Function iadftview

Synopse

Generate optical Fourier Spectrum from DFT data.

g = iadftview(F)
- OUTPUT
  - g: Image.
- INPUT
  - F: Image. n-dimensional DFT complex data.

Description

Generate the logarithm of the magnitude of F, shifted so that the origin stays at the center of the image. The objective of this function is to provide DFT spectrum visualization.



In [1]:

    
import numpy as np

def dftview(F):
    import ia898.src as ia

    FM = ia.dftshift(np.log(np.abs(F)+1))
    return ia.normalize(FM).astype(np.uint8)

Examples



In [1]:

    
testing = (__name__ == "__main__")

if testing:
    ! jupyter nbconvert --to python dftview.ipynb
    import numpy as np
    import sys,os
    import matplotlib.image as mpimg
    ia898path = os.path.abspath('../../')
    if ia898path not in sys.path:
        sys.path.append(ia898path)
    import ia898.src as ia









    



[NbConvertApp] Converting notebook dftview.ipynb to python
[NbConvertApp] Writing 1649 bytes to dftview.py

Example 1



In [2]:

    
if testing:
    import matplotlib.image as mpimg
    import numpy.fft as FFT
    f = mpimg.imread('../data/cameraman.tif')
    ia.adshow(f, "Original 2D image - Cameraman")
    F = FFT.fft2(f)
    Fv = ia.dftview(F)
    ia.adshow(Fv, "Cameraman DFT optical spectrum")









    




                    
            Original 2D image - Cameraman







    




                    
            Cameraman DFT optical spectrum

Equation

$$ \begin{matrix} Gaux &=& \log(|F_{xc,yc}| + 1)\\xc &=& \lfloor W/2 \rfloor \\yc &=& \lfloor H/2 \rfloor\\ G &=& Gaux|_0^{255} \end{matrix} $$



In [3]:

    
if testing:
    print('testing dftview')
    print(repr(ia.dftview(np.array([[10+6j,20+5j,30+4j],[40+3j,50+2j,60+1j]]))) == repr(np.array(
          [[254, 190, 226],
           [146,   0, 86]],np.uint8)))









    



testing dftview
True

Contributions

André Luis da Costa, 1st semester 2011