Deconvolution of Sensor Anti-Alias filter? - Page 2

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In article <boO_e.117692$G8.15563@text.news.blueyonder.co.uk>, David J
Taylor
<david-taylor@blueyonder.co.not-this-bit.nor-this-part.uk.invalid>
writes
>Kennedy McEwen wrote:
>[]
>> Minimum criteria for 50% probability of identification of a well
>> defined object on static images is at least 12 pixels linearly (more
>> correctly, 6 cycles resolved across the minimum dimension). This is
>> a well known standard that has been in use since the work of Johnson
>> etc. in the 1940s and 50s. With more closely related objects or
>> where a higher probability is necessary the requirement can be more
>> than 4-5x this.
>
>Remember as well that a well-trained observer (i.e. expert) can manager
>with a picture that looks like a blur to us. Example: doctors examining
>X-ray images.

Yes, and these figure assume a trained expert - even more resolution is
required to enable a novice to achieve the same probability of
identification.

> Also motion can play an important part - a human does not
>move in the same way as a vehicle, so you don't need to see the limbs to
>identify one versus the other.

Yes, motion does play a part and the resolution requirements for moving
images are substantially lower than for still frames. However, we are
talking about DSLRs here, producing still frames. It doesn't actually
matter that you can identify an object in the viewfinder if you can't do
so in the resulting photograph.

"Honest Guvnor, that fuzzy blob is a Yeti, you could tell by the way it
moved" doesn't really cut much ice. ;-)
--
Kennedy
Yes, Socrates himself is particularly missed;
A lovely little thinker, but a bugger when he's pissed.
Python Philosophers (replace 'nospam' with 'kennedym' when replying)

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"David J Taylor" <david-taylor@blueyonder.co.not-this-bit.nor-this-part.uk.invalid> writes:

>Thanks for that - I hadn't realised they were such crude filters compared
>to those we use in audio! It seems to me, therefore, all the more
>important that the lens has a well curtailed MTF.

Yes, it's not a low-pass filter at all, in and of itself.

The low-pass anti-alias filtering in a camera is actually provided by
at least 3 things:

- the blur spot of the lens
- the image-shifting "AA" filter, with its cos(pi*x) response
- integration over the area of the sensor pixels, or the lenslets
if the sensor is so equipped, with its sin(pi*x)/(pi+x) response

I suspect that the main contribution of the crystal "anti aliasing"
filter is not the prevention of aliasing at all, but:

- It acts as a notch filter to remove luminance modulation at Fs/2
because the Bayer filter array operates by *generating* modulation
of the signal from the sensor at exactly Fs/2 when the image is
coloured instead of grey. With the AA filter, the demosaicing
algorithm can reliably decode modulation at Fs/2 as colour,
avoiding luminance crosstalk into colour.

- It also acts to attenuate frequencies somewhat *below* Nyquist, which
is a good thing. In theory, any frequency below Nyquist could be
sampled and reproduced accurately - but only by using an infinitely
large reconstruction filter with "brick wall" response. Real computer
displays and real resampling algorithms do not use such filters, and
in practice television and digital photography can only resolve up to
about 70-80% of Nyquist before you start seeing artifacts. So it's
useful to attenuate these troublesome frequencies slightly below
Nyquist.

The lens blur provides a gradual falloff of MTF. Integration in the
sensor pixels gives a falloff with its first zero at the sampling
frequency; there's not much attenuation at Nyquist yet. Only the
AA filter provides significant attenuation below Nyquist.

Dave

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Ilya Zakharevich <nospam-abuse@ilyaz.org> writes:

>> A regular pattern in object space produces some finite amplitude of a
>> particular set of frequencies in image space.

>Nope. You forget about the light fall off.

What light fall off?

>> But if you want to be precise, if you managed to have image content at
>> exactly the Nyquist frequency, it would not be reliably sampled.

>Correct under the assumption. But the assumption is never satisfied.

It's still useful to write accurately.

>Again, this example contradicts what you say, and confirms what I
>said. You consider the image of a pattern at 1.32 of Nyquist, not of
>a pattern at Nyquist. With AAF with 0 at 0.9 of Nyquist (which you,
>apparently, like),

No, I've never said that. The best location for the filter zero is
right at Nyquist.

>the contrast of the fake image will be decreased by
>1/3, to 0.67 of the original value. With what I think is prefereable
>(0 at about 1.2 of Nyquist), the fake image will completely disappear:
>its contrast will decrease 6x.

Only for that particular frequency. But other frequencies closer to
Nyquist will be less attenuated than if the zero was at Nyquist.
The AA filter provides most of the attenuation for frequencies near
Nyquist, and that's where it's most important. At higher frequencies,
lens blur and integration over the sensor area start to provide more
attenuation and the AA filter is less important there.

The Sigma SD-9 is an extreme example because it (a) had no AA filter
at all, and (b) has a poor fill factor for its pixels, so the pixels
provide little filtering, and (c) has no lenslets. The SD-10 got
lenslets and showed less artifacts, though it still had no AA filter.
(And it doesn't need the AA filter to prevent luminance crosstalk
into chroma).

Dave

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"David J Taylor" <david-taylor@blueyonder.co.not-this-bit.nor-this-part.uk.invalid> writes:

>Thanks, Dave. I think there are a couple of messages I take from that:

>- the whole area is at least somewhat art as well as science, and full of
>best-judgement engineering compromises

There are a bunch of problems that make sampling images more difficult
than sampling 1D electrical signals (like audio), and thus everything's
a compromise:

In audio, you can build brick-wall analog filters that operate in the
time domain. There is no equivalent spatial-domain brick-wall filter
for images that I know of.

You can massively oversample audio, then do the brick-wall filter
cheaply digitally. Oversampling images is not practical because of
loss of sensitivity (light-collecting area), fabrication problems, and
the amount of data that would result.

You can use many-tap filters in audio because the data rate is modest.
Large 2D filters are often not practical in imaging, so most filters
are small (4x4).

>- having a fixed lens (as in point-and-shoot) might allow the overall
>system to be better optimised than where a variety of interchangeable
>lenses has to be accommodated.

Perhaps, but lens blur spot size (and profile) is still heavily
dependent on the aperture of the lens. Fixing the lens aperture fixes
that, but also removes depth-of-field control and gives only one
shutter speed choice for any given lighting conditions (unless you add
variable ND filtering).

Dave

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[A complimentary Cc of this posting was sent to
Dave Martindale
<davem@cs.ubc.ca>], who wrote in article <dhh31f$b4h$1@mughi.cs.ubc.ca>:
> >> I am not familiar with the expected response of optical AA filters. Can
> >> you point me to a plot of what you mean by cosine response - I hope you
> >> don't mean that if the zero is at half the sampling frequency, the
> >> response at the sampling frequency is -1.
>
> >Yes it is (but this is for the splitter which separates the (two)
> >images by 2 pixels). A splitter which separates the images by 1 pixel
> >has 0 response at Nyquist frequency, and response -1 at twice the
> >Nyquist.

>
> No, David was right - it's the response of a filter with one pixel
> separation. That has a zero at the Nyquist frequency, which is half the
> sampling frequency, and a -1 response at the sampling frequency which is
> twice Nyquist.

I see; so he said the same as me!

Thanks,
Ilya

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"Dave Martindale" <davem@cs.ubc.ca> wrote in message
newshh36a$b4h$2@mughi.cs.ubc.ca...
> "winhag@yahoo.com" <winhag@yahoo.com> writes:
>>Could the deconvolution of this be implemented in some sort of
>>Photoshop 'Custom filter'?
>
> Deconvolution can't bring back frequencies that are completely
> gone, where the filter has zero response. It could boost some
> of the frequencies that were only attenuated somewhat, at a
> cost of boosting noise.

Indeed , noise amplification is an issue in regular deconvolution.

> But the finer control you want over the shape of the filter, the
> larger the filter will be.

That's correct.

> I wonder how much better this approach could be than simple
> unsharp masking with well-chosen parameters.

One can try for themselves. This
<http://www.xs4all.nl/~bvdwolf/main/downloads/Batavia_Crop.jpg>(bottom-right)
is what I 'restored' from the bottom-left crop.

Bart