Re: [WM]: Watermark Detection Threshold Determination

[Teddy Furon <teddy.furon@ieee.org>]

There are roughly two ways to set a threshold T.
Before detailing them, let's denote what is important:
- Pfa : probability of false alarm
- Pp  : power of the detection test : probability that it detects a
watermark content. 

You have the following general equations
Pfa = f(T)
Pp = g(T)

1) You find a theoretical way to calculate the functions f(.) and g(.).
You may even express Pp without the need of T: Pp = h(Pfa).
This the ROC curve.
For gaussian signals, one has the famous equation:
Pp = Q ( Q^-1(Pfa) - sqrt(GN))
where Q is the cumulative probability function of a gaussian distribution, N
is the length of your vectors, and G is watermark to original content power
ratio.

You set T imposing a condition on Pfa or Pp. Usually, the condition is: Pfa
< a (so that the best decision rule strategy is a Neyman-Pearson test.)

2) Experimentally.

- Feed your detector with a lot of original contents. Store the results in a
vector C0 (i.e. the NCs).
- Feed your detector with a lot of watermarked contents. Store the results
in a vector C1...

you choose some thresholds T between min(C0) and max(C1). for each value,
you count the number of samples of C0 < T and the number of samples of C1 >
T. This gives you an estimation of Pfa and Pp. We can then plot the
experimental ROC curve. Of course, if you interested in low Pfa we will have
to feed your detector with a lot of original contents... hence, you won't be
able to go very far away.

hope this helps.
Teddy




> De : Eric Sheo <digitonkr@yahoo.com.sg>
> Date : Wed, 28 Nov 2001 06:45:55 +0800 (CST)
> À : <watermarking@watermarkingworld.org>
> Objet : [WM]: Watermark Detection Threshold Determination
> 
> Hi everyone,
> 
> I have doubts on the determination of the 'detection
> threshold'.
> 
> By approaching experimentally, assuming watermark
> (org_wm) is the original gaussian sequence of
> pseudo-random real numbers of length N.
> 
> Step 1. I generate 1000 gaussian sequences of
> pseudo-random real numbers of length N.
> 
> Step 2. I calculate the normalized correlation (NC)
> using org_wm with respect to each generated gaussian
> sequences of pseudo-random real numbers (step1).
> 
> To determine the detection threshold, do i sum all the
> normalized correlation (NC) and take the average of
> the NC and is there anything wrong with my steps? Pls
> give me your valuable advises. Thank you.
> 
> Eric
> 


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