Re: Is fourier descriptors invariant to starting point

"Abhishek" <abhisheksgumadi@xxxxxxxxx> wrote in news:1156966049.133621.95760
@e3g2000cwe.googlegroups.com:

Hi,
I have the following question:
I have extracted the signature from the 2D closed curve using
the complex coordinates method. The complex coordinates are
z(t) = [x(t) - xc] + i[y(t) - yc]
This is invariant to translation. xc are the centroids.
I take the forurier transform for these coordinates and normalize them
for scaling. I neglect the phase to take care of rotation. The
signature themseleves are invariant to translation.

If the fourier descriptors for another image are taken for a signature
extracted from a different starting point than the original signature,
will the fourier descriptors change?
If yes, how will they change and how do I take care of this situation?.




Carefull here: z(t) as well as the Fourier descriptors are transformations of your base data and
parametric against (t). Thus, if you start from a different point (t0) your signature will be "shifted"
accordingly. Only the -statistics- of this signature is invariant to the starting point, e.g. if you calculate
some roughness index (moving average). The only way to treat z(t) as invariant against (t0) is to make
it cyclic, i.e. make sure its "head" is linked to its "tail" during your calculations later on.


--
Harris
.

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