Discussion of 'Equivalence'

[Bjørn Rørslett]

One thing is for sure, the 'theory' creates a lot of confusion. Thus we now end up with 'theory of confusion' instead of blur circles

Can we close this debate soon? it is really not going anywhere. Even the debate is becoming circular.

[simsurace]

The requirement that the same scene is reproduced at a standardised output size creates the circularity.  As soon as that requirement is accepted everything else follows, but if it is rejected the equivalence argument falls to the ground. 

But why should that requirement be accepted?  Other than to make the argument possible, of course, which is as clear a definition of circularity as you could ask for.  Under what real-world circumstances does anyone use different cameras to take the same photograph, for a standardised output size?

You don't have to accept it. Nothing will change if you don't.

Under what real-world circumstances does anyone use different cameras to take the same photograph, for a standardised output size?
It happens all the time. People switch between systems with different formats but continue to view their images in the same or in a similar way, leading to perceptual differences in the output.
Or a new camera hits the market and you want to test its capabilities by comparing its output with a known benchmark.
Etc.

It's a conceptual tool. If you don't need a hammer, leave the hammer in the toolbox. 

[Akira]

One thing is for sure, the 'theory' creates a lot of confusion. Thus we now end up with 'theory of confusion' instead of blur circles

No worries!  NikonGear is THE circle of confusion!   

[Bjørn Rørslett]

No worries!  NikonGear is THE circle of confusion!   

FINALLY a point we all can wholeheartedly agree on. Or so I surmise

[Jack Dahlgren]

FINALLY a point we all can wholeheartedly agree on. Or so I surmise

Wait... Is it a point or a circle?

[Jack Dahlgren]

A very compact mathematical description of the entire imaging chain could be achieved by considering the transformation T between the (normalized) image space light density map (light intensity as a function of normalized image space coordinates) and the (normalized) reflectance map (for a print) or screen light intensity map (for on-screen viewing). The criteria of equivalence would be formulated as the changes of parameters of the intermediate stages of this transformation, such that T does not change. Or more concisely: two imaging chains are called equivalent if they have the same T. This terminology fits with the mathematical notion of 'equivalence class'.

I would argue that it is precisely equivalence theory that attempts to consider the whole chain, and treat it more or less as a black box with a small set of parameters, for better or worse. As someone already said: a useful (to some extent) abstraction and simplification.

Yes you are treating as a black box, but are hijacking pixel dynamic range(a constant for the same sensor) by multiplying by size (a variable) and then calling it sensor dynamic range. It is this redefinition which is bothering me. It needs a different name.

[Andrea B.]

Bjørn, you fierce bear, you are correct to recognize that there is an "inevitable ceiling" reached for certain variables (magnification, for example) when comparing systems. You are also correct in recognizing that one specific characteristic of a sensor (dynamic range, for example) should not be used to judge the entire system.

But I want to stand up for the folks here on UVP, like Simone, myself and our other interested NG members, who also understand the various limitations of "Equivalence" and really have no argument against what you say (as long as the definitions, etc., are understood, etc., by all).

Using the "Equivalance" definitions (and the accompanying physics) to determine the differences between systems or the relative merits of each system is useful. It can help us configure any system to its most advantageous settings. It can help us understand better which system to choose for a particular photographic task. So I feel that we should not "throw out the baby along with the bathwater", as the old saying goes. 

******

I'm still thinking about the Dynamic Range definitions. And what Jack has just observed. I'll spare everyone from my mental DR muddle for now. 

[Les Olson]

A very compact mathematical description of the entire imaging chain could be achieved by considering the transformation T between the (normalized) image space light density map (light intensity as a function of normalized image space coordinates) and the (normalized) reflectance map (for a print) or screen light intensity map (for on-screen viewing). The criteria of equivalence would be formulated as the changes of parameters of the intermediate stages of this transformation, such that T does not change. Or more concisely: two imaging chains are called equivalent if they have the same T. This terminology fits with the mathematical notion of 'equivalence class'.

I would argue that it is precisely equivalence theory that attempts to consider the whole chain, and treat it more or less as a black box with a small set of parameters, for better or worse. As someone already said: a useful (to some extent) abstraction and simplification.

Mathematical descriptions of the imaging chain abound, and they are singularly useless for photographers.  The reason is that photographs are intended for viewing by humans, so that human evaluation is essential for any photographically credible notion of equivalence.  There is a vast scientific literature about how to do that, using "just noticeable difference" techniques.  There are plenty of studies using that procedure to evaluate reproduction of luminance maps - the term of art for the result is "image fidelity" - but that correlates quite poorly with evaluation of pleasingness.   

[Andrea B.]

But Equivalence is not used to evaluate photographs. It is used to compare/contrast certain variables of the photo gear.

[Les Olson]

Under what real-world circumstances does anyone use different cameras to take the same photograph, for a standardised output size?
It happens all the time. People switch between systems with different formats but continue to view their images in the same or in a similar way, leading to perceptual differences in the output.
Or a new camera hits the market and you want to test its capabilities by comparing its output with a known benchmark.
Etc.

People switching systems do not re-visit every location they have been for the past two years and re-photograph every image they made.  Why would you get a different camera if not to take different photographs? 

And as for comparing a new camera which has "hit" the market with other cameras, the reason that is a foolish undertaking is that the conditions under which a comparison is possible - same photograph, same output - are photographically irrelevant.

[Andrea B.]

Be that as it may, some people do want to compare cameras on a technical, gear-head basis. I myself enjoy it because I like techie stuff. I also manage to separate my artistic, photographic aspirations (such as they may be, it is questionable, <smiling>) from techie stuff.

We can enjoy and maybe even be good at more than one thing:  Gear vs. Photographs, Tech vs. Art. The two opposites can be combined meaningfully. For example, for all his fussing in this thread, Bjørn is a master of Tech in addition to being a photographic Artist (my opinion). He just gets ahead of himself with these definitions in english (that crazy language!!).

[simsurace]

Mathematical descriptions of the imaging chain abound, and they are singularly useless for photographers.  The reason is that photographs are intended for viewing by humans, so that human evaluation is essential for any photographically credible notion of equivalence.  There is a vast scientific literature about how to do that, using "just noticeable difference" techniques.  There are plenty of studies using that procedure to evaluate reproduction of luminance maps - the term of art for the result is "image fidelity" - but that correlates quite poorly with evaluation of pleasingness.

I was not trying to -- as you seem to have interpreted -- derive mathematical conditions for the pleasingness of an image. That is a different subject for neuroscience to figure out, but not entirely futile, e.g. how certain geometrical relationships in faces can be correlated with pleasingness across multiple viewers.

Instead, I was describing a possible definition of what it means that an image can look 'the same' despite differences along the imaging chain. There is no notion of subjective quality or pleasingness to this, merely the notion of sameness of measurable quantities, like noise, DOF, framing etc.

Are you saying that humans might perceive two images as different, despite the fact that all possible measurements on the image say they are the same? If yes, what would you attribute the difference in perception to? The brain can only pick up stuff that is there, or would you like to invoke some supernatural senses?

For example, color management is an aspect of this that exists despite the fact that color perception is complicated. It is still possible to roughly model color perception, and derive methods to get consistent colors across media (or to get close, at least). Sometimes color accuracy is needed, sometimes not. But the fact that color management exists and is well developed indicates that there is a need for it that goes beyond pure academic interest. Even though it is grossly imperfect, having no color management at all would be much worse.

You are saying that such concepts are 'singularly useless' for photographers, as if this matters, or is an objective fact. Instead, we are merely discussing conceptual tools that any photographer, camera designer, scientist or interested individual can freely choose to make use of or not. Obviously, you have decided that they are useless for you, but the fact that there is a lot of literature on the subject indicates that there is considerable interest in them.

[simsurace]

People switching systems do not re-visit every location they have been for the past two years and re-photograph every image they made.  Why would you get a different camera if not to take different photographs? 

And as for comparing a new camera which has "hit" the market with other cameras, the reason that is a foolish undertaking is that the conditions under which a comparison is possible - same photograph, same output - are photographically irrelevant.

I don't know why people do what they do, but they do it. For example, they buy a lighter camera with a smaller sensor because of declining body strength and then compare their favourite print size to understand what they are trading against the weight saving.

Yes, sometimes they buy new gear to get different possibilities. But who am I to judge them or what they do?

I'm saying that if they want an apples-to-apples comparison, they are advised to evaluate images of the same size at the same viewing distance. Not by looking at a 10m print with a loupe for one camera, and at a 1000px web JPEG for the other camera. Is it so controversial to suggest that such a comparison would be totally meaningless?

[Bjørn Rørslett]

But Equivalence is not used to evaluate photographs. It is used to compare/contrast certain variables of the photo gear.

To what end(s)?

I have nothing against counter-intuitive theories, after all any progress depends on such thoughts being formulated, tested, and refined. However, counter-productive theories that fail to predict phenomena already known, or muddles their understanding, are less than useful. It is a simple fact that the 'equivalence theory' fails us in understanding why there should be a difference in film vs a digital sensor regarding dynamic range when a part of the "sensor" (film strip, say, or a cropped DX from FX frame) is used to capture illumination. We *know* from film a piece of the film sheet responds identically to the entire sheet. It is not only intuitive it has been used in practice for ages. So why should a digital sensor be magically different? The proponents of the 'equivalence theory' repeatedly claim there is an area dependency involved. See, for example, the calculations for DX to FX in an earlier post.,

It all boils down to a small piece of film or photo site having a log D-E curve basically of the same functional shape. The film has the "toe" (= shadow noise in digital") and has a much higher headroom at the upper end of the curve simply because the linear relation log D - E starts breaking down; the digital sensor clips more brutally. No need to dismiss film because it "lacks full-well"capacity, it certainly has but is manifested differently. But then film and digital are different recording media. In any case, film is not area dependent on dynamic range meaning the range of light values that can be recorded; digital is claimed to be. This assertion has been posted over and over again here; sometimes stating that one "throws away" dynamic range by sampling from the initial file, which simply ignores the fact that the entire chain up to the final output (print of fixed size, another of those constraints that remove degrees of freedom) tends to "waste" information as much more is recorded initially than can be presented in the final stage. We expressly don't need 36 MPix cameras to make a 30x40 cm print or post a picture of 2000x1300 pix on a web page. Most of the collected data at the first step is discarded unless one want mural prints and in that particular case, few of today's consumer models deliver enough pixels to avoid significant extrapolation,  which negatively impacts the output quality in its own manner.

[simsurace]

Yes you are treating as a black box, but are hijacking pixel dynamic range(a constant for the same sensor) by multiplying by size (a variable) and then calling it sensor dynamic range. It is this redefinition which is bothering me. It needs a different name.

Dynamic range is always tied to a certain signal (or device, but in this case we use different DR definitions for the same device, so they must be referring to different signals). What is called a 'signal' differs from case to case. Sometimes the same quantity that is noise in one case, can be a signal in another.

- If the signal is the brightness of a patch of the normalized output image (either the entire image or a certain predetermined fractional part of it, does not matter), then the definition that was used by John and me, or alternatively Bill Claff's PDR, applies.

- For the per-pixel DR, the signal is the charge measured in the photosite.

The name is still valid because it is a ratio of the biggest and the smallest recordable signals.
What name would you propose?