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ND Fourier Transform in Python

  1. Aug 26, 2014 #1
    Hi,

    My aim is to get a series of images in 2D space that run over different timestamps and put them through a 3D Fourier Transform. So my 3D FT has 2 spatial axes and one temporal axis. However I have never done anything like this before, and I have a very basic knowledge of Python.

    So far, I can do the FFT for a list (or 1D array) of point sources as follows:

    ##
    # Import libs
    import matplotlib.pyplot as plt
    import numpy as np

    # create point sources
    tmp = range(100)
    source = [0 for x in tmp]
    source.insert(50,1)
    source.insert(5,1)
    source.insert(60,0.5)

    # make t useable later
    t = np.array(source)

    # equations for later
    f = np.fft.fft(t)
    g = np.sqrt(np.abs(f)**2)

    # set up plot
    fig = plt.figure()

    # add sources to plot
    ax1 = fig.add_subplot(211)
    plt.plot(source)
    ax1.set_title('Source')
    ax1.xaxis.set_visible(False)

    # add FT of sources to plot
    ax2 = fig.add_subplot(212)
    plt.plot(f)
    ax2.set_title('Fourier Transform')
    ax2.xaxis.set_visible(False)

    # show plot
    plt.show()
    ##

    Now I would like to turn my 1D image into a 2D image, and I just can't work out how to do this. I've tried by doing something like this for my point sources:

    ##
    # Array of 3 source lists
    # Create list of lists - seems dodgy
    tmp_array = range(3)
    array_list = []

    # create source lists to go in array
    tmp = range(10)
    source1 = [0 for x in tmp]
    source1.insert(5,1)
    source2 = [0 for x in tmp]
    source2.insert(4,1)
    source3 = [0 for x in tmp]
    source3.insert(2,1)

    # put lists in array
    array_list.insert(1,source1)
    array_list.insert(2,source2)
    array_list.insert(3,source3)
    ##

    Though calling it "source" instead of "array_list" would fit better with previous code.
    However it is not working and I cannot figure out why.

    I was also wandering if I need to bother with getting the 2D FT working before trying the 3D, or if I can just jump forward? Not that I have any idea how to do that yet.

    Thank you for your help
     
  2. jcsd
  3. Aug 26, 2014 #2
    I would suggest creating arrays as numpy arrays first, not as Python lists:

    For the 1d array:

    t = np.zeros(103)
    t[5] = 1
    t[51] = 1
    t[60] = 0.5

    (if that was your intention)

    For the 2d array:

    array_list = np.zeros((3, 11))
    array_list[0,5] = 1
    # etc...

    For a 2d fft of with real-valued input, use rfft2 or rfftn.

    Note that for large FFT sizes, try to avoid a size with large prime factors, or pad out to the next largest power of 2 if that is unavoidable (using the optional size parameter). Fftpack seems to handle small prime factors like 3 or 5 OK, though.
     
  4. Aug 26, 2014 #3
    One more comment:

    The sqrt and square here are unnecessary: np.abs(f) is already sqrt(f.real**2 + f.imag**2).
     
  5. Aug 26, 2014 #4
    Thank you :)

    I've gone for a slightly different approach now than above, and hitting different problems.

    # A lot of this is taken from http://matplotlib.org/users/image_tutorial.html
    # as well as http://opencv-python-tutroals.readt...y_fourier_transform/py_fourier_transform.html

    ##
    img=mpimg.imread('stinkbug.png')
    img_red = img[:,:,0]
    img_green = img[:,:,1]
    img_blue = img[:,:,2]
    # I assume this is taking the data in each of the red, green and blue columns?

    array_list = []
    array_list.append(img_red)
    array_list.append(img_green)
    array_list.append(img_blue)

    t = np.array(array_list)
    f = np.fft.fftn(t)
    fshift = np.fft.fftshift(f)
    magnitude_spectrum = np.log(np.abs(fshift))

    fig = plt.figure()

    ax1 = fig.add_subplot(211)
    imgplot=plt.imshow(img)
    ax1.set_title('FT this Bug')
    imgplot.set_cmap('gray')
    plt.colorbar()

    ax2 = fig.add_subplot(212)
    plt.imshow(magnitude_spectrum)
    plt.colorbar()

    plt.show()
    ##

    I get the following error

    ###
    Traceback (most recent call last):
    File "<stdin>", line 1, in <module>
    File "image_test2", line 51, in <module>
    plt.imshow(magnitude_spectrum)
    File "/usr/lib/pymodules/python2.7/matplotlib/pyplot.py", line 2892, in imshow
    imlim=imlim, resample=resample, url=url, **kwargs)
    File "/usr/lib/pymodules/python2.7/matplotlib/axes.py", line 7300, in imshow
    im.set_data(X)
    File "/usr/lib/pymodules/python2.7/matplotlib/image.py", line 429, in set_data
    raise TypeError("Invalid dimensions for image data")
    TypeError: Invalid dimensions for image data
    ##

    Which I believe is because I'm trying to plot 3 images in 1 2D image, where I should be making a very thin rectangular cube. Because the images are basically the same, I expect that all the information will be in the first part and only left-over stuff in the others as I am sampling a limited sized image. I just don't know how to do that!
     
  6. Aug 27, 2014 #5
    Try plotting the red, green, and blue sections separately.

    A few other comments on the code

    This could more easily be achieved using rollaxis(img, 2, 0):

    img_rgba = img.rollaxis(img, 2, 0)
    img_rgb = img_rgba[:3]

    Again, for real-valued input, the fft will have a second set of redundant conjugate negative-frequency values (the shift just moves them to to the beginning of the array, IIRC). I suggest using rfftn.
     
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