Lecture 6

Question 1

Particle tracking

Answer 1

Hard to analyse moving and reshaping object in motion

• thresholding
• Gaussian PSF model fitting (best)
• Laplacean of Gaussian filtering (LoG)

Question 2

Cell tracking

Answer 2

• Intensity thresholdign
• Watershed segmentation
• Active contour fitting
• Level set segmentation

Question 3

Popular methods for particle tracking

Answer 3

• Detection

- Linking

Question 4

Detection

Answer 4

• Thresholding
• Centroid callculation
• Least-squares Gaussian fitting
• LoG filtering

Question 5

Linking

Answer 5

• Nearest-neighbor searching
• Multiple hypothesis tracking
• Interacting multiple models

Question 6

Centroid calculation

Answer 6

In the LS Gaussian fitting
Least squares: S(x0,y0)=sum[I(x,y)-G(x-x0,y-y0)]^2. This is the Gaussian centered at (x0,y0) with sigma to approximate PSF. If you take derivative and set it to zero you can find it in postion x or y.

Question 7

Least-squares Gaussian fitting

Answer 7

Wide Field Fluorescence Microscopy: sigma=0.21lambda/NA
Laser Scanning Confocal Fluorescence Microscopy: sigma=0.16lambda/NA.
Take the Gaussian image profile and find the best fit. For each position you compute the difference between intensity adn Gaussian approach. If there is a nice match, the difference is very smalln The squared value is very small. So we want to minimize the PSF.

Question 8

Nearest neighbor searching

Answer 8

Connects the dots to the nearest neightbour in the next frame

Question 9

Multiple hypothesis tracking

Answer 9

All possible connections ro new pixels are stored and remembered. In the end, you created a network and you want to find the most low-cost route, usually shortest route.

Question 10

Interacting multiple models

Answer 10

Combine NNS and MHT: predict beforehand what you think the route is going to be and make decision of the next pixel based on that prediction.

Question 11

Measures and approaches to quantify dynamics

Answer 11

• Traveled distances
• Speed measures
• Mean-squared displacement
• Kymograph analysis

Question 12

Traveled distances

Answer 12

done with mean squared displacement

Question 13

Speed measures

Answer 13

done with kymograph analysis

Question 14

Mean-squared displacement

Answer 14

Distance between track points d(pi,pj)=abs(pi-pj)

For a given time lag t: MSD(t)=sum(d^2(pi,pi+t))/(N-t)

Question 15

Kymograph analysis

Answer 15

Time and space are integrated in one image. This way you can calculate the speed: v=dx/dy.

Question 16

Popular methods for cell tracking

Answer 16

• Segmentation

- Linking (same as in particle tracking)

Question 17

Segmentation

Answer 17

• Thresholding
• Watershed segmentation
• Active contours
• level sets

Question 18

Watershed segmentation

Question 19

Active contours

Answer 19

Hard to do when there is cell division, because the contour then also has to split

Question 20

Level sets

Answer 20

Useful for cell division

Question 21

Gaussian fitting RMSE

Answer 21

RMSE=sqrt(((s^2+(a^2/12))/N)+(8pis^4b^2/(a^2N^2))

s-spotsize (larger gives bad fit)
a-pixelsize (Small pixels, more accurate)
b-background noise (more noise, bad fit)
N-number of photons from spot (more photons, more accurate)

Question 22

Bayesian estimation based tracking

Answer 22

Computing the degree of belief in the object state by taking into account all available evidence up to the current time point.
- Predict: Prior=transitionposterior
- Update: Posterior=likelihoodprior
Posterior-most likely previous position knowing all past images
Transition-predicted transformation Function, like the likelihood.

Question 23

Pure diffusion

Answer 23

MSD(t)=4Dt

D=b/4

Question 24

Directed motion with perhaps a diffusion component.

Answer 24

Dynamics equation: “MSD” (t)=4Dt+(vt)^2 (quadratic equation).
that D=b/4 and v=√c