Temporal ICS - UU-cellbiology/Correlescence GitHub Wiki

This command performs temporal image correlation spectroscopy analysis.
Basically, for every x,y pixel's intensity time trace it calculates the autocorrelation function of time delay and analyzes it. Plus optionally analyzes Fourier transform (spectrum) of the time trace.

As an input, this command takes an 8-,16-,32- bit image stack with more than two time frames.
As an output, it generates "TICS stack", i.e. stack containing autocorrelation function (and z/t values becomes time delay).
It also can perform some analysis on this stack, see options below.

Preprocessing

If selected, this option allows subtracting from the original input stack a chosen type of projection. Usually "Average intensity" projection is recommended.

TICS

Maximum period parameter (in frames) sets the limit on the maximum time delay of the autocorrelation. In principle, it cannot be longer than half size of the stack (zero value). One can reduce it to eliminate slow periodic movements.

Resize CC stack? option allows resizing the output to the specified X (width), Y (height) values. This option can be helpful for coarse-graining the data to get rid of some noise. In this case TICS autocorrelation stack will be scaled before displaying and further analysis.

TICS period/frequency estimation

Estimate period/frequency? option finds the first maximum (peak) of the autocorrelation function, i.e. the maximum with minimum delay. If there is a periodicity in the intensity time trace, the autocorrelation function will have a peak at the time delay value equal to this period. If the duration of the movie/analysis is longer than this period, there would be multiple maxima at larger delay values (two periods, three periods, etc), therefore the first maximum is chosen.
If this option is selected, the plugin will output an additional image with pixel values equal to the period (or frequency, defined below) corresponding to this maximum.

Tolerance of CC maximum specifies the minimum "height" of the autocorrelation peak (maximum). It is usually in the range of 0.1-0.9 (same as autocorrelation) with a good initial guess being around 0.2. Smaller values of this parameter will lead to picking up less pronounced oscillations (and sometimes more noise). Larger values are going to cut off weak periodicity.

Analyze CC maximum specifies which peak of the autocorrelation is located, either the first, the highest, or all of them. In the last case the plugin outputs a z-stack, where the z-slice position corresponds to the delay in frames. Pixels with values of 1.0 mark the position of detected peaks.

Subframe precision? option will perform sub-frame estimation of period/frequency. The autocorrelation function is defined with a time delay step of one frame, so this is the initial precision of the first maximum estimation. With this option selected, the plugin will analyze nearby autocorrelation values and provide "subframe" peak estimation.

Show TICS stack? is going to show the calculated "autocorrelation function" stack. Now for each pixel position the time axis will correspond to the time delay of the autocorrelation. To see these values, select an ROI and use ImageJ's Image->Stack-> Plot Z-axis Profile command.

FFT

If Calculate dominant frequency/phase map option is selected, the plugin will calculate a Fourier (FFT) spectrum for each intensity time trace and report two images: the frequency with the highest amplitude and its corresponding phase value (in radians). So the pixels oscillating "synchronously" at the same frequency should have the same phase values.
Since the plugin is using FFT for the spectrum calculations, the possible reported frequency values are limited to 1/N, 2/N, 4/N, 8/N ... etc. Where N is the number of frames in the input stack. Due to these "gaps", the Fourier frequency estimation is less precise compared to TICS (which has precision of one frame or less).

Output

Output image value defines if period or frequency are going to be reported in TICS and FFT analysis.

Units of output option specifies if the reported value will be measured in frames or Stack's time units.
If the last option is selected, make sure that the proper "Frame interval" value is set for the input stack. You can check it using ImageJ's menu Image -> Show info... command. And change it using Image -> Properties...