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Article on texture generation - can't get the math

  1. May 21, 2015 #1
    There is an article on procedural texture generation by example.
    I'm trying to implement it, and got lost in the mathematics.
    http://graphics.cs.kuleuven.be/publications/LVLD10PISTE/

    The outline of the algorithm is thus:
    We start with a noise-like photo.
    tONUt63.png

    Do a 2D DFT of it:
    lWHUVy8.png

    Compute the power band coefficients and reconstruct the image with wavelet noise:
    AcMa4IH.png

    Wavelet noise is band limited, which makes it a good base block for such synthesis:
    54YFoLv.png

    That's the theory.

    In practice, i can't figure out the formula for the coefficients.

    Formula (E is the input image):
    dageAzm.png
    Definition of the power band:
    6vq2mqv.png

    What does it mean?
    Should i sum all the magnitudes of the elements in each band?
    This gives me nonsense if i divide it by the amount of elements, and randomly unscaled value if i don't (that's the above picture, guesstimately scaled).
    If i sum the real parts of the elements, then i get wildly wrong and out of scale figures. Normalising them also gives me something plausible.
    And so on, for any way i can think of.

    I guess i misunderstand something in the notation.
    Does the integral sign means summing here?
    Or how should i read it?

    That's basically the question - what does it mean?
    Bonus question - anyone heard of this method being used somewhere? A working implementation to peek at would be nice.
     
  2. jcsd
  3. May 27, 2015 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
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