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

[Amr Nasr <amr128@yahoo.com>]

hi
 why are dealing with cartezian coordinates
  the polar coordinates are better , 
you will deal with the magnitude spectrum alone 
   so you can change it easily.
        as x=M.exp(theta)
            M is to be changed alone but preserving
the symmetric property
                                  AMR NASR
--- netzero <phsamuel@netzero.net> wrote:
> 
> Hi,
> 
> I didn't really look at your expression carefully.
> But there seems to be
> something wrong in a glance. You see, your
> expression only depend on
> tan(theta) alone instead of theta. tan(theta) has
> period of pi instead of 2
> pi. To be specific, you are counting theta+pi and
> theta as the same phase.
> 
> I think a more reasonable expression is simply:
> 
> let original= x+iy
> 
> The new coefficient=  x+iy * (mag' / mag)
> 
> i.e. Re'= x *(mag'/mag)
>      Im'= y *(mag'/mag)
> 
> where mag = sqrt(x*x+y*y) and mag' is your new
> magnitude.
> 
> Samuel
> 
> -------------------------------------
> Samuel Cheng
> Electrical Engineering Department
> Texas A&M University
> email: phsamuel@ee.tamu.edu
> 
> 
> -----Original Message-----
> From: watermarking-owner@watermarkingworld.org
> [mailto:watermarking-owner@watermarkingworld.org]On
> Behalf Of Editha A.
> DeLuna
> Sent: Wednesday, July 11, 2001 7:00 AM
> To: watermarking@watermarkingworld.org
> Subject: [WM]: On DFT/FFT-based Watermarking
> 
> 
> Hello everyone.
> 
> I am confuse with one very simple question.
> 
> On the DFT based watermark embedding, for instance,
> the watermark is
> embedded into the 1000 largest DFT Magnitude
> coefficient [Cox. et al].
> 
> So, for the color image, the process is:
> (1) Transform RGB into YCrCb components
> (2) FFT the Y component
> (3) Compute the magnitude & phase which is
>    mag = sqrt (Re*Re + Im*Im): MAGNITUDE
>    theta = atan2(Im,Re)  :PHASE
> (4) Embed the watermark into the magnitude
> (5) Compute for the new Re, Im components  after
> modifying the mag into
> mag'
> (6) IFFT
> (7) YCrCb --> RGB
> 
> My question is in no. (5). I don't know how to
> compute the Re and Im
> components of the modified magnitudes, I assumed
> that it can be computed
> by:
> 
>  Re'= sqrt((mag'*mag')/ 1+ tan(theta)*tan(theta))
>     since phase: tan(theta) = Im/Re didn't change.
> 
>  Im' = tan(theta)* Re'
> 
> But I am getting all (+) values for the Re, which is
> because I think my
> program takes only the positive results calculated
> from the square root.
> Thus, the resulted image is quite different from the
> original image.
> 
> Is my calculation wrong? Please advise me on this
> matter!
> 
> Thank you in advance.
> 
> Editha
> --------------o0o-------------------
> Editha A. DeLuna
> Graduate School of Electronics Engg.
> Nagaoka University of Technology
> Niigata, JAPAN
> email: edith@circuit.nagaokaut.ac.jp


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