2D DFT Filter Butterworth BP Tiled ( IA2DDFTBPTiled )

Parameters:

Name	Short Name	Type	Description
Number of tiles in x	tilesx	integer	The image consists of this number of equal sized tiles in x dimension.
Number of tiles in y	tilesy	integer	The image consists of this number of equal sized tiles in y dimension.
Cut On ω	cuton	real	Cut on of the band pass Butterworth filter
Cut On order	ordon	real	Order of the cut on of the band pass Butterworth filter
Cut Off ω	cutoff	real	Cut off of the band pass Butterworth filter
Cut Off order	ordff	real	Order of the cut off of the band pass Butterworth filter
unit of ω	units	string	Unit of cut on and off values above
Filter normalization	normalization	string	Normalizes the integral of the 1D or 2D filter function
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 in tiled images for sharpening, blind deconvolution, background removal or blurring purposes. A band pass Butterworth filter with rotationally symmetric filter characteristics is defined parametrically.
Each tile of a tiled image is processed independently. The edge protection or paper size is applied for each tile, not for the same image.
Typical use: background removal on tiled images.
Performs spatial filtering in Fourier domain for sharpening, blind deconvolution, background removal or blurring purposes. A band pass Butterworth filter with rotationally symmetric filter characteristics is defined parametrically.
The Butterworth filter can be defined using pixels or cycles/μm as spatial frequency units. Pixel value of 1 means one sine wave spanning the image peaking in the middle. To calibrate spatial frequencies (ω) as cycles/μm the pixel size given in the Setup DFT Filter dialog/Calibration is used. This value is loaded from the image, or if an image does not contain calibration information then the default value in the Edit/Preferences/(Data / Scaling)/Distance Calibration is used.
Use "Filter Normalization" if the resultant pixel values are too low.
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 of the filtering and the filter function in Gerencser et al. Biophys J. 2008 Sep;95(5):2583-98