Re: analyzing FFT images

[dpoburkoSFU]

Dear all,

   My apologies in advance if this specific question has been covered,
but I couldn't find an answer parsing the Nabble list.

   I am trying to characterize the alignment of actin filaments using
the built in FFT transform in ImageJ. We can extract some information
about when actin filaments are well organized based on the shape of the
thresholded central portion of the FFT image. But we would like to be
able to quantify the relative amounts of power over specific ranges of
frequencies in the FFT image.

  My first question is whether there is a good resource out there for
interpreting ImageJ FFT images. I understand the notion of the polar
coordinates, and I assume that the 8-bit FFT image is a saturated,
scaled version of the raw fft image, but it would be great if someone
could confirm this.

  Second, can someone enlighten me as to why the FFT images often seem
to have cross hairs along the X and Y axes?

  Third, is there a consistent formula that describe the distance in
pixels from the center of the FFT image and the corresponding frequency
encoding at that distance? I have compared the pixels/cycle shown in the
ImageJ window with the length of a line from the center of the image,
and it is fit well by a double exponential, but I don't know if that
makes sense.

  Last, is there an easy way to access the polar coordinate data in the
FFT images via macros?

Thanks,
Damon

--

*Damon Poburko*, Assistant Professor | Biomedical Physiology &
Kinesiology | Simon Fraser University

Tel: [phone] | Fax: [phone] | Office L8004

Mail to: Room K9625, 8888 University Drive, Burnaby BC V5A 1S6

http://www.sfu.ca/bpk/faculty_directory/poburko.html


--
ImageJ mailing list: http://imagej.nih.gov/ij/list.html

[Michael Schmid]

Hi Damon,

a few answers:

The 8-bit image displayed by ImageJ is the power spectrum with logarithmic scaling, between the log of the minimum and maximum values of the power spectrum.  To avoid problems with values of zero or very close to it, the number of decades is limited.
Pixel values of 0 and 255 do not occur in the displayed power spectrum; these values are reserved for the filtering operations.

What you call "cross hairs along the X and Y axes" is artifacts of the edges of the original image.
Let's first assume an image with a size of 512x512 or an other power of 2:
For an FFT, you should have an image with periodic boundary conditions, e.g. f(x, y) = f(x+n*512, y+m*512), where n, m are integers (replace 512 with any other power of 2 for other image sizes).  Typical image data are rather smooth, but the borders of the image and its periodic repetitions are not smooth.  These sharp transitions of the pixel value at the borders produce vertical and horizontal lines in the FFT.
If the image size is not a power of 2, ImageJ pads it to a power of 2, with the remaining image filled with a constant (the mean of the original image).  Also this gives you a step between the actual image and the area padded with a constant.
These "cross hairs" due to the sharp border are worst if the image has a background that is like a grayscale ramp.  Subtract the background from such images.

Spatial frequency as a function of the distance in pixels from the center of the FFT:  You can read this number in the 'status' field of the ImageJ panel when moving the cursor over the FFT.
The relationship is simple:  Spatial frequency is proportional to the distance from the center.  The edge of the FFT, i.e. a distance of size/2 (size=width=height in pixels) in the FFT corresponds to the Nyquist frequency in the original image, i.e., one cycle per 2 pixels.  (A distance equal to the full width of the FFT image would correspond to one cycle per pixel, but this distance does not exist)
  http://en.wikipedia.org/wiki/Nyquist_frequency

Thus, cycles/pixel_of_input_image = distance_fron_center_in_FFT/size

The 'wavelength' in the original image is simply pixels/cycle, the inverse of what you get from the formula above.


Michael
________________________________________________________________
On May 14, 2014, at 20:40, Damon Poburko wrote:

> Dear all,
>
>  My apologies in advance if this specific question has been covered, but I couldn't find an answer parsing the Nabble list.
>
>  I am trying to characterize the alignment of actin filaments using the built in FFT transform in ImageJ. We can extract some information about when actin filaments are well organized based on the shape of the thresholded central portion of the FFT image. But we would like to be able to quantify the relative amounts of power over specific ranges of frequencies in the FFT image.
>
> My first question is whether there is a good resource out there for interpreting ImageJ FFT images. I understand the notion of the polar coordinates, and I assume that the 8-bit FFT image is a saturated, scaled version of the raw fft image, but it would be great if someone could confirm this.
>
> Second, can someone enlighten me as to why the FFT images often seem to have cross hairs along the X and Y axes?
>
> Third, is there a consistent formula that describe the distance in pixels from the center of the FFT image and the corresponding frequency encoding at that distance? I have compared the pixels/cycle shown in the ImageJ window with the length of a line from the center of the image, and it is fit well by a double exponential, but I don't know if that makes sense.
>
> Last, is there an easy way to access the polar coordinate data in the FFT images via macros?
>
> Thanks,
> Damon

--
ImageJ mailing list: http://imagej.nih.gov/ij/list.html