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Photo Forum / Digital Photography / Digital Photo / September 2005

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Deconvolution of Sensor Anti-Alias filter?

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winhag@yahoo.com - 09 Sep 2005 21:42 GMT
Folks,

Another 'do they do that and if not, why?' question.
Canon's sensors have an anti-alias filter for good reason.
Most everyone uses some sort of Unsharp-Mask to 'restore'
the 'sharpness' to the somewhat soft images.
Since the anti-alias filter is known and well defined,
wouldn't it make more sense to use a true 'reconstruction filter' (vs.
USM)
when processing RAW files as is typically done in sampled data systems?
I would think this could avoid some of the USM artifacts.
Does anyone know if this is done or is practical?

W
Jim - 09 Sep 2005 22:19 GMT
> Folks,
>
[quoted text clipped - 10 lines]
>
> W

No, the best place to put a filter is before the data gets sampled.  Analog
filters also don't present much of a computational load on the camera.
Deconvolution is a very different process.
Jim
winhag@yahoo.com - 09 Sep 2005 22:59 GMT
I may not have been clear. The optical anti-alias filter is before the
sensor. What I am suggesting is that a software reconstruction filter
be used on the RAW data to undue the in-band suppression caused by the
optical anti-alias filter.
Leonard - 10 Sep 2005 00:19 GMT
> I may not have been clear. The optical anti-alias filter is before the
> sensor. What I am suggesting is that a software reconstruction filter
> be used on the RAW data to undue the in-band suppression caused by the
> optical anti-alias filter.

Makes sense to me. Possibly USM is 'good enough' that there isn't enough
interest in doing what you suggest. Especially as it seems to be the
fashion that the 'appropriate' amount of sharpening is 'as much as
you can possibly get away with without introducing gross artefacts'.

- Len
Jim - 10 Sep 2005 00:28 GMT
>I may not have been clear. The optical anti-alias filter is before the
> sensor. What I am suggesting is that a software reconstruction filter
> be used on the RAW data to undue the in-band suppression caused by the
> optical anti-alias filter.

There might not be any in-band suppression.  In any case, only Canon would
know.  You can think of the anti-aliasing filter as a kind of UV (low pass)
filter.  These filters don't have much affect on visible light.
Jim
Andrew Haley - 10 Sep 2005 14:24 GMT
> I may not have been clear. The optical anti-alias filter is before
> the sensor. What I am suggesting is that a software reconstruction
> filter be used on the RAW data to undue the in-band suppression
> caused by the optical anti-alias filter.

The transfer function of the anti-aliasing filter is multiplied by the
transfer function of whetever lens you use, so it makes sense to
compensate for both together.  

In theory it is undoubtedly possible to muliply by the inverse
transfer function, but there is a really easy way to achieve the same
effect by using Imatest.  All you have to do is measure the MTF of the
system and then adjust unsharp mask parameters until you get a sharp
black-to-white edge with no ringing.  This doesn't take very long to
do, and it's unlikely that anything more mathematically sophisticated
would look much different.

Andrew.
Bart van der Wolf - 10 Sep 2005 00:45 GMT
> Folks,
>
[quoted text clipped - 6 lines]
> filter' (vs. USM) when processing RAW files as is typically
> done in sampled data systems?

Yes, but you should ideally also include the interaction of the lens
with the AA-filter in the same equation.

> I would think this could avoid some of the USM artifacts.
> Does anyone know if this is done or is practical?

I do it,
<http://www.xs4all.nl/~bvdwolf/main/downloads/Batavia_Crop.jpg>
demonstrates capture sharpening only, and it's very practical for
special (low volume) cases but also computationally expensive (very
slow). It is however not a widespread practice outside
astronomical/scientific photography.

One could, as an alternative, create a high-pass 'capture-restoration'
filter based on the Point-Spread-Function (PSF) of the imaging chain,
and it will largely compensate for capture losses without introducing
halo, but it will enhance noise if used without an edge mask.

There are several programs that allow deconvolution sharpening,
including Photoshop CS2 (Smart Sharpen filter), and DxO, and a few
others as well. The success usually depends on a good description of
the system blur (PSF), which can be obtained with e.g. Imatest
(www.imatest.com) software.

Bart
winhag@yahoo.com - 10 Sep 2005 03:51 GMT
Looks interesting. I understand your point about including the whole
chain, but I would be happy to
'attack' the anti-alias filter only. Since this is a known quantity (at
least by Canon) it would be nice
if they supplied software to compensate for it. I will look into the
options you mentioned.

Thanks
Bart van der Wolf - 10 Sep 2005 14:38 GMT
SNIP
> I will look into the options you mentioned.

You may also want to check out Image Analyzer
<http://meesoft.logicnet.dk/>, a free image analyzer/editor
(unfortunately only 8-bit/channel) written to assist with several
scientific imaging tasks.

Look at the "Filters|Restoration by deconvolution ..." option.
Choosing a Gaussian blur model with 0.70 to 0.95 radius, will add
sharpness with each iteration (often maxing out at 6 or 7) while
mostly avoiding typical USM artifacts.

Bart
Charles Schuler - 10 Sep 2005 01:13 GMT
> Folks,
>
[quoted text clipped - 8 lines]
> I would think this could avoid some of the USM artifacts.
> Does anyone know if this is done or is practical?

The anti-alias filter no doubt has a specified Bode response.  I have no
idea what the production variation parameters are.  Ignoring production
variations, it should indeed be possible to correct for the filter in RAW
post processing (with a hell of a lot less guessing than USM).  You have
asked a very good question.
MitchAlsup@aol.com - 12 Sep 2005 21:24 GMT
The blur pattern created by the AA filter is 'remarkably' Gaussian, and
can be effectively nulled out with the ubiquitous USM filter. If it
were far from Gaussian, then you might do better with a matched spatial
filter, but this seems unnecessary at this point.
winhag@yahoo.com - 21 Sep 2005 14:56 GMT
Thanks. Do you have any reference for the AA filter characteristics?
Bart van der Wolf - 23 Sep 2005 01:32 GMT
> Thanks. Do you have any reference for the AA filter characteristics?

The camera manufactures are not clear on what they really/actually
chose as a compromise.

The closest one may come to it is what Canon discloses:
http://www.canon.com/technology/d35mm/01.html

The "point blur' introduced by such a filter will usually spread the
signal pixel signal over 2 pixels, although the exact PSF
(point-spread-function) remains a bit of an "unknow". Given a choice
of material (Lithium Niobate) "thickness", and layers' orientation,
distance will determine the amount of actual spread.

Bart
Dave Martindale - 24 Sep 2005 18:46 GMT
>The closest one may come to it is what Canon discloses:
>http://www.canon.com/technology/d35mm/01.html

>The "point blur' introduced by such a filter will usually spread the
>signal pixel signal over 2 pixels,

4 pixels, because there are layers that provide horizontal and vertical
separation.  The illustration shows how a high-frequency dot image gets
spread into 4 dots.

>Given a choice
>of material (Lithium Niobate) "thickness", and layers' orientation,
>distance will determine the amount of actual spread.

I've been told that manufacturers treat this is a tunable parameter.  If
the spread is exactly one pixel pitch, you get a null in the response of
the system right at the Nyquist frequency, which is theoretically good.
But if you reduce the spread to perhaps 0.8 pixels, you get slightly
sharper-looking images at the risk of having more aliasing.

    Dave
Bart van der Wolf - 25 Sep 2005 01:25 GMT
SNIP
> 4 pixels, because there are layers that provide horizontal and
> vertical separation.  The illustration shows how a high-frequency
> dot image gets spread into 4 dots.

You're right, I was thinking about a single dimension spread.
The spread is obviously taking place in two dimensions.

Bart
Ilya Zakharevich - 26 Sep 2005 08:26 GMT
[A complimentary Cc of this posting was sent to
Dave Martindale
<davem@cs.ubc.ca>], who wrote in article <dh43ej$6ce$1@mughi.cs.ubc.ca>:
> >Given a choice
> >of material (Lithium Niobate) "thickness", and layers' orientation,
[quoted text clipped - 3 lines]
> the spread is exactly one pixel pitch, you get a null in the response of
> the system right at the Nyquist frequency, which is theoretically good.

I do not see how this may be "theoretically good".  There is no
aliasing at the Nyquist frequency, it appears *above* Nyquist.  So
having a zero at Nyquist has absolutely no point.

Extending this by continuity: if you have an image with visible
frequency at 1.1 Nyquist, you get it aliased to 0.9 Nyquist.  My
impression is that such a small difference between "actual" and
"recorded" frequency will not create any *visible* moire.

The "annoying" Moire is when some frequency in the image is aliased
into a *LOW* frequency in the recorded data.  E.g., if some frequency
is aliased into one 1.5x smaller (I think this is the practical limit
of visible moire).  This give 1.2 Nyquist aliased into 0.8 Nyquist.

So one should not care *much* about efficiency of anti-aliasing filter
below the frequency of 1.2 Nyquist.  So it looks like optimal position
for a zero of MTF is about 1.4 Nyquist (so the critical range 1.2--1.6
Nyquist is "well-covered").

Of course, the actual numbers I used are hunches only; it is easy to
simulate the process on computer and compare results *visually* to
obtain the "best" choices.

Hope this helps,
Ilya
David J Taylor - 26 Sep 2005 09:48 GMT
[]
> So one should not care *much* about efficiency of anti-aliasing filter
> below the frequency of 1.2 Nyquist.  So it looks like optimal position
[quoted text clipped - 7 lines]
> Hope this helps,
> Ilya

It would be interesting to see the results of such tests.  My hunch is
that images from cameras with AA filters having a zero MTF just /before/
Nyquist would look subtly better than those where above Nyquist (e.g. 1.2)
is allowed.

Indeed, it may be factors like this which help fuel the Nikon/Canon
"wars" - different people have differing sensitivities to the artefacts
introduced by such MTF/aliasing differences.

David
Ilya Zakharevich - 27 Sep 2005 06:50 GMT
[A complimentary Cc of this posting was sent to
David J Taylor
<david-taylor@blueyonder.co.not-this-bit.nor-this-part.uk.invalid>], who wrote in article <mBOZe.115880$G8.51148@text.news.blueyonder.co.uk>:

> It would be interesting to see the results of such tests.  My hunch is
> that images from cameras with AA filters having a zero MTF just /before/
> Nyquist would look subtly better than those where above Nyquist (e.g. 1.2)
> is allowed.

Why do you think so?  E.g., consider 0.9 vs 1.2; consider a pattern
with frequency 1.5 Nyquist.  Your choice will pass through 87% of the
aliased pattern; mine only 38%.  [*]  Note that the aliased pattern
has frequency of 0.5 Nyquist, so should be very noticable.

> Indeed, it may be factors like this which help fuel the Nikon/Canon
> "wars" - different people have differing sensitivities to the artefacts
> introduced by such MTF/aliasing differences.

Sure, it is a human-centered design, so different people will like
different choices.  However, IIUC, the choice of 0.9 should be
"practically always" worse than 1.2.

Hope this helps,
Ilya

[*] This assumes that the performance of the splitting filter is
   governed by the cosine law.  In other words, the length of
   coherence of the light reflected by the pattern is smaller than
   difference in two optical paths through the splitter.

   If the length of coherence is high enough, the law becomes cosine
   squared.  Who knows which one is applicable on practice?
David J Taylor - 27 Sep 2005 09:26 GMT
> [A complimentary Cc of this posting was sent to
> David J Taylor
[]
>> It would be interesting to see the results of such tests.  My hunch
>> is that images from cameras with AA filters having a zero MTF just
[quoted text clipped - 5 lines]
> aliased pattern; mine only 38%.  [*]  Note that the aliased pattern
> has frequency of 0.5 Nyquist, so should be very noticable.

That's not what I meant - I meant a filter which had a cut-off of 0.9 of
the sampling frequency.  You were suggesting a cut-off just above, I'm
suggesting keep it below as theory requires.

David
Ilya Zakharevich - 27 Sep 2005 22:32 GMT
[A complimentary Cc of this posting was sent to
David J Taylor
<david-taylor@blueyonder.co.not-this-bit.nor-this-part.uk.invalid>], who wrote in article <Rm7_e.116477$G8.86155@text.news.blueyonder.co.uk>:
> >> It would be interesting to see the results of such tests.  My hunch
> >> is that images from cameras with AA filters having a zero MTF just
> >> /before/ Nyquist would look subtly better than those where above
> >> Nyquist (e.g. 1.2) is allowed.

> > Why do you think so?  E.g., consider 0.9 vs 1.2; consider a pattern
> > with frequency 1.5 Nyquist.  Your choice will pass through 87% of the
> > aliased pattern; mine only 38%.  [*]  Note that the aliased pattern
> > has frequency of 0.5 Nyquist, so should be very noticable.

> That's not what I meant - I meant a filter which had a cut-off of 0.9 of
> the sampling frequency.  You were suggesting a cut-off just above, I'm
> suggesting keep it below as theory requires.

As I show above, the theory requires exactly the opposite.  Or did I
misunderstand you?  What is a "cut-off"?  AAFs have no cut-off, their
MTF is given by cosine law.  What I was discussing was the position of
the first zero.

Hope this helps,
Ilya
David J Taylor - 28 Sep 2005 10:17 GMT
> [A complimentary Cc of this posting was sent to
> David J Taylor
[quoted text clipped - 22 lines]
> Hope this helps,
> Ilya

There's a factor of two missing here!  My last message was confused, I
meant 0.9 of the Nyquist frequency - half the sampling frequency.  Sorry!
I'm more used to electrical AA filters, where you aim to get a brickwall
response (whilst not compromising phase linearity too much).

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.

David
Ilya Zakharevich - 29 Sep 2005 00:12 GMT
[A complimentary Cc of this posting was sent to
David J Taylor
<david-taylor@blueyonder.co.not-this-bit.nor-this-part.uk.invalid>], who wrote in article <0dt_e.117155$G8.29444@text.news.blueyonder.co.uk>:

> 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. [*]

All AAF does it breaks image into two, and moves the parts aside a
little bit (well, the actual AAF does it twice: horizontally and
vertically).  If it moves it the distance A, then from signal 2f(X) you
get f(X + A/2) + f(X - A/2).

Hope this helps,
Ilya

[*] Again, this assumes completely in-coherent light.  For
completely-coherent light you get the square of this.  This is why my
question about length of coherence is relevant.
winhag@yahoo.com - 29 Sep 2005 04:09 GMT
Could the deconvolution of this be implemented in some sort of
Photoshop 'Custom filter'?

> [A complimentary Cc of this posting was sent to
> David J Taylor
[quoted text clipped - 21 lines]
> completely-coherent light you get the square of this.  This is why my
> question about length of coherence is relevant.
Dave Martindale - 29 Sep 2005 17:02 GMT
>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.  But the finer control you want over the shape of the filter, the
larger the filter will be.

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

    Dave
Bart van der Wolf - 30 Sep 2005 02:50 GMT
>>Could the deconvolution of this be implemented in some sort of
>>Photoshop 'Custom filter'?
[quoted text clipped - 3 lines]
> 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
Ilya Zakharevich - 30 Sep 2005 08:47 GMT
[A complimentary Cc of this posting was sent to
Bart van der Wolf
<bvdwolf@no.spam>], who wrote in article <433c9a36$0$11078$e4fe514c@news.xs4all.nl>:

> 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.

This is an interesting exersize.  However, note that IMO application
of Richardson - Lucy to "ordinary" photographic images is misplaced.

AFAIU, Richardson - Lucy "improves" the image basing on two assumptions:

 a) What you have is a convolution of the initial signal with known
    PSF with some noise;

 b) The initial signal is non-negative.

The usefulness of RL in astrophotography is, IMO, mostly due to the
fact that for this application part "b" carries as much information
content as the part "a" (at least in images where the improvements
given by RL are most striking).  Since the information in "b" is "very
nonlinear" in nature, very resource-consuming algorithms are needed to
use this information.  [*]

However, "traditional" photography does not have the 100000:1 contrast
ratio of the night sky; neither has it most of the image "manifestly
black" (unless you consider some styles of night photography - some
night cityscapes should be very similar to astro).  For such images
(where the information content of "b" is close to 0) simple
deconvolution may give *exactly the same result* as application of RL.
Thus using RL is not going to improve image a bit comparing to the
simple deconvolution.

The simple litmus test for usefulness of RL: if the image produced by
RL has no (or almost no) "absolutely black" parts (those with 0 at one
of the channels), then it did not use the information in "b", and it
did not use the information about the distibution of noise in the
signal.  Thus its results coincide with pure deconvolution.

Likewise, if pure deconvolution did not produce negative signal, then
its results will coincide with those of RL.

[*] Although I very much suspect that I would be able to deduce a
   better algorithm than just the plain iteration method
   traditionally used to solve RL equations...

Hope this helps,
Ilya

P.S.  And, of course, the question remains on how to obtain the PSF of
     the lens.  But this question is common to RL and "pure
     deconvolution".

     Note that in

ilyaz.org/software/tmp/KM_A200-resolution-chart-ACRraw-quadratic-58percent-quartic-60percent.jpg

     I obtained the PSF to deconvolve via spectral analysis of edges
     of big black sloped squares.  You won't get such nice reference
     points on the "real" images, like one of yours.

     And on my image is it is not "full" deconvolution; I had chosen
     coefficients so that the throughput MTF is practicaly flat up to
     50% of Nyquist:

1   """"""""""""""""xxxx____'''''''''''''''''''''''''''''''''''''''|
   |                       ""xx__                                 |
   |                             ""xx_                            |
   |                                  "xx_                        |
   |                                      "_                      |
   |                                        "x                    |
   |                                          "x                  |
   |                                            "_                |
   |                                              x               |
   |                                               "_ |           |
   |                                                 _|           |
   |                                                  x           |
   |                                                  |x          |
   |                                                  | x         |
   |                                                  |  x        |
   |                                                  |   "       |
   |                                                  |    "      |
   |                                                  |     "     |
   |                                                  |      "_   |
   |                                                  |        _  |
   ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,|,,,,,,,,,x,,
-.05|..................................................|.........."_
   0                                                           3000

     The scale is in single lines per picture height, and the
     vertical line is the Nyquist frequency.

P.P.S.  Looking at the above graph, you can immediately see that the
    AAF for this camera has its first zero about 1.17 of Nyquist.
Bart van der Wolf - 30 Sep 2005 02:51 GMT
>>Could the deconvolution of this be implemented in some sort of
>>Photoshop 'Custom filter'?
[quoted text clipped - 3 lines]
> 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 oneselve. This
<http://www.xs4all.nl/~bvdwolf/main/downloads/Batavia_Crop.jpg>(bottom-right)
is what I 'restored' from the bottom-left crop.

Bart
David J Taylor - 29 Sep 2005 10:19 GMT
> [A complimentary Cc of this posting was sent to
> David J Taylor
[quoted text clipped - 24 lines]
> completely-coherent light you get the square of this.  This is why my
> question about length of coherence is relevant.

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.

David
Ilya Zakharevich - 29 Sep 2005 16:57 GMT
[A complimentary Cc of this posting was sent to
David J Taylor
<david-taylor@blueyonder.co.not-this-bit.nor-this-part.uk.invalid>], who wrote in article <ZkO_e.117691$G8.109896@text.news.blueyonder.co.uk>:
> > All AAF does it breaks image into two, and moves the parts aside a
> > little bit (well, the actual AAF does it twice: horizontally and
> > vertically).  If it moves it the distance A, then from signal 2f(X)
> > you
> > get f(X + A/2) + f(X - A/2).

> 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.

Since any lens has "a well curtailed MTF" (at least at some F-stops)
this translates (in the age of cheap electronics):

 it is important that Nyquist frequency of the sensor is close to the
 first zero of the "best" MTF of the lens.

E.g., as I shown in another thread, pushing about 2.5 more pixels into
current FF (or close) cameras AND removing AAF should produce (with a
good lens) practically the same "resolution-wise quality of the
picture" (i.e., will allow 1.5x larger magnification).  It will also
produce no degradation in the visible noise - as far as you stay 1.5x
further away from the picture.

So you can "dive 1.5x deeper" into the resulting picture: when you
stay far away, the resolution is limited by the resolution and the
field of view of the eye; but you can come close to inspect a smaller
area of the image.  The range of viewing distances where you are
limited by resolution of the eye is going to be 1.5x larger with this
sensor.  (If you do a lot of postprocessing, the dark area of the
image may be noisier at the closest viewing distances, which were not
satisfactory resolution-wise with the coarser sensor.)

Apparently, currently such sensors are not yet realistic due to
limitations of firmware of cameras.

Hope this helps,
Ilya
Dave Martindale - 29 Sep 2005 17:16 GMT
>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
David J Taylor - 29 Sep 2005 17:28 GMT
[]
> Yes, it's not a low-pass filter at all, in and of itself.
>
[quoted text clipped - 32 lines]
>
> Dave

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

- 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.

Cheers,
David
Dave Martindale - 29 Sep 2005 20:57 GMT
>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
Ilya Zakharevich - 30 Sep 2005 00:14 GMT
[A complimentary Cc of this posting was sent to
Dave Martindale
<davem@cs.ubc.ca>], who wrote in article <dhhgv4$eo0$1@mughi.cs.ubc.ca>:
> 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.

IIRC, audio brick-wallish filters use about 18 different delays of the
signal (e.g., you can count one resistor-capacitor pair as one delay).
So, in principle, you can expect to get similar performance with
2*18-layer splitter.  ;-) [Of course, you need polarization rotators
too. ;-)]

> 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.

Obviously, there is neither loss of sensitivity, nor fabrication
problems (at least as you go down from 8micron to 2.2microns).  And I
hope that the last problem you mention will disappear in 2-3 years
too.

> >- 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.

IMO, this is definitely a factor.  However, a larger factor is that
the price of similar-quality lens (measured via MTF at a given F-stop)
decreases *enormously* when the sensor size decreases.  Thus current
small-sensor cameras have lenses with MTF one cannot even dream of for
sub-$100000 budget in 35mm format.

Hope this helps,
Ilya
Dave Martindale - 30 Sep 2005 17:14 GMT
>[A complimentary Cc of this posting was sent to

>> 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.

>Obviously, there is neither loss of sensitivity, nor fabrication
>problems (at least as you go down from 8micron to 2.2microns).  And I
>hope that the last problem you mention will disappear in 2-3 years
>too.

We had this argument a couple of months ago.  Everyone except yourself
seems to agree that making smaller sensor pixels reduces useful
sensitivity as well as dynamic range.  In audio, increasing the
digitizer sample clock does not do that.

If you're building a DSLR sensor, you could use current technology to
build a sensor with 2-3 um pixel pitch instead of 8 um.  But if you're
talking about a P&S camera that *already* has a 2-3 um pixel pitch,
you're going to have sever problems reducing that by a factor of 4.
Handling more data could be now, at some increase in cost, if the other
problems were not there and the benefits of oversampling seemed worth
the cost.  I really don't think memory or signal processor speed is the
important limitation.

>IMO, this is definitely a factor.  However, a larger factor is that
>the price of similar-quality lens (measured via MTF at a given F-stop)
>decreases *enormously* when the sensor size decreases.  Thus current
>small-sensor cameras have lenses with MTF one cannot even dream of for
>sub-$100000 budget in 35mm format.

If you measure MTF in terms of line pairs per mm.  But the small-sensor
images have to be enlarged further, cancelling much of this advantage.
When comparing different sensors, it makes more sense to compare in
units of line pairs per picture height (or width).  Then the lenses on
small-sensor cameras won't look so good in comparison to 35 mm or larger
format lenses.

    Dave
Ilya Zakharevich - 30 Sep 2005 22:18 GMT
[A complimentary Cc of this posting was sent to
Dave Martindale
<davem@cs.ubc.ca>], who wrote in article <dhjoa1$r8$1@mughi.cs.ubc.ca>:
> >> 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.

> >Obviously, there is neither loss of sensitivity, nor fabrication
> >problems (at least as you go down from 8micron to 2.2microns).  And I
> >hope that the last problem you mention will disappear in 2-3 years
> >too.

> We had this argument a couple of months ago.

Right.

> Everyone except yourself seems to agree that making smaller sensor
> pixels reduces useful sensitivity as well as dynamic range.

First of all, this would not make my statement any bit less true.
This is similar to saying "I have a paper on this subject" assuming
that it somehow substantiates some (obviously) BS claim [I can recall
several prominent people on this newsgroup who suffer from this].

Second, I think your memory is about this is faulty.  Even Roger (who
looks a very slow learner) finally agreed that having a read noise of
5 electrons or less would allow a major oversampling; and now he even
says that 2 electrons is not a big deal with today's technology.

> In audio, increasing the digitizer sample clock does not do that.

There is no big difference between sampling video and sampling audio;
you noise is a combination of several terms with different dependence
on sample size.  What is important is the relative magnitude of parts
whose relative contribution increases as sampling rate increases.
This is readout noise for video.

> If you're building a DSLR sensor, you could use current technology
> to build a sensor with 2-3 um pixel pitch instead of 8 um.

Right.  And this is 4x oversampling.  It is an overkill:  with most of
35mm format lenses, you do not need anything better than about 3-4
microns.  As I explained in another thread, decreasing the pitch to
5.5 microns will remove aliasing as much as the current AAF do.

And it will not change the narrow-band noise.  So by filtering out
high frequencies ("oversampling") you can get the same picture as with
current sensor - if you are in really low-light situation.

> But if you're talking about a P&S camera that *already* has a 2-3 um
> pixel pitch, you're going to have sever problems reducing that by a
> factor of 4.

Why do you chose 4, and not 40?  In this thread I was talking about
factor of 1.5.  This is about 2-3 years timeframe (to get decent fill
factor) if the Moor law continues to hold.

> Handling more data could be now, at some increase in cost, if the other
> problems were not there and the benefits of oversampling seemed worth
> the cost.

What cost?  AAF can cost of an order of magnitude of $1000...
And what other problems?  As you saw, there is no other problem.  So
if I did not oversee something, the data handling is the only limitation.

> >IMO, this is definitely a factor.  However, a larger factor is that
> >the price of similar-quality lens (measured via MTF at a given F-stop)
[quoted text clipped - 4 lines]
> If you measure MTF in terms of line pairs per mm.  But the small-sensor
> images have to be enlarged further, cancelling much of this advantage.

*Much*?  Try to find 35mm lenses which have similar resolution (in
lines per picture height) to current 2/3'' offerings.  I can even
allow you compare $4000 35mm format lenses with (apparently) $200
2/3'' lenses...  :-(

Hope this helps,
Ilya
Dave Martindale - 29 Sep 2005 16:59 GMT
>> 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.

Here, the -1 means that a signal at the sampling frequency is not
attenuated at all, but it is shifted half a pixel which is a 180 degree
phase shift which is equivalent to multiplying the signal by -1.

    Dave
Ilya Zakharevich - 30 Sep 2005 00:16 GMT
[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
[quoted text clipped - 10 lines]
> 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
Bart van der Wolf - 26 Sep 2005 21:31 GMT
SNIP
> Extending this by continuity: if you have an image with visible
> frequency at 1.1 Nyquist, you get it aliased to 0.9 Nyquist.  My
> impression is that such a small difference between "actual" and
> "recorded" frequency will not create any *visible* moire.

Also note that the Green sampling density is different from Red and
Blue (in an GRGB mosaic). This can lead to false color-moire unless
properly dealt with in the Raw conversion.

Bart
winhag@yahoo.com - 27 Sep 2005 01:56 GMT
Anyone venture a guess on why (I believe) Kodak does not put AA filters
on their sensors a la the Hasselblad H1/H2 and
(discontinued) Kodak SLR's?
David J. Littleboy - 27 Sep 2005 02:17 GMT
> Anyone venture a guess on why (I believe) Kodak does not put AA filters
> on their sensors a la the Hasselblad H1/H2 and
> (discontinued) Kodak SLR's?

A cynical marketing sleaze to fool mathematically naive photographers into
thinking their products are sharper than they really are.

David J. Littleboy
Tokyo, Japan
Dave Martindale - 27 Sep 2005 07:16 GMT
>Anyone venture a guess on why (I believe) Kodak does not put AA filters
>on their sensors a la the Hasselblad H1/H2 and
>(discontinued) Kodak SLR's?

At least one Kodak DSLR did have an AA filter, and it was removable!  I
know I've seen a Kodak web page that showed the tradeoff: less moire
with the filter, higher apparent sharpness (with moire) without the
filter.

    Dave
David J Taylor - 27 Sep 2005 09:16 GMT
> Anyone venture a guess on why (I believe) Kodak does not put AA
> filters on their sensors a la the Hasselblad H1/H2 and
> (discontinued) Kodak SLR's?

- cost - leaving out the AA filter lowers cost

- they didn't think that the lenses used would be good enough to produce
significant information abouve Nyquist?

- "the pictures look better without" ?

- "the resolution is already low enough - don't reduce it further" ?

- they didn't realise one would be required?  Nah!

David
Dave Martindale - 27 Sep 2005 07:15 GMT
>> I've been told that manufacturers treat this is a tunable parameter.  If
>> the spread is exactly one pixel pitch, you get a null in the response of
>> the system right at the Nyquist frequency, which is theoretically good.

>I do not see how this may be "theoretically good".  There is no
>aliasing at the Nyquist frequency, it appears *above* Nyquist.  So
>having a zero at Nyquist has absolutely no point.

More precisely (though you really ought to know this): the sampling
theorem says that the input frequencies must be strictly *less than* the
Nyquist limit of 0.5 cycles/pixel.  Although input at exactly the
Nyquist frequency does not alias, it cannot be sampled reliably either.
The measured amplitude can be double the true amplitude (if the sample
points are all at peaks) or zero (if the sample points are all at zero
crossings) or anywhere in between, depending on the relative phase of
the signal and the sampling clock.  So input at the Nyquist frequency is
supposed to be filtered before sampling.

>Extending this by continuity: if you have an image with visible
>frequency at 1.1 Nyquist, you get it aliased to 0.9 Nyquist.  My
>impression is that such a small difference between "actual" and
>"recorded" frequency will not create any *visible* moire.

It may not be Moire, but it's still wrong.  This is visible in
resolution tests of the Sigma SD-9, where the 9-line resolution target
appears to be "resolved" at 2000 lines per picture height (1000 lp/ph),
but there are only 5 bars.  It's a lovely example of aliasing.  I don't
want *my* camera doing this.

>The "annoying" Moire is when some frequency in the image is aliased
>into a *LOW* frequency in the recorded data.  E.g., if some frequency
>is aliased into one 1.5x smaller (I think this is the practical limit
>of visible moire).  This give 1.2 Nyquist aliased into 0.8 Nyquist.

Again, Moire isn't the only problem introduced by aliasing.

>Of course, the actual numbers I used are hunches only; it is easy to
>simulate the process on computer and compare results *visually* to
>obtain the "best" choices.

Though note that the "best" choice obtained this way depends on both the
subject material and the viewer.  The advantage of the conservative
approach of putting the filter's null right at the Nyquist frequency is
that the image content is more often correct, even if it appears a bit
less sharp than when a higher-cutoff AA filter was used.

    Dave
Ilya Zakharevich - 27 Sep 2005 22:43 GMT
[A complimentary Cc of this posting was sent to
Dave Martindale
<davem@cs.ubc.ca>], who wrote in article <dhao16$pm6$1@mughi.cs.ubc.ca>:

> More precisely (though you really ought to know this): the sampling
> theorem says that the input frequencies must be strictly *less than* the
> Nyquist limit of 0.5 cycles/pixel.  Although input at exactly the
> Nyquist frequency does not alias, it cannot be sampled reliably either.

This is irrelevant, since the image on the focal plane has a
continuous Fourier spectrum, so each *individual* frequency comes with
0 amplitude.  [You can calculate the "signal power" inside any
*region* of frequencies, but the power goes down when the region
narrows.]

Thus quoting Nyquist in this context is not relevant.  There may be
some effects at frequencies close to limit frequency, but they should
be attributed to finite size of the sensor.

> >Extending this by continuity: if you have an image with visible
> >frequency at 1.1 Nyquist, you get it aliased to 0.9 Nyquist.  My
[quoted text clipped - 6 lines]
> but there are only 5 bars.  It's a lovely example of aliasing.  I don't
> want *my* camera doing this.

Interesting; do you have an URL?  Although my immediate suspicion
would be the demosaicing software, not AAF.

> Though note that the "best" choice obtained this way depends on both the
> subject material and the viewer.  The advantage of the conservative
> approach of putting the filter's null right at the Nyquist frequency is
> that the image content is more often correct, even if it appears a bit
> less sharp than when a higher-cutoff AA filter was used.

As I had shown in my other messages, what you propose is *less often*
correct than a milder AAF.

Hope this helps,
Ilya
Dave Martindale - 28 Sep 2005 00:23 GMT
>> More precisely (though you really ought to know this): the sampling
>> theorem says that the input frequencies must be strictly *less than* the
>> Nyquist limit of 0.5 cycles/pixel.  Although input at exactly the
>> Nyquist frequency does not alias, it cannot be sampled reliably either.

>This is irrelevant, since the image on the focal plane has a
>continuous Fourier spectrum, so each *individual* frequency comes with
>0 amplitude.  [You can calculate the "signal power" inside any
>*region* of frequencies, but the power goes down when the region
>narrows.]

A regular pattern in object space produces some finite amplitude of a
particular set of frequencies in image space.  The power is there no
matter how narrow you make the region of frequencies.  So power does
*not* go to zero as you narrow the region, for a single-frequency
signal.  It doesn't matter that the focal-plane image is continuous, or
that its Fourier transform is continuous.

But, in practical photography, any given frequency is either above or
below Nyquist - you can never hit exactly Nyquist.  So we should not use
it in examples (like you did).

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.  That's
why the sampling theorem says "less than", not "less than or equal".

>> It may not be Moire, but it's still wrong.  This is visible in
>> resolution tests of the Sigma SD-9, where the 9-line resolution target
>> appears to be "resolved" at 2000 lines per picture height (1000 lp/ph),
>> but there are only 5 bars.  It's a lovely example of aliasing.  I don't
>> want *my* camera doing this.

>Interesting; do you have an URL?  Although my immediate suspicion
>would be the demosaicing software, not AAF.

Look at the dpreview review of the SD9.  Find the resolution test chart,
and download the full-size image.  Take a look at the resolution wedge
at its narrowest point.

    Dave
Ilya Zakharevich - 28 Sep 2005 02:47 GMT
[A complimentary Cc of this posting was sent to
Dave Martindale
<davem@cs.ubc.ca>], who wrote in article <dhckae$9gm$1@mughi.cs.ubc.ca>:
> >> More precisely (though you really ought to know this): the sampling
> >> theorem says that the input frequencies must be strictly *less than* the
[quoted text clipped - 9 lines]
> 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.

> It doesn't matter that the focal-plane image is continuous, or
> that its Fourier transform is continuous.

The first one does not matter indeed.  The second one matters: it
makes "less than given frequency" and "less or equal to given
frequency" indistinguishable.

> But, in practical photography, any given frequency is either above or
> below Nyquist - you can never hit exactly Nyquist.

Right, this is exactly my point.

> 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 may not be Moire, but it's still wrong.  This is visible in
> >> resolution tests of the Sigma SD-9, where the 9-line resolution target
[quoted text clipped - 8 lines]
> and download the full-size image.  Take a look at the resolution wedge
> at its narrowest point.

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), 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.

Hope this helps,
Ilya
Dave Martindale - 29 Sep 2005 17:24 GMT
>> 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
Ilya Zakharevich - 30 Sep 2005 00:22 GMT
[A complimentary Cc of this posting was sent to
Dave Martindale
<davem@cs.ubc.ca>], who wrote in article <dhh4fl$bj2$2@mughi.cs.ubc.ca>:
> >> 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?

The light coming to edges will not be as bright as light coming to the center.

> >> 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.

If you use a correct statement as a "proof" of wrong one, it is not useful.

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

As I explained in another message, this is actually *the worst* location.

> >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
[quoted text clipped - 3 lines]
> Only for that particular frequency.  But other frequencies closer to
> Nyquist will be less attenuated than if the zero was at Nyquist.

Right.  For a very narrow band of frequencies, the attenuation is
better with your choice.  For most of them, it is better with mine.

> 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.

This may be applicable if you consider 1.1 Nyquist with 1.7 Nyquist.
But not when you compare 1.1 Nyquist with 1.2 Nyquist.  And all the
examples in this thread are in this "within 1.4 of Nyquist" range.

Hope this helps,
Ilya
Kennedy McEwen - 28 Sep 2005 01:52 GMT
>[A complimentary Cc of this posting was sent to
>Dave Martindale
[quoted text clipped - 10 lines]
>*region* of frequencies, but the power goes down when the region
>narrows.]

Sorry Ilya, but that is just BS.  It doesn't matter that the power in an
infinitesimal spatial bandwidth tends to zero, the important parameter
is the power density.

>Thus quoting Nyquist in this context is not relevant.  There may be
>some effects at frequencies close to limit frequency, but they should
>be attributed to finite size of the sensor.

No.  At Nyquist, the finite size of the sensor results in an MTF of at
least 64% based on a 100% fill factor, or more for reduced fill factors.
Signature

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)

Ilya Zakharevich - 28 Sep 2005 02:54 GMT
[A complimentary Cc of this posting was sent to
Kennedy McEwen
<rkm@kennedym.demon.co.uk>], who wrote in article <cSbpNzDIleODFwEO@kennedym.demon.co.uk>:

> >This is irrelevant, since the image on the focal plane has a
> >continuous Fourier spectrum, so each *individual* frequency comes with
> >0 amplitude.  [You can calculate the "signal power" inside any
> >*region* of frequencies, but the power goes down when the region
> >narrows.]

> Sorry Ilya, but that is just BS.

I'm forced to return the compliment...

> It doesn't matter that the power in an infinitesimal spatial
> bandwidth tends to zero, the important parameter is the power
> density.

With finite power density, what happens at *one particular frequency*
does not matter.  So a sampling theorem holding for "less than
Nyquist" implies that it also holds for "less or equal to Nyquist";
actually, for continuous spectrum there is no difference between these
two formulations.

Hope this helps,
Ilya
Kennedy McEwen - 28 Sep 2005 09:35 GMT
>[A complimentary Cc of this posting was sent to
>Kennedy McEwen
[quoted text clipped - 17 lines]
>With finite power density, what happens at *one particular frequency*
>does not matter.

Again, that is just plain wrong.  If you want proof of this, create a
test image with sinusoidal modulation.  ie. one that *only* contains a
single spatial frequency.  If it didn't matter what happened at one
particular frequency then it wouldn't matter what scale you imaged that
at.  Unfortunately, and contrary to your argument, it does - that single
spatial frequency aliases if it is undersampled just as much as a range
of frequencies would.  Similarly, replacing the single sinusoidal
pattern with a spatial frequency sweep produces a flat range of spatial
frequencies and again, despite the power in an infinitesimal bandwidth
falling to zero, those individual spatial frequencies which are
undersampled alias just as much as the original.
Signature

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)

Ilya Zakharevich - 29 Sep 2005 00:16 GMT
[A complimentary Cc of this posting was sent to
Kennedy McEwen
<rkm@kennedym.demon.co.uk>], who wrote in article <EpYfzbBEXlODFw0B@kennedym.demon.co.uk>:
> >With finite power density, what happens at *one particular frequency*
> >does not matter.

> Again, that is just plain wrong.

Well, if you think so, you do not know the subject...

> If you want proof of this, create a test image with sinusoidal
> modulation.  ie. one that *only* contains a single spatial
> frequency.

You can't create such image by an optical system.

Hope this helps,
Ilya

P.S.  If these hints are not enough to help find you the error in your
arguments, let me know.
Kennedy McEwen - 29 Sep 2005 09:16 GMT
>[A complimentary Cc of this posting was sent to
>Kennedy McEwen
[quoted text clipped - 6 lines]
>
>Well, if you think so, you do not know the subject...

Fortunately, I do know the subject and have written several published
papers on the topic.

>> If you want proof of this, create a test image with sinusoidal
>> modulation.  ie. one that *only* contains a single spatial
>> frequency.
>
>You can't create such image by an optical system.

Ignoring the DC and low frequency component necessary to define the
overall intensity of the pattern, which is entirely irrelevant to this
arguments, you certainly can.  Almost all modern lens MTF measuring
equipment utilise such patterns.
Signature

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)

Ilya Zakharevich - 29 Sep 2005 01:28 GMT
[A complimentary Cc of this posting was sent to
Dave Martindale
<davem@cs.ubc.ca>], who wrote in article <dhao16$pm6$1@mughi.cs.ubc.ca>:
> >> I've been told that manufacturers treat this is a tunable parameter.  If
> >> the spread is exactly one pixel pitch, you get a null in the response of
> >> the system right at the Nyquist frequency, which is theoretically good.

> >I do not see how this may be "theoretically good".  There is no
> >aliasing at the Nyquist frequency, it appears *above* Nyquist.  So
> >having a zero at Nyquist has absolutely no point.

> More precisely (though you really ought to know this):

[Irrelevant argument omitted; see discussion in another subthread.]

Actually, I think I found an easier argument to convince you that an
AAF which has its first zero at Nyquist frequency (in other words, which
shift the image by exactly 1 pixel) is absolutely useless.  I hope it
is a much more convincing argument than calculating cosine at some
random points.  ;-)

Here it is:

 The effect of AAF which shifts the image by width of 1 pixel can be
 *completely* reconstructed by postprocessing the digital image (just
 shift the digital image by 1 pixel, and average).

As everyone knows, no aliasing can be removed by post-processing.
Ergo: such a "filter" *does not remove any aliasing*.

Is it more convincing now?

Hope this helps,
Ilya
Kennedy McEwen - 28 Sep 2005 01:52 GMT
>[A complimentary Cc of this posting was sent to
>Dave Martindale
[quoted text clipped - 10 lines]
>aliasing at the Nyquist frequency, it appears *above* Nyquist.  So
>having a zero at Nyquist has absolutely no point.

Its onset is infinitesimally above Nyquist, hence Nyquist is the
effective limit and is why the null should be there or below.

>Extending this by continuity: if you have an image with visible
>frequency at 1.1 Nyquist, you get it aliased to 0.9 Nyquist.  My
>impression is that such a small difference between "actual" and
>"recorded" frequency will not create any *visible* moire.

Perhaps not moire, since that requires an extended regular spatial
frequency source, but it will have deleterious effects, such as making
specular reflections larger than they should be.  In terms of direct
moire, misrepresenting 1.1x Nyquist as 0.9x Nyquist is an exaggeration
of spatial frequencies by 20%, which certainly is noticeable when a
dominant image component of that rate occurs in the image.

In my particular field, I have seen images of tank with 8 regularly
spaced wheels on their tracks appearing to have only 6 wheels and
therefore being identified as a different vehicle completely as a
consequence of less aliasing than the 20% example that you reference. If
you don't think that is significant then I guess you don't think "blue
on blue" attacks are significant either!

>The "annoying" Moire is when some frequency in the image is aliased
>into a *LOW* frequency in the recorded data.

Not at all - when a high spatial frequency is aliased to a low one the
image distortion is so obvious as not to be objectionable in many cases.
The really objectionable distortion is the one that is not immediately
obvious, but unintentionally misrepresents the image.

Signature

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)

Ilya Zakharevich - 28 Sep 2005 03:01 GMT
[A complimentary Cc of this posting was sent to
Kennedy McEwen
<rkm@kennedym.demon.co.uk>], who wrote in article <jTt2tOEQleODFwCc@kennedym.demon.co.uk>:
> >Extending this by continuity: if you have an image with visible
> >frequency at 1.1 Nyquist, you get it aliased to 0.9 Nyquist.  My
[quoted text clipped - 4 lines]
> frequency source, but it will have deleterious effects, such as making
> specular reflections larger than they should be.

Exactly the opposite.  As you know, stronger AAF blur stronger.

> In terms of direct
> moire, misrepresenting 1.1x Nyquist as 0.9x Nyquist is an exaggeration
> of spatial frequencies by 20%

This may sound impressive, but we are talking about difference *much*
smaller than the pixel size.

> In my particular field, I have seen images of tank with 8 regularly
> spaced wheels on their tracks appearing to have only 6 wheels and
> therefore being identified as a different vehicle completely as a
> consequence of less aliasing than the 20% example that you reference.

Well, if you do not know your tools, errors are always possible.

> If you don't think that is significant then I guess you don't think
> "blue on blue" attacks are significant either!

Since I do not know what you mean, I suppose that "I do not think so" indeed.

> >The "annoying" Moire is when some frequency in the image is aliased
> >into a *LOW* frequency in the recorded data.

> Not at all - when a high spatial frequency is aliased to a low one the
> image distortion is so obvious as not to be objectionable in many cases.
> The really objectionable distortion is the one that is not immediately
> obvious, but unintentionally misrepresents the image.

This depends much on what is the purpose of your image.  If you want
to distinguish 152mm howitzer (sp?) from 156mm one, then your choice
of tools may be very different from that of a bird photographer.

Hope this helps,
Ilya

Kennedy McEwen - 28 Sep 2005 09:48 GMT
>[A complimentary Cc of this posting was sent to
>Kennedy McEwen
[quoted text clipped - 10 lines]
>
>Exactly the opposite.  As you know, stronger AAF blur stronger.

However that blur of the AAF is simply the rejection of higher spatial
frequencies.  Aliasing is the misrepresentation of high spatial
frequencies with lower ones.  The AAF does not represent fine detail
such as specular reflections with coarse detail - aliasing does.

>> In terms of direct
>> moire, misrepresenting 1.1x Nyquist as 0.9x Nyquist is an exaggeration
>> of spatial frequencies by 20%
>
>This may sound impressive, but we are talking about difference *much*
>smaller than the pixel size.

If you want an estimate of how bad that actually is, talk to any of the
film scanner people about the effect known as grain aliasing - exactly
the same effect, misrepresenting fine undersampled grain as coarse grain
in the final image.  The same effect occurs here - fine textural
information being misrepresented as coarse texture with the same
contrast.

>> In my particular field, I have seen images of tank with 8 regularly
>> spaced wheels on their tracks appearing to have only 6 wheels and
>> therefore being identified as a different vehicle completely as a
>> consequence of less aliasing than the 20% example that you reference.
>
>Well, if you do not know your tools, errors are always possible.

Which is why correct filtering of the sensor is important - the end user
shouldn't need to understand the detailed operation of the system or be
required to compensate for the tools errors.

>> If you don't think that is significant then I guess you don't think
>> "blue on blue" attacks are significant either!
>
>Since I do not know what you mean, I suppose that "I do not think so" indeed.

Misinterpretation of targets results in errors which can, and in many
cases have, resulted in fratricide or engagement of innocent bystanders.
Seeing the wrong number of wheels on a vehicle can be enough to cause it
to be identified as foe instead of friend.

>> >The "annoying" Moire is when some frequency in the image is aliased
>> >into a *LOW* frequency in the recorded data.
[quoted text clipped - 7 lines]
>to distinguish 152mm howitzer (sp?) from 156mm one, then your choice
>of tools may be very different from that of a bird photographer.

So it would be unimportant to a bird photographer if a seagull was
misinterpreted to be an albatross?  I don't think so!  The differences
between species of bird can be negligible compared to the difference
between combatants.
Signature

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)

Ilya Zakharevich - 29 Sep 2005 00:33 GMT
[A complimentary Cc of this posting was sent to
Kennedy McEwen
<rkm@kennedym.demon.co.uk>], who wrote in article <FpJfjPCAjlODFw0p@kennedym.demon.co.uk>:
> >Exactly the opposite.  As you know, stronger AAF blur stronger.

> However that blur of the AAF is simply the rejection of higher spatial
> frequencies.  Aliasing is the misrepresentation of high spatial
> frequencies with lower ones.  The AAF does not represent fine detail
> such as specular reflections with coarse detail - aliasing does.

To see the error in your arguments, put an AAF designed for sensor
with step 8microns on a sensor with step 2.2microns; make a shot of
the same subject with the same lens.  Aliasing disappears.  Blur
remains.

> >This may sound impressive, but we are talking about difference *much*
> >smaller than the pixel size.

> If you want an estimate of how bad that actually is, talk to any of the
> film scanner people about the effect known as grain aliasing - exactly

All discussion I saw about the so called "grain aliasing" is pure
uneducated guesses.  They see some effect, introduce a fancy name for it,
and try to discuss as if they know what they are talking about.  (Maybe
I saw wrong sites; if you know something better, I would be glad to
revisit the question.)

> the same effect, misrepresenting fine undersampled grain as coarse grain
> in the final image.  The same effect occurs here - fine textural
> information being misrepresented as coarse texture with the same
> contrast.

Again, you stray from the topic: if fine structure is aliased into
coarse, we are not talking about aliasing *near Nyquist limit*.

> >> In my particular field, I have seen images of tank with 8 regularly
> >> spaced wheels on their tracks appearing to have only 6 wheels and
> >> therefore being identified as a different vehicle completely as a
> >> consequence of less aliasing than the 20% example that you reference.

> >Well, if you do not know your tools, errors are always possible.

> Which is why correct filtering of the sensor is important - the end user
> shouldn't need to understand the detailed operation of the system or be
> required to compensate for the tools errors.

This depends on the application area of a tool.  Most tools are not
subject to this requirement.

=======================================================

Moreover, your arithmetic is way wrong: in your example (8 aliased to
6) is NOT "less aliasing than the 20% example that you reference".  To
nitpick, my example is actually 22% aliasing.  Yours is 33% aliasing
(using the same metric).

> >> If you don't think that is significant then I guess you don't
> >> think "blue on blue" attacks are significant either!

> >Since I do not know what you mean, I suppose that "I do not think
  so" indeed.

> Misinterpretation of targets results in errors which can, and in many
> cases have, resulted in fratricide or engagement of innocent bystanders.
> Seeing the wrong number of wheels on a vehicle can be enough to cause it
> to be identified as foe instead of friend.

Some people are ready to solve problems of "social" nature by
"technical" means (like: just introduce cleverly designed taxes, and
people will become nicer to each other).  Your example looks of
similar flavor.  It is people who fire weapons, not cameras.  By
changing a design of AAF you won't decrease fratricide (even if all of
it is caused by results of misreading an image); most you can do is
decrease one kind while increasing some other kind.

> >This depends much on what is the purpose of your image.  If you want
> >to distinguish 152mm howitzer (sp?) from 156mm one, then your choice
> >of tools may be very different from that of a bird photographer.

> So it would be unimportant to a bird photographer if a seagull was
> misinterpreted to be an albatross?  I don't think so!

Let us get more details: you mean 2-pixel wide image of a seagull, or what?

Hope this helps,
Ilya
Kennedy McEwen - 29 Sep 2005 09:37 GMT
>[A complimentary Cc of this posting was sent to
>Kennedy McEwen
[quoted text clipped - 11 lines]
>the same subject with the same lens.  Aliasing disappears.  Blur
>remains.

And this demonstrates what precisely?  Of course blur remains because,
as I stated previously, the blur is caused by the attenuation of the
higher spatial frequencies in the image, NOT their misrepresentation at
lower spatial frequencies as occurs in aliasing.

>> If you want an estimate of how bad that actually is, talk to any of the
>> film scanner people about the effect known as grain aliasing - exactly
[quoted text clipped - 4 lines]
>I saw wrong sites; if you know something better, I would be glad to
>revisit the question.)

Try sampling white noise - what happens?  HF noise is aliased to low
frequencies.  It occurs in every sampling system that is inadequately
filtered and film grain is a high frequency noise.  Perhaps you did
visit the wrong sites, but it would appear that you are the person who
doesn't understand this.

>> the same effect, misrepresenting fine undersampled grain as coarse grain
>> in the final image.  The same effect occurs here - fine textural
[quoted text clipped - 3 lines]
>Again, you stray from the topic: if fine structure is aliased into
>coarse, we are not talking about aliasing *near Nyquist limit*.

As I pointed out in the example you provided, the misrepresentation is
quite significant and can readily cause mis-identification of objects,
even quite near the Nyquist limit.

>Moreover, your arithmetic is way wrong: in your example (8 aliased to
>6) is NOT "less aliasing than the 20% example that you reference".  To
>nitpick, my example is actually 22% aliasing.  Yours is 33% aliasing
>(using the same metric).

My example was one that I have actually presented to over 100 trained
observers and consistently results in target misidentification.  It is
at a level where problems can be guaranteed to occur, well beyond their
onset.  Whilst 22% aliasing may result in less problems, even in
something as well defined as a military vehicle, misidentification will
certainly not be zero and is likely to be higher in objects (such as
birds) where the difference between species or gender is much less
dramatic.

>> So it would be unimportant to a bird photographer if a seagull was
>> misinterpreted to be an albatross?  I don't think so!
>
>Let us get more details: you mean 2-pixel wide image of a seagull, or what?

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.
Signature

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)

David J Taylor - 29 Sep 2005 10:23 GMT
[]
> Minimum criteria for 50% probability of identification of a well
> defined object on static images is at least 12 pixels linearly (more
[quoted text clipped - 3 lines]
> 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.  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.

David
Kennedy McEwen - 29 Sep 2005 17:01 GMT
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
>[]
>> Minimum criteria for 50% probability of identification of a well
[quoted text clipped - 8 lines]
>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