What should be the dimensions of a Fourier Transformed image? I have applied Fourier Transform to the following image.



I have downloaded this image from the Internet. I re-sized (without maintaining the aspect ratio) it using MS Paint application of Win7 to make it 512x256. 

Then I have used two applications to observe its Fourier Transformed appearance.

IPLab gives the following output:



ImageJ2-20160205 gives the following output:



As you can see, the first output is a 512x256 image. The second one is a 512x512 image.

Why are those outputs different?

How would they effect processing of an image?
Here is a third different output. So I have tried to perform an FFT with Matlab, on four versions of your image:


the grayscale version of the colored image,
the red, green, and blue channels.


I do get  the following, with $512\times256$ size, in a $\log$ scale.



If as suggested by @Peter K. you zero-pad below, with $512\times512$ size, one gets:



Looks like  the FFT of the Red component, padded.
If you have the opportunity to do other tests, we can settle this riddle