Summary | Background | Methods | Results | Publications

Probabilistic plus-ends tracing

Given the segmented microtubules, their end points can be used to search for the plus-end structures. The fact that the plus-ends are filamentous features connected with microtubule body suggests the usage of tracing for the segmentation task. To this end, we design a probabilistic tracing method in the framework of particle filtering. To make the tracing robust, we model the plus-ends filaments as piecewise parabolic curves based on prior knowledge about the regularity of the plus-ends shape. This model is then integrated into the prior dynamics of the particle filter. In addition, the intensity similarity between the plus-ends and the microtubule body is utilized to provide a robust clue for the tracing. 

Radial slicing of the volume containing the individual microtubule

The radial slicing is performed around the microtubule, as illustrated below. The plus-end filaments can then be approximated as planar curves in each radial slice. Compared with tracing in 3D, tracing in such 2D planes leads to robust performance because the adverse influence from other structures is significantly decreased.





(a) a model of plus-end filaments as planar curves. (b) radial slicing through the center of the microtubule. (c)(d) two selected radial slices

Probabilistic framework



The plus-end filaments under tracing is represented as an ordered point sequence

The point sequence is then modeled with second order prior dynamics that allow appropriate balance between smoothness and flexibility.

Using Bayesian rules and Markovian hypothesis, the tracing is to find the most probably next point based on the posterior recursion



The posterior can be approximated by sampling

The weights are given by the likelihood


The prediction is given by the prior dynamics

where R is a rotation matrix.

Since plus-ends filaments are unlikely to have inflections, we approximate the mean tracing direction change by fitting a parabola segment to a set of traced points. The tracing direction change is then modelled by a normal distribution



The likelihood is calculated from the similarity between the intensity at the predicted point and

the intensity of the microtubule wall:

The intensity of the microtubule wall is estimated as a Gaussian distribution based on the segmented microtubule body in previous step.


Tracing in multiple radial slices

Results capture different plus-ends features in different slices





Summary | Background | Methods | Results | Publications