2D DFT Filter ( IA2DDFT )

Parameters:

Name	Short Name	Type	Description
Filter file*	filter	string	Filter files can be saved by the Setup DFT Filter dialog.
Preserve edges	edges	boolean	Performs mirrored tiling to prevent edge artifacts. Slows down processing by 4x.
Enlarge paper	enlarge	boolean	Enlarges image by mirrored tiling to quadrangular. Prevents edge artifacts and distortions from non-quadrangular images
Enlarge image to power of 2	enlargeto	integer	Size of image during filtering as power of 2.
Leave only phase	phase	boolean	Sets complex amplitudes in Fourier space to 1 keeping their original arc.
Absolute	absolute	boolean	Calculates absolute value after filtering. Required for intensity measurements on high pass and band pass filtered images.
Protect MASK	protect	boolean	Fills up masked areas with zeros before processing. Required for masked images.

Description:

Performs spatial filtering in Fourier domain for sharpening, blind deconvolution, background removal or blurring purposes. A pre-defined, rotationally symmetric filter is loaded from an *.flt file. Design and save filter in the Setup DFT Filter dialog. Saved filters are scaled for the size of the image (in pixels), but not for the physical resolution, therefore design and use separate filters for different image sizes / resolutions. Fourier transformation is generally a periodic transform, therefore strongly different intensities in opposite edges of the image result edge artifacts. Edge artifacts can be avoided by tiling a larger image with the original and its mirror images in a symmetric, thus periodic manner. To protect edges use "Preserve edges" when an image is quadrangular and size of power of 2.
Non-quadrangular images are disproportionally filtered in x and y directions, therefore use "Enlarge paper" to tile a larger quadrangular image using the original image before filtering. The result will be cropped to provide an image corresponding to the original one.
"Preserve edges" and "Enlarge paper" do not change the size or spatial calibration of the resultant image, the result is obtained by cropping the enlarged image to the original size. Fourier transformation is incompatible with masking (pixels without a real value), therefore the mask has to be filled up with zeros "Protect MASK" before filtering.
See details in Gerencser and Adam-Vizi, Cell Calcium 2001 Nov;30(5):311-21
Mathematica usage:
*filter format instead of filename= {{x,y},{x,y}...} where 0<=x<=1 and y is the filter coefficient