Re: [Algorithms] Gaussian blur kernels

[Sam M. <sam...@ge...>]

I'm not sure I quite understand what you mean by antialiasing in your
experiment? 

If you have a line which you rasterise using the usual point sampling,
you will immediately produce aliasing (jaggies). Blurring the result
with any filter may make the output more acceptable - and some filters
may be more pleasant any others - but it doesn't remove the aliasing. It
just reduces the objectional high frequencies.

To remove the aliasing completely you can't blur after sampling*. You'd
need to rasterise the line by doing the integral over each pixel
properly, rather than point sample. This will produce an alias-free
result, but isn't exactly easy in general :). 

There are further details here though. When working with a pixel-basis
we aren't in exactly the same territory as when we point-sample. There
is a more general theory of sampling worked out largely by Papoulis and
another dude I forget. The concepts of band limited signals and the
reconstruction filters change as your basis changes. 

Cheers,
Sam

* In general - but using blue noise can help push the aliasing into high
frequencies which helps.

-----Original Message-----
From: Simon Fenney [mailto:sim...@po...] 
Sent: 17 July 2009 11:51
To: Game Development Algorithms
Subject: Re: [Algorithms] Gaussian blur kernels

Olivier Galibert wrote:
> On Thu, Jul 16, 2009 at 09:56:58AM +0100, Simon Fenney wrote:
>> 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...
> 
> Aren't we talking about graphics here?  Vision is area sampling,
> making box filters perfect for integer downsampling.  It's sound that
> is point sampling and hence sensitive to high frequency aliasing.  
> 
>   OG.

Oh, I agree that there is a difference between what is 'best' for audio
and graphics** but a box filter is far from an ideal way of downsampling
graphics. I had a test image which was rendered with 10k samples per
pixel but downfiltered*** using a box filter. The amount of aliasing
surprised people. 

To show why a box is inadequate, as a thought experiment, *temporarily*
consider the pixels as little squares (apologies to Alvy Ray Smith), and
draw, say, a 1/8th pixel wide, *nearly* horizontal white line on a black
background. Now imagine antialiasing it with a box filter.

Now consider either animating the line, shifting it vertically by a
fraction of a pixel per frame (and watch it jump), OR alternatively just
consider a static frame. Assuming we do the latter, start from a point
where the line crosses from one scanline into the next and run along the
row to the next crossing. With the box filter, except for the areas
where the line actually crosses the pixel boundaries, there will be a
large number of pixels with exactly the same intensity. AFAICS, your
brain expects to see more variation as the line sweeps across the
pixels.

Simon

** I have my own hypothesis on what is the root cause of this difference
which is being hotly debated here in our research office. I now just
need to install a better mathematical brain in my head to prove it :)

***In a linear colour space. This is V. important.


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