**Deterministic and probabilistic approaches for tracking virus particles in time-lapse fluorescence microscopy image sequences.**

W.j Godinez et al. (2007)

W.j Godinez et al. (2007)

**Probabilistic tracking approaches**

Deterministic

Introducción

Understanding of viral infection.

Double flourescent labelled virus particles produce two-channel images.

Need to evaluate a large number of events and large amount of viruses in an image.

Small size viruses.

Little visual information

Complex motion behavior

Virus may move aout of the focal plane.

Tracking?

1. Object representation

and localization

2.Spatial-Temporal filtering

and motion correspondence

Object localization by spot-enhancing filter

Intensity structure of a virus resembles a 2D Gaussian function

Threshold-base segmentation

High number of false detection

Spot-enhancing filter. Consist in convolving an image with laplacian-of-Gaussian kernel

After filtering we apply threshold. This is compute for each image.

Object Localization by Gaussian fitting

Fitting a function to candidate regions-of-interest

Employ intensity clipping and Gaussian filter for noise reduction.

For each candidate ROI we apply 2D Gaussian fitting.

Final step: reject false positives.

Motion Correspondence by global nearest neighbor

Given a set of N predicted position estimates

And a set of N' measured position estimates:

Need to find one-to-one correspondance, represented by matrix A

A global nearest neighbor algorithm aims at finding the correspondences between both sets by optimizing A

Spatial-temporal filtering

Sequential state estimation

Objetc represent by x_t and noisy measurement y_t wich reflect the true state x_t.

The aim is to estimate x_t, given a sequence mesurements y_1:t.

3 elements:

A dinamical model

Measurement model

Initial prior

Bayesian approach :

Represent a degree of "belief"

Each time step, Bayesian filter computes recursively the posterior pdf by first generating the prior pdf

Particle filter

Succesful for nonlinear and/or non-Gaussian models.

Key: The posterior pdg is approximated with a set as random samples (the 'particles')that are associated with importance weights.

Candidates samples

are generated from a proposal distribution q(.) which is typically set to be equivalent to the dynamical model:

Weigh of each sample:

Boosted particle filter

Performance of the particle filter may be enhanced by selecting an appropriate proposal distribution q(.)

Take into account image information to explore areas with high likelihood. (Deterministic object localization).

Combines a particle filter with position estimates obtained by a deterministic object localization algorithm

Multiple objects?

Mixture of particle filters

Use a single particle filter defined on a one-body state space. Each mode corresponds to one object.

Problem: Cannot maintain the multimodality over several time steps.

One approach:

Modeling the posterior distribution as a M-component mixture model

denotes the component weight of the non-parametric mth component

The multimodal posterior is now approximated as follows:

Problems:

Leads to tracking errors in cases where objects lie in close proximity

Does not handle objects entering and leaving the field of view.

**Independent particles filters**

Another approach for tracking multiple objects that have a similar appearance consist in instantiating one particle filter per object.

Based on the boosted particle filter

Operates on a small state space.

Gives a good approximation with relatively few samples.

Low computational demand.

However, the approach generally fails in cases where objects pass close to each other.

Penalization scheme for independent particle filters

Take into account the positions of neighboring objects.

**Experimental results**

Perfomance measure.

Seq A:

A temporarily desappearing object. 50 images (64x64pixels, 16 bit).

spot-enhancing filter in combination with a global nearest neighbor scheme (SEF&GNN)

SEF&MPF

SEF&IPF

GaussFit&MPF

GaussFit&IPF For comparison with another probabilistic approeach, implement two additional approach:

SEF&Kalman

GaussFit&Kalman

Six tracking schemes used:

Deterministic approach accuracy:

P_track=58.23%

Probabilistic approach accuracy:

P_track=100%

Different way by which the probabilistic approaches handle object disappearances.

Seq. B

50 images (64x64 pixels, 16-bit).

Spurious particles

During the initial 30 steps, the particle presents random motion

at time 31 the particle disappears. At the same time a spurious object appears in the vicinity.

Deterministic approach: P_track=59.44%

Probabilistic approach: P_track=100%

**Real microscope image sequence.**

150 images (256x256 pixels)

Selects a ROI .

In this sequences, some of the virus particles go out of focus. Blurring effect.

150 images (256x256 pixels)

Selects a ROI .

In this sequences, some of the virus particles go out of focus. Blurring effect.

**Conclusions**

**The experiments indicates that the performance if the deterministic approaches is not very accurate under realistic imaging situations. This arises mainly because of errors in both localization algorithm and the motion correspondence step.**

In contrast, the approaches based on particle filters are more robust and accurate under such conditions. The reason is meanly due to the comprehensive tracking machinery of the particle filter, wich includes the steps of particle localization, motion correspondence, and position estimation. Manages to localize particles with poor contrast.

In contrast, the approaches based on particle filters are more robust and accurate under such conditions. The reason is meanly due to the comprehensive tracking machinery of the particle filter, wich includes the steps of particle localization, motion correspondence, and position estimation. Manages to localize particles with poor contrast.

Deterministic approach:

P_track=49.9%

Probabilistic approach:

P_track=83.39%