Setup DFT Filter and Optimizations Dialog

• Design of  lowpass, bandpass, highpass spatial filters
• 'Hand draw' filter function or generate with Butterworth filter functions
• Transform filter functions
• Perform optimization for the "thinness ratio technique"
• Perform optimization for the "highpass filtering technique"
• Perform optimization for lens distortion correction

Basic usage:

• An Image Window must be opened in order to access the Setup DFT Filter and Filter Optimizations Dialog in the Tools menu.
• Set the spatial resolution of the image in the Calibration tab, if w is intended to be used as cycles/mm. The spatial calibration is automatically filled from the image metadata if available. If w is used in pixels, this calibration value is indifferent.
• Press preview to see the effect of the filter. The default unity filter does not alter the image, even though the image data is forward and reverse Fourier transformed.
• Alter filter function. Either by double-clicking the trace and adding points, or using the Generate tab.
• See detailed protocol here.

Filter function: move points by mouse
Scale graph by dragging the '1'
Basic parameters of the filter, see details here

Non-calibrated spatial frequency of pointer position:
% of Fourier domain image in its diagonal (sqrt(2)*width/2) w in pixels half wavelength (l/2) corresponding to the w	filter coefficient (k) and w calibrated in cycles/mm

		reset to unity filter open filter (*.flt) save filter (*.flt) to load in Multi-Dimensiona lOpen Dialog or in the 2D DFT Filter function Process active image with the current filter Preview Online help on selected function
'Calibrate' tab: Set spatial resolution (x,y scaling) of the image here. Alternatively the maximal or the per pixel w can be given in cycles/mm

Transform tab:

• Scale function by the given factors
• Shift the function by the given offset
• Invert the function

Optimization tab:

• Use Optimization tab to generate filter functions for the optimized ratiometric spatial filtering, or thinness ratio technique and highpass filtering technique
• The optimization works on an Image Window selected from the Image Windows linked to the window active in the time of opening the Set DFT filter dialog.
• The optimization requires the presence of an ROI on the image

To perform optimization:

1. Set target image
2. Set mask image (which is a binarized image where '1' is corresponding to the detail of interest): Note: this is an optional parameter, can be set by the "Use Mask" parameter of the selected function.
3. Select 'Differential Evolution Optimizer' at the 'Select parameters of' and set parameters. This controls the optimizer algorithm, and typically default parameter are used.
4. Select the function to be optimized ('Thinness Ratio Filter Pair', 'High Pass, Band Pass, Long Pass Filter' or 'Lens Distortion Parameters') at the 'Select parameters of' and set parameters as described for each function (use the button to access help on function parametering).
5. Press Optimize. Optimization may take several minutes, while actual tested filter functions briefly graphed in the dialog. Use ESC or the Stop button to abort it.
6. When optimization is finished select the last two items in the Results list and save filter functions or note down parameters.
7. See detailed protocol here.

• Select image to undistort as "Image" to align it to another image selected as "Mask" (this is not a mask here). Typically "Image" and "Mask" show the same fluorescent structures, but recorded at different emission wavelengths. "Image" and "Mask" are eg. red and green channels, and the red is substantially distorted because of the chromatic/spherical aberration of the lens.
• Select at "type of correction" that which parameters are to be optimized and set the range of optimization below.
• Press Optimize. Optimization may take several minutes. Use ESC or the Stop button to abort it.
• Copy optimized parameters from the Results list to the Editing/Correct Lens Distortion function.

Generate tab:

The usage of these functions is identical to the ones with the same names accessible from the Main menu/Filters.

• 2D DFT Filter (this is identical to load *.flt)
• 2D DFT Butterworth BP Filter to generate lowpass, bandpass and highpass filters with the Butterworth function.
• 2D DFT Butterworth BP Filter tiled to generate lowpass, bandpass and highpass filters with the Butterworth function and perform filtering independently for each tile of a tiled image.

To generate filters:

• Handle function parameters identically as for functions with the same name using the parameter bar of the Main Window.
• Press the 'Generate' button to update the filter function on the left according to the parameters set in the Generate tab. The basic parameters below the graph on the left side of the dialog will be populated from the function parameters.
• Press 'Set as Default' in order to reuse the parameters, when using the corresponding function from the Main menu or adding to Pipeline.