Re: [Algorithms] Gaussian blur kernels

[Simon F. <sim...@po...>]

Jon Watte wrote:

> Actually, they are both low-pass filters, so
> downsampling-plus-upsampling is a form of blur. However, box
> filtering (the traditional downsampling function) isn't actually all
> that great at low-pass filtering, so it can generate aliasing, which
> a Gaussian filter does not.

AFAICS a box filter won't "generate" aliasing, it's just that it's not
very good at eliminating the high frequencies which cause aliasing. A
Gaussian, OTOH, has better behaviour in this respect...

> (AFAICR, the Gaussian filter kernel
> shares some properties with a sinc reconstruction kernel, and thus is
> "optimal" under certain conditions/assumptions, but details are
> hazy).       

...again, (and my recollection, too, is a bit hazy), the shape of a
Gaussian filter in the frequency domain is, again, a Gaussian, so it's
still going to let through some amount of illegally high frequencies. In
order to stop that, one will probably need to make it a bit wider which,
unfortunately, means it'll over-filter some of the legal frequencies
you'd want to keep.

A sinc filter, when mapped into the frequency domain, is a box and so
has a hard cut-off of higher frequencies, which should be ideal.

OTOH, I think that a box filter, when mapped into the frequency domain,
looks a bit like a sinc, which is why it behaves so poorly.

Cheers
Simon