RE: [WM]: Creating ROC Curves

["Bloom Jeffrey" <Jeffrey.Bloom@thomson.net>]

There is a good explanation and plenty of examples in the book "Digital Watermarking" by Cox, Miller, and Bloom (me) (see section
6.4).  You need to run enough images, both for true detection and for false detection, so that you can fit a good model.  It is
typical to model either the true detection or the false detection and to use actual data for the other.  You mentioned Gaussian
models, but depending on the detection statistic, a Gaussian model might not be the best fit.  You need to do some theoretical work
to predict how you expect the detection
values to be distributed.    (for example M. L. Miller and J. A. Bloom,
``Computing the Probability of False Watermark Detection'', Proceedings of the Third International Workshop on Information Hiding,
pp. 146-158,
1999.)

With these two models, you can determine the probability of false detection and probability of false rejection for a specific
threshold.
Those two values map to a single point on the ROC curve.  As you increase the threshold, the probability of false detection will
decrease and the probability of false rejection will increase. That's how you get the curve.

Hope this was helpful.

-----------------------------------------------------------------
Jeffrey A Bloom, Multimedia Security Group Thomson Multimedia Corporate Research, Princeton, NJ 08540
(609) 987-7727, (609) 987-7299 fax
http://www.geocities.com/Jeffrey_Bloom



-----Original Message-----
From: watermarking-owner@watermarkingworld.org
[mailto:watermarking-owner@watermarkingworld.org] On Behalf Of Mr jim jim
Sent: Thursday, July 21, 2005 10:22 AM
To: watermarking@watermarkingworld.org
Subject: [WM]: Creating ROC Curves

Hi all,
   I am new to watermarking and have been implementing some techniques.
I have come across the use of ROC curves and wondered if anyone could explain how I create them?
   I have seen somewhere that you test an image with watermarks which are embedded and also ones not embedded. How many of these
tests should I do? You need to create histograms from the detector output - is this just the ranges of values which the detector
returns? Do you create ranges which the output falls into? You then need to fit Gaussians to these two pdfs
- how does one do this and from there calculate the probability of false and probability of false rejection. 

Any help would be really appreciated,
Jim


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