Why is the Fourier Transform Power Spectrum of any Image not in the color range 0 to 255?

1
votes

I have calculated the Fourier Transform and Fourier Transform Power Spectrum of my Image. Fourier Transform is easily visible whereas the Power Spectrum is not. I can further normalize the contrast to 0-255 level experimentally and logarithmically. But I am not able to explain why the Power Spectrum is not visible and if there is any standard method for making the contrast visible. The Power Spectrum is not visible but I also do not have any idea and how can I explain. I know Power Spectrum is the square of summation of both the real and imaginary component of Fourier Transform so the value is going to be high but can anyone provide be a reliable and convincing explanation .....

By logarithmically, I mean 

Visible_Power_Spectrum = log(1+Power_Spectrum,10)//Java language

Further, I am also confused why the centre of the Power Spectrum value is so high that normal method of normalization doesn't work properly.

I have already gone through other questions that are similar....

Thanks a lot

2
fftspectrum
Can you elaborate on what you mean by not visible, possibly providing an example image? – Clarissa G
hi @ClarissaG : Sorry for not being clear. By not visible, I mean if I calculate the Power Spectrum of any image in ImageJ, the values for each pixels are so high that it does not come under 0-255 color range to display as a jpeg file in ImageJ or just any default image viewer. When I convert the resultant image to text, the centre value would be 4654693875712 for a normal image. Hoper it helps. – Psi Lambda Delta

2 Answers

1
votes

Many FFT implementations (not all) seem to scale the result by the size (length or height*width) of the data in order to preserve total energy (Parseval's rule) between the data and the FFT result. If so, scale the data down by the size before taking the log.

0
votes

it is because the spectrum is not uniform distributed.