Posted by
Joachim Wesner on
URL: http://imagej.273.s1.nabble.com/convolution-versus-PDE-tp3701910p3701914.html
Hi
I´d mostly second this, for small kernels direct convolutions are surely
the quickest way (besides any edge/padding problems)
Convolutions (especially for large kernels) and PDEs can also both be
solved effectively by FFT methods, which however (might) have (depending on
your
problem) their own edge/padding/periodicity quirks. Those spectral methods
are often prefered because of their more "smoother", "global" solutions,
also because even multidimensional FFTs can be calculated pretty quickly on
today's computers.
See for ex.
http://www.pma.caltech.edu/~physlab/ph22_spring06/assgmt-4.pdfIt all depends....!?
Duane & Julie
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On Jul 27, 2006, at 9:31 AM, Martin du Saire wrote:
> Hi,
>
> This may be off topic but hopefully you won't mind too much: I
> recently "discovered" that many convolution operations can be
> performed using partial differential equations, quite often some
> form of the heat equation. Is there some advantage to this, and
> when would this be an appropriate route to take?
>
> Thanks.
>
> Martin
Convolutions are closed form. PDEs are solved using an iterative
process (in my experience), during which you have to decide when
you've reached an answer that is good enough or has quit changing.
I can't imagine how solving a PDE could be quicker than doing a
convolution. I don't see a real difference in answers. I'm trying
to come up with a reason to use PDEs over convolution, but I'm having
a hard time.
Perhaps if the convolution kernel is quite large, and you are willing
to have an approximate answer to avoid having to worry about padding
and/or edge effects?
duane
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