Posted by
Gabriel Landini on
May 04, 2007; 4:25pm
URL: http://imagej.273.s1.nabble.com/Filtering-with-Savitzky-Golay-tp3699606p3699610.html
On Friday 04 May 2007 14:11:00 Michael Schmid wrote:
> cleaning up my e-mails, I just stumbled over your old
> message to the ImageJ mailing list:
Thanks for the reply!
> > Then I realised something curious: the X0Y0 filters (the ones that
> > I think one
> > uses for smoothing), are the same for orders 2 and 3, and the same
> > for orders
> > 4 and 5 for a particular kernel size.
>
> I think this is ok. If you fit a polynomial of 3rd order into
> data points spaced symmetrically around x=0, the third order
> term will have an average of zero, thus it will never influence
> the 0 order term (i.e., the constant offset).
I see. So I wonder why are they given for the odd sized kernels if they are
not really different than the even ones... (I may be missing something).
> Looking at the Savitzky-Golay smoothing kernels, they have
> negative values at the edge. This means that they are not
> really the kind of functions one would usually like to have for
> smoothing. Also, to get the derivative of a function, the
> Savitzky-Golay kernels have positive edge values on the
> negative side, and vice versa.
> So, to get the derivative, if the standard 3x3 Sobel kernels
> produce too much noise, I would do some other type of smoothing.
Thanks again. If anybody wants to try these, I input the values listed in the
cpp program (from the original webpage) into a Convolve() macro string.
They do smooth the image... but I am not sure in which instances they would be
of particular use.
Cheers,
Gabriel