[opendtv] Re: Math of oversampling - a simple comparison
- From: Jeroen Stessen <jeroen.stessen@xxxxxxxxxxx>
- To: opendtv@xxxxxxxxxxxxx
- Date: Thu, 28 Apr 2005 09:09:48 +0200
Hello,
Tom Barry wrote:
> (...)
> this brings the total collection to 5 images, listed below in
> chronological order:
> (...)
> 4) Jeroen's Leno image creating by scaling to 544p and then back
> up to 1088p. Possibly softer but with fewer artifacts.
> http://www.trbarry.com/Leno_1080_544_1080p.jpg
>
> 5) Jeroen's Leno image creating by scaling all the way down to
> 480p and then back up to 1088p. Definitely softer but again with
> fewer artifacts.
I think you forgot to include the last link:
> http://www.trbarry.com/Leno_1080_480_1080p.jpg
My images are necessarily a bit softer than yours, because:
- I used realistic filters, you used a DCT truncation that is
equivalent to a brick-wall filter (with severe ringing),
- I actually performed the down-sampling and up-sampling, so
I had to worry about anti-aliasing. You did only a low-pass
filter (within each 8x8 block), and you assume that this is
good enough for down-sampling. It's not a bad assumption,
but you do show bad blocking artefacts.
- I tend to choose soft filters because I like to balance
between sharpness, aliasing and ringing artefacts. We have
to worry about moving pictures too, and motion tends to
reveal more of the aliasing artefacts.
I find it interesting to note that with otherwise identical AA
filters, there is a significant difference in sharpness between
the 544p and 480p intermediate steps. Due to the transposed
sample-rate converter design, the anti-aliasing filter scales
automatically with the output sample-rate (544p versus 480p).
So my filter has always 8 taps in the output space, this is
equivalent to 16 or 18.13 taps respectively in the input space.
The difference in bandwidth is only 480/544 = 88%, I had not
expected it to be so visible ! Anyone care to explain this ?
(Wasn't the original question about down-sampling to 480p ?)
I believe that I have designed my polyphase filters carefully
to have approximately equal bandwidth over all phases, for
sofar as this is mathematically possible.
(The half-pixel delay filter has a zero at 1/2*fS, it always
has less bandwidth than the zero-pixel delay filter. I designed
for a -3 dB point at 3/8*fS, which is not too high, I know.)
Tom:
> BTW, I was thinking again about the discussion of artifacts being
> caused at the edges of the 8x8 blocks. Of course I believe they
> will be created by MPEGx compression anyway.
Well... there is a difference between blind truncation of
higher DCT coefficients and adaptive quantisation of them.
Quantisation leaves at least something to soften the block
edges, but your choice for truncation of 48 out of 64 coefs
will always cause bad blocking. This is unnecessary if you
just down-sample the entire image before MPEG encoding.
> But it on the way home today it occurred to me that for the
> cost of a few hundred vectorized multiplies and additions per
> pixel it would probably be possible to treat the entire image
> as one big block and avoid this problem anyway.
Come on, re-sampling is not that expensive ! For the down-
sampling, for each of the H and V directions I paid 7
multiplies and 7 additions per input pixel (times 2 Mpixels
times 3 colors). Add to this the cost for converting to the
linear-light domain and back, but this is optional. (It does
improve the brightness of details.) For the up-sampling, for
each of the H and V directions I paid 5 multiplies and 5
additions per output pixel (times 2 Mpixels times 3 colors).
So in total it cost (7+5)*2M*3 = 72 Meg multiplies + 72 Meg
additions for the entire frame, down and back up. Decent
hardware these days can literally do it in 1/60th second.
> I need a faster computer.
I bet my computer is much slower than yours, but this was
only a few seconds work. I also had to convert jpeg to bmp
and back, because my simple scaler eats only bmp files.
And no, it is not open source code and I can not distribute it.
But I can give you all an impression of the 16-taps and 6-taps
filter coefficients that I have used in the process, so that
you may analyse the two filters for bandwidth.
Best regards,
-- Jeroen
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| From: Jeroen H. Stessen | E-mail: Jeroen.Stessen@xxxxxxxxxxx |
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