For David Millier

David,

You have serious misconceptions about "aliasing" .... To continue our discussion - here is your last response:

This is absolutely wrong.

The Nyquist limit is a hard stop. You cannot reconstruct anything above Nyquist. Any energy available above Nyquist cannot be rendered. What happens is that energy folds back to lower frequencies as a kind of beat pattern.

There is no partial aliasing, partial real detail, as you suggest; no slight loss of accuracy as you move further beyond Nyquist, that is not how it works. All meaningful information above this point is lost. This is sampling in action. The reason for this is that without enough samples, things become ambiguous, there is no unique reconstruction of the details: is that a 2000 lp/h detail or is it 20 lp/ph or 40 or 80 or 500. The sampling mechanism can't tell.

What you get instead is distortion overlayed on proper detail at lower frequencies. The damage is not done above Nyquist as you suggest, but lower down the frequencies where it corrupts detail that would otherwise be fine. That is why it is objectionable (eg jaggies).

Anything you think you see above Nyquist isn't remotely detail, it's noise. When we say it hints at texture we mean exactly that: it's not a slightly distorted version of what's there, it's garbage.

Which brings us to the central argument. Does this noise convince the eye that it is real detail or is it just noise. You argue that it does. If this is true for most people, what we rely on perceptually is that the garbage is rendered sufficiently small that you can't tell its garbage, it just looks like a suggestive roughness.

An example of this is my pier shot I've use a few time over the years. There is a lifeboat boathouse on the pier with a tiled roof. The tiles are standard tiles that run horizontally. If you look at the aliased image, the Sigma renders the roof as a series of diagonal stripes fading in and out in brightness alternately. Nothing the sensor is doing has anything to do with the real tile pattern, it's pure distorted aliasing. However... if you print it, this area of the image is so small you can't really see it properly. The vaguely stripy pattern can be perceived as being what you might expect: a roof pattern. It's the wrong pattern but it fools the eye. If you up close, it looks plain wrong, a roof doesn't look like that but at a distance you can get away with it.

And that's the crux of the argument in favour of aliased images.

My conjecture is simply that if aliasing seen like this provides some textural benefit, maybe other textures (like for example grain) can also do the same job. Perhaps a distant rock surface whose detail is beyond the sensor, can be made to look a little better by adding some grain if the grain gives the impression of a surface texture (even fake as it is).

It's an idea worth exploring - I've seen suggestions before that added grain can make digital prints look less plastic."

First, "jaggies" are not caused by anything remotely resembling "distortion overlaid on proper detail at lower frequencies."

Jaggies are caused by attempting to construct smooth lines and curves with square or rectangular building blocks of light (pixels). When the contours are small enough that they are represented by very small numbers of these "pixels" then the irregular "stairsteps" are seen in enlargements. Antialiasing filters simply blur this jagged appearance by interspersing additional and softer (blur) pixels offset sufficiently to fool the eye.

Second, above Nyquist as indicated on the SD1 photographed resolution chart what do "you" see? If you see "noise" then you and I have essentially quite different eyesight. What I see are quite plainly "lines." Lines just like the ones below Nyquist only fewer of them.

Do you "really" believe in magic? Do you think that these "lines" appear on every photograph by the SD1 above Nyquist regardless of whether the subject of the photograph has any "lines" in it?

Funny thing - when I shoot a photograph of a distant pine tree with one of my Foveon based sensors and greatly enlarge it, I see no black and white "lines" where the image begins to break down. What I do see are pine needles. Now pine needles somewhat resemble "lines" in shape so do you actually think that they magically become black and white lines such as the ones seen in the resolution chart above Nyquist, or do you think that perhaps fewer pine needle than actually exist in reality might be seen? Or do you believe that the photography fairy has duped me into believing that black and white lines actually look like pine needles?

Choosing to refer to what is seen above Nyquist in Foveon photos as "grain" is simply your way of avoiding reality in attempting to support your opinions. I'll choose to believe my eyes and you continue to believe your "theory" about what is going on and we will simply have to agree to disagree.

Best regards,

Lin

--
learntomakeslidshows.net

http://whisperingcat.co.uk/wp/wpblog/

jhgchjgcjhgcjhgcjhgc jhgv vhjgvhjgvjhgvjhgvhh hjgv

Lin

We have had discussions about aliasing many times before. We both know we don't agree, and I also know that the regular correspondents here don't support my preference. That's OK, it's just a preference. There is no point in going over old ground and having another fight. Can we agree on this?

Let's stick to the new question which in my mind is this:

- if aliasing is present in an image (Bayer or Foveon), does it add "a hint of texture" beyond Nyquist like DPR amongst others claim.

- If it does, and people generally agree under unbiased conditions, that they prefer this to the effect of an AA filter, is it possible to generate a hint of texture beyond Nyquist in the files of cameras with AA filters using some other technique - and do people prefer this too.There is nothing here about trying to disguise aliasing with grain or anything like that.

I suggested the first one that came to mind, which was adding grain. The reason I thought of this is because a fine grain pattern on a surface can easily be mistaken for detail, but it doesn't have to be grain if someone has any other ideas.  There's no rocket science in this, nor should there be any kind of controversy, this isn't a Foveon or Bayer specific issue, it affects all sensor techs.

I find this an interesting avenue to explore and if anyone has an inclination to discuss this can we do it by experiment rather than by opinion/prejudice/religious affiliation, please.

- the other (rather wistful) point I made is that it would be nice to see what a Foveon image would be like with an AA filter. We have never seen such an image because they don't exist.
It subsequently occurred to me that you can simulate something of the AA filter using diffraction, so actually it ought to be reasonably easy to do. I could do this but it would take effort and I'm not sure I can be bothered. It would be handy if someone has already got some careful comparisons of Foveon shots at different apertures including f/16 and f/22 so we can check and see if this banished aliasing as theory says it should.

--
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Flickr: http://www.flickr.com/photos/davidmillier/

You and David has different views on the problem of aliasing.

Aliasing is a technically well known problem. You can simulate it or do computations about it. And you can read about it on the net ... in lots of places. Its not an unknown phenomena.

But ... its VERY misunderstood.

Almost all examples for laymans uses point sampling of 1D signals. And then you see some sine waves that are sampled at those points, and the resulting samples. And then you show, that you have sample more than twice as fast as the sine's frequency.

Very nice and pedagogic ... NOT.

We are NOT taking photos of sine curves and the sensor do NO such thing as point sampling.

The sensor do a box filtering and the lens is not perfectly sharp. And, e.g. the lines in the test pattern are no sines, its rather a square function.

Its quite amazing that with only 9+10=19 pixels you can see 9 sharp lines. Those 9 sharp lines represent sine waves that have a much, much higher frequency than the Nyquist frequency.

If we should do this properly, using the sampling theorem (and allowing for some negligible unsharpness) then you probably have to sample the lines with at lest 10-20 times the frequency used in those examples.

So --- for both Bayer and Foveon (or B&W sensor), resolving those sharp lines are already cheating. It cant be done.

And this can easily be seen in the picture. Look at the Foveon image. At one position you have 9 sharp lines. But, what happens below and above? Just a mess IMHO. Yeah ... and then, below the mess you get 7 lines, and then the mess is there again.

Its all cheating, both for Bayer and Foveon. The 15 MP sensor needs to be 1.5 GP to be able to sample those sharp lines sharp and accurately.

Now, we dont have that kind of sensors today. So ... we have to buy whats available. Or .. maybe stitch

--
/Roland
X3F tools:
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https://github.com/rolkar/x3f

That is indeed my (retired) blog whose only function these days is as a test platform for off the shelf Wordpress themes.

--
Galleries and website: http://www.whisperingcat.co.uk/
Flickr: http://www.flickr.com/photos/davidmillier/

Glad you said it was retired

It was quite bad.

--
/Roland
X3F tools:
http://www.proxel.se/x3f.html
https://github.com/rolkar/x3f

Lin,

we already discussed this in lenght - and I mean we (both of us):

http://forums.dpreview.com/forums/post/50064368



...and in detail:

http://forums.dpreview.com/forums/post/50066138

DP2M aliasing - the higher frequencies are overlaid as a diagonal stripe pattern over the true hole pattern.

vs.:



5D MK III - the AA filter of the 5D reduces (in this case) successfully the disturbing energy above Nyquist

...where is the problem?

It is obvious, that in some cases - like the shown - the aliasing of a Foveon based camera doesn't contain a hint of the true detail, but is adding nonsense to lower frequencies, like D.Millier said.

In other cases, like the ones You mentioned, it may look less disturbing, but it is false detail - our brain may associate this false detail with what we expect to see - so most of us may see, what we expect, but not what is really there.

It is an illusion, which fits more to Your expectation than to David's - that's it.

-

If You ask me...

...one day I will show You a Foveon output with and without AA-filter and if I were Sigma,

I would let the people choose like Nikon did with it's D800 vs. D800e.

-

Enjoy the great possibilities photographer have these days - however, a few more wouldn't harm...

Best regards,

Ulrich

--
Envy is the highest form of recognition.
Stop to run, start to think.
Think twice - that doubles the fun!
Your world is as big, as Your mind.
Avoid to have only one point of view!
Uli

Lin, jaggies on straight lines ar precisely caused by "distortion overlaid on proper detail at lower frequencies", like David said. And actually your process "Jaggies are caused by attempting to construct smooth lines and curves with square or rectangular building blocks of light (pixels)" is essentially same, just expressed in very different terms. No ground for heated disputes

David, I generally agree with you, but there's one little problem. You claim that "all information above Nyquist is lost". I would say that much of information above Nyquist is not lost, but is just distorted (in some sentences you actually claim that too).

I dive into speculative land now (I have no theoretical knowledge), but think about fractals. What kind of information contain fractals? I think that in addition to exact geometrical structure (which has to be approximated anyway) they have some higher order structure, which IMO can even survive distortion by incorrect sampling (over Nyquist limit). Sure precise form of fractal elements will be destroyed, but some general structure remains.

It is known that many natural textures or forms are fractal-like. This (plus previous paragraph ideas) may create results, what Lin describes (and I have seen too) - many natural objects, like tree leaves, grass etc look pretty natural even in heavily aliased images.

Lin's "canonical" example about 5 or 7 lines visible on 9 lines resolution chart is somewhat analogous. It is not related fractal geometry, but I think (and this can be calculated) that there are some geometric structures, which can "survive" aliasing, creating similar patterns at lower frequencies. Technically they contain heavily distorted and incorrect information, but perceptually they may look plausible.

What about adding noise/grain to image - this is done often in video realm. Mostly for making gradients smoother and hide some artifacts, but sometimes just to add perceived sharpness. Note that adding random noise is not comparable to aliasing - the latest is not random.

--
Arvo
Sigma/Foveon information collection and little galleries:
http://www.stv.ee/~donq/sigma.htm
http://www.stv.ee/~donq/images.htm

Hi Arvo

Thinking about it I have come to a conclusion regarding sampling images. And this is that there are three possible ways of making a high quality image, that can be printed large with perceptual high sharpness.

1. Using a 15 MP sensor and no AA filter.
   
2. Using a 30 MP sensor and an AA filter.
3. Using a 1 GP sensor, who cares if there is an AA filter or not.
   

With 1 and 2 you cant see sharp things at pixel level. For 1 it will be aliased and for two it will be mush. 2x failure. The sharp 9 lines from the test chart are faked in both cases. If you move the camera or turn it slightly, then oops ... where did the lines go? The image might look good nevertheless, very good. But if you are looking for a photo, dont zoom in to pixel level. Number 2 needs more pixels than number 1 to get equally sharp. But ... number 1 might be ruined sometimes due to aliasing.

Number 3 on the other hand ... nemas problemas. The pattern from the test chart will be both sharp and nice looking. Because the lines are sharp lines that contains much higher frequencies than the sampling frequency in 1 and 2. OK ... the lines will be several pixels in width, but thats what it takes to make them sharp and good looking at the same time.

So personally I think David´s and all other people that talk about sampling theorems should reconsider. Do you understand how unsharp an image would be if you really should sample and reconstruct correct? A 10 um sampling frequency can only resolve 20 um wavelength sine curve. The lines in the test chart would look extremely unsharp if reconstructed correctly. They would be invisible at the Nyquist frequency and sine curves slightly below.

EDIT: Note, that correct reconstruction of an image sampled at 15 MP needs an output image of maybe 15 GP.

--
/Roland
X3F tools:
http://www.proxel.se/x3f.html
https://github.com/rolkar/x3f

Arvoj explained exactly what I wanted to, but much more clearly and plausibly with his good knowledge in science. As you requested, here is an image of the sort of pine needles Lin mentioned, as an example of what happened beyond Nyquist in real world scenarios:

The photo was taken with lens zoomed at 36mm fl. In memory, the pines trees were at least 50m away, but by reference to the size of the people that look about half way between the camera and the trees, it’s probably about 40m. For convenience sake, let’s say 36m, or 1000 times of the fl. So, the 5um pixel size of SD1M sensor covers 5mm at that distance, i.e., the sensor is capable of resolving line pairs no finer than 10mm in width that far. The pine needles, however, should be about 1-2mm in dia., and a high percentage of them are easily less than 10mm between each other. So we know they are largely beyond the capability of the sensor to resolve fully and truthfully.

Yet, we see pine needles, seemingly almost one by one. In theory much of these are just aliasing induced misinformation. In reality, they look vividly real.

Fine details and textures is everywhere in the real world: rock and timber surface, brick walls, foliage and grass in far field, human skins and fabrics up close, and what not. Pine needle is just one convenient example.

--
Maple

Edit;

Retired is not quite the right word. Never was is better. The blog is just for testing.

Blame the theme editor, it was one I applied randomly just to see how it looked. It didn't look very good. I've swapped it for one called Elegant Grunge. Wordpress is entertaining, you can re-skin a site in about 10 secs.

--
Galleries and website: http://www.whisperingcat.co.uk/
Flickr: http://www.flickr.com/photos/davidmillier/

This has more to do with contrast and the size of the airy disk...

...look at the needels in brighter light at the same distance in comparison to the ones in low contrast areas...

...You mainly see colored mush and not needels in the low contrast areas.

-

Remember the stars at night...

...one can see them because of the very high contrast and the size of the airy disk, which is often spread over several pixel, so that a bright star can cover several pixel - even with a wide angle lens in front of the sensor, despite of it's "real" size.

What You missed in Your assumption is what already was explained with a thin wire of a fence,

which seems thicker than it should be - did Roland explain this?

-

What You show in this example, is a mixture of several effects and not really the issue "real looking detail despite of aliasing".

However, this is a example, where the high contrast at pixel level of the Foveon design can show it's strenght.

--
Envy is the highest form of recognition.
Stop to run, start to think.
Think twice - that doubles the fun!
Your world is as big, as Your mind.
Avoid to have only one point of view!
Uli

Yes please!

I suspect (but don't know for sure) that a properly anti-aliased Foveon sensor - even if somewhat reduced in resolution and acutance around Nyquist - would offer a remarkably smooth and beautiful artefact free quality. But I guess we will never find out, as it's going to have to be sharpness all the way.

We are straying away from those original questions again - can grain or some other kind of texture producing process trick the eye into accepting random texture as plausible substitute for real detail? or is it only aliasing that can pull off this deceit.

--
Galleries and website: http://www.whisperingcat.co.uk/
Flickr: http://www.flickr.com/photos/davidmillier/

Thank you for the correction. Lost was not the correct word. But it is shorter than "twisted into some horribly distorted form then melded into some poor innocent area that never deserved the insult"

The line jaggies and rope type artefacts look to my eye to have a similar distortion to the moire patterns and the nine lines thing. What you see is a repeating pattern with a short patch of something sharp looking followed by a kind of faded out blurry bit slightly offset, then another sharp patch offset the other way, then another faded out blurry bit and so on. It would be helpful to have a simplified explanation of why it looks like this if anyone would care to try.

I can see how sometimes these kinds of patterns look like real detail at a distance. But it very much depends where  it occurs. In architecture shots it almost always looks terrible (like that stripy grill). Maybe you get away with it better in landscapes because of the more chaotic subject detail which hides the unnatural regularities???

--
Galleries and website: http://www.whisperingcat.co.uk/
Flickr: http://www.flickr.com/photos/davidmillier/

For sure, because it is a very interesting experiment!

I guess that one has to do it by oneself...

Have a look:



plausible texture, artifacts, details, or even a hint of 3D?

What do You think?

--
Envy is the highest form of recognition.
Stop to run, start to think.
Think twice - that doubles the fun!
Your world is as big, as Your mind.
Avoid to have only one point of view!
Uli

A complex discussion - very interesting to see the points of view. Roland makes a telling point or two.

Firstly, the mention of Nyquist should never be made in sentence involving random arrangements of twigs at a great distance and we should firstly know why that is so. Anyone who does not know why should leave the room and write out 1000 times "Nyquist is in the spatial frequency domain, the home of the humble sine wave" or something like that.

Secondly, a single line seen at a great distance, can be quite visible in an image - as is well-known in a separate but related area, that of the "point spread function" and it's cousin, the "line spread function" which itself ican be calculated from the "edge spread function" (slant edge test per ISO).

Such a line is visible in a similar way that stars are visible in night sky. An intense source of light, many, many times smaller than 1 minute of arc in size actually becomes a blob (we all know why) on the sensor and hence visible in an image. So it is that distant lines (may I say pine needles?) in their turn, given sufficient contrast at their point of origin will also appear - will they not - and they will be real.

It's like, along the tree-line, there are a good few impulse functions all waiting to excite a pixel or two on your Merrill . . .

--
Regards,
Ted http://tcktek.blogspot.com
SD10/70mm macro

I agree!   This is plainly seen also in the resolution test shot for the X-E1 at around 2800 lines per picture height:  http://www.dpreview.com/previews/fujifilm-x-e1/6

Of course the SD1 resolves better but the basic idea is the same: http://www.dpreview.com/reviews/sigmasd1/11

Other cameras such as the 6D show some moire: http://www.dpreview.com/previews/canon-eos-6d/8

Canon 5DIII: http://www.dpreview.com/reviews/canon-eos-5d-mark-iii/20

--
Tom Schum

I disagree.  Couldn't a non-sharp lens such as the 50-200mm F4-5.6 DC OS HSM deliver the equivalent of an anti-alias filter on a SD1M?

--
Tom Schum

high ISO images that have a lot of noise reduction. That includes images from my very own DP2.

--
Raist3d/Ricardo (Photographer, software dev.)- I photograph black cats in coal mines at night...
“The further a society drifts from truth the more it will hate those who speak it.” - George Orwell

It could, Tom, but violets would be filtered about 40% "less" than reds with a diffraction-limited approach, would they not? (400nm versus 700nm diffraction) Whether that is good or bad, I have no idea!

On the other hand, I haven't too much trouble with aliasing when I bolt on my high-quality non-EX non-macro DC kit lenses, so maybe you have a point . . .

"properly anti-aliased", Dave? "Somewhat reduced"? "Around Nyquist"? Are you getting vague on us, by any chance?

My SD10 with no sharpening

A little lacking in contrast "below Nyquist" MTF50 should be at least up near 800 lph, IMHO. The good news is an MTF of about 9% at Nyquist meaning that artifacts would be barely visible, would they not? In this case the softness of the capture provided some quite good filtering, eh?

--
Regards,
Ted http://tcktek.blogspot.com
SD10/70mm macro