Re: [WM]: some explanation

["Jeffrey Bloom" <jbloom@sarnoff.com>]

At 04:22 AM 4/22/2005, Michel Chekrallah wrote:
>Hi great community,
>
>Can someone give me an explanation about what is Invariant to Rotation 
>and Translation?
>
>Thanks,

Good question.  Also a good time to make a distinction between invariance and synchronization.

Many watermarks will not be correctly detected in the face of temporal and geometric distortions.  For example, consider a white
noise pattern that is added to an image.  Since the white noise pattern itself has a very peaky autocorrelation function, detection
can be high when the watermarked image is correlated with the white noise pattern.  However, detection will be very low if the
watermarked image and the white noise pattern are not properly registered.  Misregistration will occur when the watermarked image is
subsequently scaled, rotated, translated, or geometrically distorted in any way.

One approach is to try to resynchronize the two prior to detection.  This can be done with a second registration pattern, or by
normalizing some moments of the image prior to both embedding and detection, or by embedding the pattern relative to salient points.
It is easy to resynchronize if the detector has another copy of the image known to be free of geometric distortions.

A second approach is to create a watermark that will be detected even in the presence of geometric distortions without the need for
resynchronization.  Such a watermark will be invariant to geometric distortions.  An obvious example is a watermark embedded in the
magnitude of the Fourier Transform of the image.  The magnitude of the Fourier Transform is known to be invariant to translation.
Thus, modulo cropping, the FFT magnitude of a translated image is the same as the FFT magnitude of an untranslated original.  So,
translation does not have a negative effect on detection.  The Fourier-Mellin Transform and other log-polar variants have been shown
to provide similar invariance to scaling and rotation.


=============================
Dr. Jeffrey A Bloom, Sarnoff Corporation, 201 Washington Road, CN 5300, Princeton, NJ 08543-5300 jbloom@sarnoff.com,
http://www.geocities.com/Jeffrey_Bloom, (609) 734-3287,
(609) 734-2662 fax


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