RE: [WM]: On DFT/FFT-based Watermarking

["Martin, Christopher \(cmarti02\)" <Cmarti02@harris.com>]

I think you can avoid the symmetry issues (at least w/FFT methods) by
performing a "real" FFT. This way you only get half the frequency domain
data and thus don't have to worry about symmetry. The packing of the data is
a little complex but not too bad. I've successfully used the routines by
www.fftw.org for this purpose.

Chris

-----Original Message-----
From: Samuel Cheng [mailto:phsamuel@netzero.net]
Sent: Thursday, July 12, 2001 10:47 AM
To: watermarking@watermarkingworld.org
Subject: RE: [WM]: On DFT/FFT-based Watermarking


and one more thing as supplement, be careful not to count the first row and
first column when locating the "center" of the magnitude matrix. for
example, if your matrix (i.e, your size of y-component) is 5x5, your
magnitude change should have symmetry around row "3.5" and col "3.5". for
instance, let m be your matrix of magnitude change. m(3,3)=m(4,4),
m(2,2)=m(5,5)...,etc. (see fig)

.... . . . .
.... x . . .
.... . o . .
.... . . o .
.... . . . x


however, for another example, if your matrix is 4x4, you should have
symmetry around row 3 and col 3. i.e., m(2,2)=m(4,4), m(2,3)=m(4,3),... etc.
(see fig)

.... . . .
.... x o .
.... . . .
.... . o x

am i right, amr?

Samuel

-----Original Message-----
From: watermarking-owner@watermarkingworld.org
[mailto:watermarking-owner@watermarkingworld.org]On Behalf Of Amr Nasr
Sent: Thursday, July 12, 2001 9:26 AM
To: watermarking@watermarkingworld.org
Subject: Re: [WM]: On DFT/FFT-based Watermarking


Hello Mr.AMGee,
   the symmetric properties are simple
  that means when you the fourier transform
 the output will be magnitude and phase angle
   the phase angle is critical so we will not change
it
 So we will work with the magnitude ,ok.
  In order to change the magnitude properly
 we should know that the center frequency component at
the center of the magnitude matrix .
                 [.................]
                 [.................]
                 [........x........]
                 [.................]
                 [.................]
      like the x in the figure.
   any points around it changed , their mirror around
this point should be changed in the same manner.
  according to the symmetric property these values are
identical , and if they are not identical you will
face tough problems of the complex magnitudes
                               that is it.
                                   AMR NASR


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