[SciPy-User] How to do symmetry detection?

Charles R Harris charlesr.harris@gmail....
Wed Jan 20 13:39:06 CST 2010


On Wed, Jan 20, 2010 at 12:26 PM, iCy-fLaME <icy.flame.gm@gmail.com> wrote:

> Thanks for the replies!
>
> Perhaps I should clarify that the input data can be int or float, and
> most of them will have a very large DC offset (i.e. sum(data) >> 0),
> and no, the signal duration can be anything, I can not "guess"
>
>
You should remove the offset, it is translation invariant anyway and gives
no symmetry information.


> The problem with convolution (scipy.signal.convolve) with self is, it
> will only produce one "valid" point in the middle, because anywhere
> else there is a mis-match of array shape.
>
>
This can be a problem if the symmetry is near an end, but won't matter much
if the relevant part is short or near the middle. The end effect will be a
problem no matter what method you use. Think of convolution as a matched
filter.


> I believe scipy.signal.convolve do not take into account of the number
> of points being integrated, and in the case of a large DC offset, any
> matches far from the middle of the data will be drowned by other areas
> which has more points to integrate over.
>
> Self convolution also has a problem of signal features matching
> itself. Imagine the input of the following:
>
> data: ______W____M_____
> data[::-1]: _____M____W______
>
> As you do the convolution, feature W will match itself first, then the
> W-M pair matching, then the M-M matching. Where a valid algorithm
> should only produce results for the W-M pair matching.
>
>
Well, there is no symmetry in that example. If you don't know if there is
symmetry then you have to account for that possibility in setting up the
statistics. I'm thinking Bayesian here.

Chuck
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