June 10, 2004
The Fast Fourier Transform is useful for blurring, deblurring, removing specific types of features or noise, cross correlation, and other things. This exercise illustrates the use of the Process -> FFT menu in conjunction with the Process -> Image Math menu.
Here is the relevant information from the ImageJ doc page on the Process Menu: http://rsb.info.nih.gov/ij/docs/menus/process.html#fft, under FFT / Inverse FFT:
You can filter or mask spots on the transformed (frequency domain) image and do an inverse transform to produce an image which only contains the frequencies selected or which suppresses the frequencies selected. Use ImageJ's selection tools and fill/clear commands to draw black or white areas that mask portions of the transformed image. Black areas (pixel value=0) cause the corresponding frequences to be filtered (removed) and white areas (pixel value=255) cause the corresponding frequences to be passed. It is not, however, possible to both filter and pass during the same inverse transform.
I have enhanced the contrast of the FFT (Power Spectrum) image with the Process -> Enhance Contrast menu.
For the following, you need to add drawing tools to in ImageJ.
The fuzzy diagonal line from the upper left to lower right corresponds to the lines of the image. To see this:
Had the inverse FFT been performed on the unaltered FFT image, the original image would have been duplicated. In this case, the information corresponding to the lines was eliminated in the FFT, and the lines were eliminated from the reconstructed image.
In this case, all but the black areas are eliminated from the transform image. (Bandpass filter.)
This time the lines are highlighted, and most everything else is lost.