How can you see which points in the spectrum is from which pixel in the original image?
As stated by @tomasz, the fourier transform relates only globally to the image since the pixels of the transform correspond to frequencies in the original image
(which you may intuitively understand - somewhat - as speed of color variation as you move on the original image). 
This is well explained on the web : An Intuitive Explanation of Fourier Theory

Look in particular at the bottom of the page.