Microtubule Filament Tracing and Estimation · 2019. 7. 21. · Anything below level 1 is 0, anything above level 4 is 2, anything between levels 2 and 3 is 1. Anything between levels

IntroductionTheoryResults

DiscussionConclusion

Microtubule Filament Tracing and Estimation

Rohan Chabukswar

Electrical and Computer EngineeringCarnegie Mellon University

December 2, 2008

Rohan Chabukswar Microtubule Filament Tracing



1 IntroductionMicrotubulesMotivation

2 TheoryBackgroundDeblurringDirection of ExtensionThinningThresholding

3 ResultsIntersecting FilamentsSimulation

4 DiscussionFuture Work — Tracing the Filaments

5 ConclusionRohan Chabukswar Microtubule Filament Tracing



MicrotubulesMotivation

Microtubules are filamentous cytoskeletal structurescomposed of tubulin protein subunits.These subunits can add on, or dissociate from, the tubulinpolymer rapidly, making them highly dynamic.Microtubules are critically involved in many essentialcellular functions, such as chromosome segregation atmitosis and intracellular cargo transport.





IntroductionMotivation

Microtubules are generally studied using three dimensionalfluorescence microscopy.The output is a 3D image of the microtubules, blurred dueto

the lensesthe imaging device,sampling and digitizationfinite size of microtubules





IntroductionAim

To automatically trace each microtubule filament in the 3Dmicroscope imageThe traced image will be used to estimate statistics, like

Number of filamentsAverage lengthDistribution of length




BackgroundDeblurringDirection of ExtensionThinningThresholding

Background

The microtubules originate from a common center andgrow outwards — density of filaments decreases fromcenter to peripheryFilaments grow in a straight line unless an obstacle exists— minimum curvature constraint can be imposed toprevent wrong tracing of the tubules.Points of intersection of microtubules glow twice as brightas any other point on a single microtubule.





TheoryDeblurring

The input images in the tests are noise free.Actual images will have Poisson noise.Richardson-Lucy deconvolution algorithm can be used.





ExamplesSingle Filament

Figure: Single Filament — Original Image





ExamplesSingle Filament

Figure: Single Filament — Input Image





Deblurring ExampleSingle Filament

Figure: Single Filament — Deconvolved Image





TheoryDirection of Extension

After deconvolution, we are not guaranteed a thin image.While thinning as well as tracing filaments, it is essential toknow the direction that the filament at that point has grownfrom, and the direction it is growing in.The Hessian is often used to determine this.





TheoryThe Hessian

For an n-dimensional image I (x1, x2, . . . , xn), the Hessianis

H =

⎛

⎜

⎜

⎜

⎜

⎜

⎝

∂2I∂x21

∂2I∂x1∂x2 · · ·

∂2I∂x1∂xn

∂2I∂x2∂x1

∂2I∂x22

· · ·∂2I

∂x2∂xn...

... . . . ...∂2I

∂xn∂x1∂2I

∂xn∂x2 · · ·∂2I∂x2n

⎞

⎟

⎟

⎟

⎟

⎟

⎠

Symmetric, real eigenvalues.Direction of extension of filament is given by eigenvectorcorresponding to minimum magnitude eigenvalue.For the discrete case, finite-difference version has to beimplemented.





TheoryThinning

Thinning of image achieved by non-maximal supression.Checks if a point is a local maximum along directionsperpendicular to the direction of extension, and puts it tozero if it isn’t.Quantize the angle, find perpendicular directions, check 4values.Thinning can be used before deconvolution, but his will notwork in presence of noise.





Thinning ExampleSingle Filament

Figure: Single Filament — Thinned Image





TheoryThresholding

Intensity data along the length of the filament can be usedin future to detect intersections.Hysteresis thresholding is used as the basic idea. Itcompletes broken filaments.3 different intensity levels, and correspondingly 4 differentthreshold levelsAnything below level 1 is 0, anything above level 4 is 2,anything between levels 2 and 3 is 1.Anything between levels 1 and 2 is 1 if one of its26-neighbors is above level 2, 0 otherwise.Anything between levels 3 and 4 is 2 if atleast 2 of its26-neighbors are 1.





Thresholding ExampleSingle Filament

Figure: Single Filament — Thresholded Image




Intersecting FilamentsSimulation

ResultsIntersecting Filaments

Figure: Intersecting Filaments — Original Image






Figure: Intersecting Filaments — Input Image






Figure: Intersecting Filaments — Deconvolved Image






Figure: Intersecting Filaments — Thinned Image






Figure: Intersecting Filaments — Thresholded Image





ResultsSimulation

Figure: Simulation — Input Image





ResultsSimulation

Figure: Simulation — Deconvolved Image





ResultsSimulation

Figure: Simulation — Thresholded Image




Future Work — Tracing the Filaments

Discussion

The non-maximal suppression works well on input imageswithout noise, but the results are not so good withdeconvolved images.Deconvolution step is essential to remove noise.Additional step of convolving the deconvolved image withthe same or different PSF should give an noise-free blurredimageGiven PSF is elongated in z-direction, which may causeproblems in finding direction of extension.




Future Work — Tracing the Filaments

Future WorkTracing the Filaments

The key idea used is the same as that of connectedcomponents labeling.Connected component labeling uses Xk+1 = (Xk ⊕ B) ∩ Aiteratively.In this case, image should be dilated only in the direction ofextension of the filament, not isotropically.Only needed near intersection of two filaments, alreadypinpointed in the preprocessed image.The initial pixels can be found out by searching inwardsfrom the periphery.




Conclusion

Preprocessing of the image is one of the most challengingaspects of automatization of this task.Future work will involve tracing the filaments.After implementing on simulated images, the algorithm canbe tested on actual images obtained from fluorescencemicroscopy.


Documents

Microtubule Filament Tracing and Estimation · 2019. 7. 21. · Anything below level 1 is 0, anything above level 4 is 2, anything between levels 2 and 3 is 1. Anything between levels