how to design 2D low pass filter that works with cycle per degree?

Discussion in 'Optometry Archives' started by kiki, Nov 16, 2004.

  1. kiki

    kiki Guest

    Hi all,

    I need to design a spatial 2D low pass filter, which cuts off high frequence
    component beyond C cycle per degree...

    Now I am given an image bitmap, which is MxN pixels...

    How can I design such a filter, how do I relate pixels to cycle per degree?

    I heard that cycle per degree is the unit of freuqency in spatial domain...

    I guess I need to do 2D FFT first, then apply an ideal rectangular
    shaped-low pass filter, or do I apply some fancy named filter such as raised
    cosine, etc.?

    Anybody has some ideas on how to do that? please help me!

    Thanks a lot
    kiki, Nov 16, 2004
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  2. kiki

    kiki Guest

    Hi Tim,

    Thanks a lot for your help! Ok, from my side I can

    1) Measure my viewing distance and the physical size of the image. And then
    I can compute the visual angles in degree...

    2) But how do I know how many cycles are there in these horizontal and
    vertical visual angles(in degree)?

    For sine/cosine grating image, I know how to count cycles... but for image,
    how do I do that?

    3) In fact, estimating the highest frequency(the highest cycles per degree)
    is one of my goal... I hope by doing 2D FFT I can determine where is the
    highest frequency...

    4) But when talking about 2D FFT, problem comes again how are those MxN FFT
    output matrix labeled, what is the unit of the FFT output? (cycle per
    degree, or pixels per degree, or pixels per meter, cycles per meter, cycles
    per pixel, etc.?)

    I don't need real-time implementation, I just need Matlab to determine the

    then I can cut off at certain cycle per degree -- Cutoff Frequency... do a
    low pass filtering...

    Why could not I find some information on the Internet? Neither did I find
    any books talking about these things... Any more thoughts? Thank you so
    kiki, Nov 16, 2004
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  3. Kiki,

    it´s perhaps simpler to use MxM pixel images by adding empty rows or
    empty columns. The FFT for non-square images is IMO wasted time.

    An interpretation by 'cycles per second':
    A pixel clock samples one pixel per second. This is a fictitious
    sampling frequency of 1 Hz. The highest signal frequency is o.5 Hz
    because of Nyquist.

    In the frequency domain we'll find frequencies up to 0.5 Hz. The lowest
    frequency is defined by the number of pixels in one row or column.

    It´s hardly possible to explain this in a post. The mathematics and some
    examples are e.g. here:

    Best regards --Gernot Hoffmann
    Gernot Hoffmann, Nov 16, 2004
  4. Like Tim (I didn't see his post, but only your reply) suggested, it is
    better to work in the spatial domain than the frequency domain, so no 2D

    Gaussian filters are something you might want to consider. They are the
    only class of filters whose spread function (a.k.a. impulse response /
    kernel) is center-symmetric when the processing is done in cascade on row
    and column data. Cheap infinite impulse response (IIR) designs exist. See
    van Vliet et al. (1998) Recursive Gaussian Derivative Filters:

    Olli Niemitalo, Nov 19, 2004
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