posted on Jul, 24 2004 @ 10:52 PM
Ah... I see now.
From:
www.cs.dartmouth.edu...
which is the actual published report.
Here is the key to his sampling: "When creating digital forgeries, it is often necessary to scale, rotate, or distort a portion of an image. This
process involves re-sampling the original image onto a new lattice. Although this re-sampling process typically leaves behind no perceptual artifacts,
it does introduce specific periodic correlations between the image pixels." (pp 10)
I currently work as a "digital image specialist" at a record archive group for a certain university. Sometimes I have to work off of contact sheets
that have numbers in grease marker written all over them. I have found, overall, using Photoshop, I never have to scale or distort segments of the
image. I admit I have had to rotate a segment. But his algorithm is cumulative (convoluted, technically
) and I doubt small instances of rotation
matter.
Most forgeries do not require wholesale scaling and rotating. Oftentimes the stamp tool, aligned with the previous sample point, is enough.
He also writes:
There is a range of re-sampling rates that will not introduce
periodic correlations. For example, consider down-sampling
by a factor of two (for simplicity, consider the case where
there is no interpolation). The re-sampling matrix, in this case,
is given by:
(fig 14)
Notice that no row can be written as a linear combination
of the neighboring rows - in this case, re-sampling is not
detectable. More generally, the detectability of any re-sampling
can be determined by generating the re-sampling matrix and
determining whether any rows can be expressed as a linear
combination of their neighboring rows - a simple empirical
algorithm is described in Section III-A.
Since he's working in a 2d matrix format, row format, left to right ("linear combination of the neighboring rows"), and rotation works diagonally,
it is unlikely to be detected.
What he has achieved, however, is amazing. Take a look at his polar Fourier graphs of the altered images. The pinpoints indicate row disparity and
hence forgery.