Re: convolution versus PDE

Posted by Duane and Julie on Jul 29, 2006; 6:07pm
URL: http://imagej.273.s1.nabble.com/convolution-versus-PDE-tp3701910p3701911.html

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