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.
I have enhanced the contrast of the FFT (Power Spectrum) image with the Process -> Enhance Contrast menu.
Since drawing tools are not available in ImageJ, I don't know how to do the following with ImageJ. An FFT plugin - FFT-Filter (Plugins / Filter / FFT Filter - when installed on your computer) will filter horizontal or vertical lines -- This same filter is in Process / FFT / Bandpass Filter. Perhaps there are other plugins that will allow filtering of diagonal lines.
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.