Particle Tracking> Elongated Particle> Biological Application

@btatmaja

Simulation secret: How - to

● Run the demo program● Error? Correct it!● Got the exact result● Modify the code● Modify the math● Improved result● Done

Tracking Elongated Particles

● Introduction● Create image with non-overlapping rectangular

particles● Create Ideal Particle● Calculate Least-Squares Fit Function● Extract End Points● Matching End Points

Intro - Background

● The angle of the particle is needed to determine the position of the particle.

● Use least-squares fitting with an elongated ideal particle. ● If we knew the angle of the particle, the entire fitting

process could not be done with a single convolution ● If the angle is unknown, then many fits with ideal particles

at different angles would need to be calculated.● The ends of long particles look more like a circle than any

other part of the particle. ● We can fit with a circle of diameter equal to the minimum

of the length and width of the object. ● This will find the two ends of the particle in one pass

Create image with non-overlapping rectangular particles

20 particles of length L, width W are placed in a NNx X NNy sized image.

Create Ideal Particle

Calculate Least-Squares Fit Function

ichi=1./chiimg(im,ip); % The inverse of the least-squares fit function is % used since it is easier to see peaks than valleys.simage(ichi); Title('Inverse of Least-Squares Fit Function');colorbar;

Extract End Points

Biological Application

IDEA:● Identify regions of the object which look more

like a circle than any other part of the object.● We can fit with a circle at two points on the

object and extract the position and angle

Examine Sample Image

Image Correction

Bright Background Correction

Dark Background Correction I

Dark Background Correction II

Zoom in I

Zoom in II

Zoom in III

Looking for circle

Least Square Fit Function

Weighted Fit Function

Fitting to a Binary Image

Extract Peak Position

Result I

Result II

Result III – Animal tracking

Result IV – Zoom in X Axis

Result V – Head track, binary

The head track is shown for both the binary image (blue) and the full image (green). The

binary is shifted by 10 pixels for clarity.

DONE

!!