl, Thomas Kepler and Mike West. "Spatial Mixture Modelling for Partially Observed Point Processes: Mixture Modelling for Partially Observed Point Processes: Application to Cell Intensity Mapping in Immunology." Bayesian Application to Cell Intensity Mapping in Immunology." Bayesian Analysis, invited revision. Analysis, invited revision.
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