Discussion of 'Equivalence'

[Jack Dahlgren]

Precisely!  Your assumption is still, however, that we have to make comparisons of camera performance, and therefore we have to do whatever is necessary to make comparisons feasible, and, for preference, easy.  It is not obvious to me that we have to make comparisons of sensor performance at all, especially when we are not making comparisons of, eg, AF performance and ergonomics, but we can leave that aside.  The idea that because including some variables, in this case output resolution, would make comparison difficult or impossible means that it is OK to arbitrarily exclude them cannot be right.  Excluding them may make the comparison possible, but it also makes it irrelevant. 

 As ever, we are back to circularity: the only reason you have advanced why we should accept the assumptions on which equivalence depends is that equivalence depends on them.

I feel we are getting close to the end of the discussion of circularity.

It is this point exactly - that equivalence leaves out factors which are not equivalent - which makes it clear that it is a false equivalency. A square is not a circle unless we round the corners enough.

It is clear to most experienced photographers that different size formats have different characteristics. Where does the desire to make them equivalent stem from anyway?

We can NOT claim that photography is just about a standardized image format as there are so many other uses that photography is put to. The thousands of different designs of cameras over time attest to this. Fitting them all into a circular bin is a fool's errand.

[simsurace]

It is not clear to me what you mean by 'assumptions'.
Equivalence is a list of 'criteria'. It is a definition. The definition does not assume anything (apart from other definitions, like DOF, perspective, etc.)

After pondering your view of definitions some more, it might actually be that your analysis of definitions is a cultural one, and that might explain some of the misunderstanding.
My bias from my mathematical training is that definitions exist independently, and have no intrinsic meaning or purpose of their own.
As such, they don't need to be justified.
In mathematics, a definition is perhaps motivated, but never justified a priori. It would not make any sense to do it.
Instead, the justification is applied retroactively by the theorems that you can prove about it.
But I'm well aware that the mathematical notion of a definition is a very small class of all possible notions.

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Still, I think that certain definitions are more useful than others.

Using a more restrictive set of criteria, e.g. one that includes all of Joseph James' criteria PLUS equal native (not output) resolution, would make it possible to talk about pictures made by the D7000 and the D4 (16MP) with the same perspective, framing, DOF, shutter speed, brightness, and display dimension as equivalent pictures, but not pictures of the D4 and D800, or the D7000 and D500, even though the pictures might have been downsampled to match the output resolution. If you also include the same output resolution, you exclude any form of resampling, which further reduces the set of possible comparisons.

On the other hand, if you do not require resolution as part of the definition of equivalence, you can compare, e.g. 'equivalent' pictures (in the sense of Joseph James) and study e.g. the effect of having different number of pixels. Similarly, you could exclude any of the six criteria because you wish to compare this aspect. For example, you might be interested in comparing the effect of display dimension. You can then compare two images shot with the D4 and D800, but the same output dpi (the D800 shot will be substantially larger).

My opinion is that comparison of sensor performance should not be mixed with different output dimensions. I would, personally, compare sensor performance at equal output size, and then separately study the effects of output dimension when working with the same files. Or, run multiple parallel comparisons at different output sizes.

You are always coming back to the question of why we should compare sensors at all. There is no imperative, but many people are interested in that stuff and we do not need to defend or attack their interests. Comparison of output is in the very nature of photography, assuming you look at your shots after producing them (this might not be true of some ultra-fast press photography where the shot is directly uploaded to the press agency after taking it).

[David H. Hartman]

A fly in the ointment regarding comparing one sensor to another is we never receive totally RAW data in a RAW file. It has always been cooked a little. We can compare them (the sensors) in theory but not in practice.

Dave Hartman

[David H. Hartman]

What we desperately need is an apples to apples comparison of apples and oranges.

Dave Hartman

[David H. Hartman]

The concept of enlargement is just as valid for digital images as film images. While the digital image data has no physical size the original image censor does and if we ever look at​ a representation of the image data that representation be it print or monitor will again have a physical size.

You will need to enlarge the DX image 1.5x that of the FX image for it to achieve the same physical size as the FX image. This is no different from enlarging a half frame 35mm negative as compared to enlarging a full frame 35mm negative.

Dave Hartman

[David H. Hartman]

With the right criteria for comparison a 1964 Volkswagen Karmann Ghia is equivalent to a 1964  Ferrari 250 GTO.

Dave Hartman

[Andrea B.]

My bias from my mathematical training is that definitions exist independently, and have no intrinsic meaning or purpose of their own. As such, they don't need to be justified. In mathematics, a definition is perhaps motivated, but never justified a priori. It would not make any sense to do it. Instead, the justification is applied retroactively by the theorems that you can prove about it. But I'm well aware that the mathematical notion of a definition is a very small class of all possible notions.

I think you have correctly identified the concept of "definition" as a source of the confusion over Equivalence. I also trained as a mathematician and, of course, agree with your comments about definitions. Optics and electronics are all based on physics, thus on mathematics, so it makes perfect sense to me to define this concept called Equivalence and then use that definition to compare different camera formats in such a way as to be able to draw some useful conclusions about which might be better for a given photographic task -- and why.The reason the definition of Equivalence is so useful for format comparisons is because you can produce the same framing (angle of view), the same perspective (distance from subject), the same DoF (or diffraction or total amount of light on the sensor), the same exposure time, the same brightness and the same display dimensions with many, many different combinations of cameras and lenses.

[pluton]

Opinion:  Equivalent, in this context, really should be re-formulated as 'near equivalent', 'rough equivalent' or 'close equivalent'.  In the most common English usage that I am familiar with, the word 'equivalent' means 'the same as', not 'nearly the same as'.
Just a thought.

[Andrea B.]

Perhaps call it Photographically Equivalent.

[bclaff]

Perhaps call it Photographically Equivalent.

Perhaps, visually equivalent ? As in visually indistinguishable.

[simsurace]

There is always a certain tension when adopting words that occur in everyday language for a technical definition. The word 'equivalent', by most dictionary definitions, does not mean 'equal' but something weaker than that. Even in everyday use, it is usually met with a question for specification. For example, if I proclaim 'It is equivalent to have a house or a flat', the natural follow-up question is usually 'equivalent in what sense?', which indicates that the word was not sufficiently precise to make the statement clear. I can then explain, e.g. 'equivalent in the sense that they both give shelter to myself and my belongings.' Once this is clarified, one can then discuss whether this list of criteria is reasonable etc. It is obvious that some people will have criteria for equivalence of housing that is much more restrictive, up to the point where only their own house qualifies (at which point the word 'equivalent' becomes meaningless).

That is, the word 'equivalent' is generic enough to be suitable for technical definitions. This would not be true of 'visually indistinguishable', because that already means something that is fairly precise, and the criteria do not match. Two equivalent images (in the sense of James) do not have to be visually indistinguishable. One example was already given by Les (different resolution), another would be if the sensors are from a very different generation: the older one will generally have more noise. The fact that the comparison is of equivalent images makes it easier to interpret the observed difference; you cannot, for example, say that the images were shot with different amounts of total light, and the noise is due to photon noise. Or that the photos show very different framing, and the noise is more obvious in one shot because of that. It is because the pictures were shot in a way that controls for these nuisance variables.

When looking at reviews of cameras, it seems to be more or less acknowledged (and practised) that one should compare at equal framing, perspective, DOF/diffraction and viewing size. But many tests compare at equal ISO. This is possible, but when the comparison is between different formats, it requires a quantitative analysis of noise in order to establish whether it is more or less than what is expected. Often, such comparisons are met with quite a bit of criticism along the lines of 'the comparison is not fair'. I think that any comparison that is done in a controlled and transparent way is 'fair', but I think that the interpretation can be facilitated by certain ways of comparing things.

To give a further example: when I see a test that compares the noise performance of an iPhone with that of a DSLR of a similar vintage (at the same framing, perspective, DOF, viewing size) at the same ISO, of course the iPhone will be much noisier, and it would be naive to expect otherwise. If you compare at equivalent ISOs (same amount of total light), I immediately get a rough idea of how bad it is. E.g. if the noise is similar at equivalent ISOs, the iPhone performance is not less than what is anyway expected from the sheer scaling of the sensor, which would lead me to believe that the performance is actually quite impressive. If on the other hand the iPhone shot is more noisy at equivalent ISOs, I cannot say 'look, this is because the sensor is so small', because that has already been controlled for. Instead, there must be something else going on (e.g. a lower quantum efficiency or fill factor, or more read noise) that explains the perceived difference.

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So far, there were two main lines of criticism of the list of criteria included in James' definition:
1) The list is too restrictive, because of either
     a) two images can only be equivalent when they are the same, or
     b) two images can look the same even though they are not equivalent
2) The list is too loose (why is resolution not included? etc.), i.e. two images can look different even though they are equivalent

From this, I would conclude that without further assumptions the definition of James' is neither necessary nor sufficient for 'visual indistinguishability'.

[Les Olson]

[...] Optics and electronics are all based on physics, thus on mathematics, so it makes perfect sense to me to define this concept called Equivalence and then use that definition to compare different camera formats in such a way as to be able to draw some useful conclusions about which might be better for a given photographic task -- and why.The reason the definition of Equivalence is so useful for format comparisons is because you can produce the same framing (angle of view), the same perspective (distance from subject), the same DoF (or diffraction or total amount of light on the sensor), the same exposure time, the same brightness and the same display dimensions with many, many different combinations of cameras and lenses.

No one is arguing about whether the square root of -1 "exists", and therefore whether it can be used to draw conclusions about alternating current.  Nor are we arguing about whether, as a term-of-art, equivalence, like "point", can have any restrictions or conditions its creator chooses (but people who wish to do that and be understood are well-advised not to choose ordinary words as terms-of-art, and instead emulate doctors and lawyers who use arcane or non-English words to signal the use of the term-of-art; confusion over whether "equivalent" = "nearly identical" = "equal" = "the same" was inherent in the choice of an ordinary word as term-of-art). 

We are arguing about whether it is true that equivalence allows us "to draw some useful conclusions about which [format] might be better for a given photographic task".  The status of axioms is irrelevant,  because there is a difference between an axiom and an arbitrary condition, and it is arbitrary conditions that are the problem with equivalence. 

There are two kinds of arbitrary condition at play in this discussion. 

One is merely irritating: starting from an arbitrary status quo that habit has lead one to suppose has some real significance: saying that if I use a 105mm f/2.5 lens on FX for portraits I need a 75mm f/1.8 lens on DX, and there is no such lens, is as inane as saying that one mile = 1.60934 km so athletics cannot possibly use SI units. 

The other, which undermines the whole equivalence enterprise, is arbitrarily ignoring factors that reverse the allegedly useful conclusions.  It is a legitimate simplification for physicists to ignore friction when teaching mechanics, because they do not pretend that the space shuttle will not get hot on re-entry.  It is not a legitimate simplification for neo-liberal economists to ignore informational asymmetry when discussing markets, because they do pretend that governments do not need to regulate markets, which depends on there being no informational asymmetry.  It is not a legitimate simplification for equivalentisti to ignore the independence of output size and output resolution, because they do conclude that at equal framing and perspective and output size, DX images will have more DoF, which depends on output resolution not being independent of output size.  It is not a legitimate simplification for equivalentisti to ignore the central role of the viewer's evaluation, because they conclude that 85mm f/1.8 on DX is not equivalent to 105mm f/2.5 on FX, which depends on ignoring the fact that viewers have no preference for one over the other.

So, let me set a problem for equivalence.  I want to reproduce the look of David Bailey's 1965 portrait of the Kray twins, Reggie and Ronnie (they were violent criminals, Reggie is on the left, Ronnie on the right; Bailey had grown up in the same neighbourhood and knew them; "I quite liked Reg, even though when he was 19 he slashed my father’s face with a razor. Ron was a basket full of rattlesnakes." https://www.theguardian.com/artanddesign/2015/jul/05/david-bailey-stardust-exhibition-edinburgh-photographer-interview - the whole interview is well worth reading).  The portrait was made with an 80mm f/2.8 on 6 x 6 film.  Does anyone think that knowing what would be equivalent on FX or DX is where I need to start? 

 

[David H. Hartman]

It is not a legitimate simplification for equivalentisti to ignore the central role of the viewer's evaluation, because they conclude that 85mm f/1.8 on DX is not equivalent to 105mm f/2.5 on FX, which depends on ignoring the fact that viewers have no preference for one over the other.

Perspective in the human face has an emotional impact on the viewer. The flatter the perspective the more aloof or distant, the rounder the perspective more personal until the perspective appears distorted. A normal conversational distance is not an arbitrary distance. It is informed by social norms and practicality. The social norms are based in part on predatory animal behavior. When an animal with binocular vision looks intently with both eyes at another animal it is frequently thinking about food, sex or combat. I rather expect you will ridicule this for lack of understanding.

Perspective in the human face has an emotional impact on the viewer and the viewer needs no preference for one focal length or format over another to feel the perspective's impact.

Dave Hartman

[Les Olson]

The concept of enlargement is just as valid for digital images as film images. While the digital image data has no physical size the original image censor does and if we ever look at​ a representation of the image data that representation be it print or monitor will again have a physical size.

You will need to enlarge the DX image 1.5x that of the FX image for it to achieve the same physical size as the FX image. This is no different from enlarging a half frame 35mm negative as compared to enlarging a full frame 35mm negative.

No.  The D500 has 20MP.  At 300 dpi, 8 x 10 is 5.4MP, 12 x 18 is 9MP, 24 x 36 is 18MP.  Because I have spare pixels, I can print all those sizes at identical resolution: there is no "enlargement" of the DX image as output size increases until I exceed 24 x 36.  It was different when a D2 only had 4MP: then printing larger was the same as enlarging a negative, because except for tiny prints the only way to print bigger was to lower dpi.   

A D810 has 36MP and a D500 has 20MP, so the sensor elements are slightly smaller on the D500 (pixel pitch 4.2 microns vs 4.9).  Suppose I have the same lens on both: the same object is imaged the same size on both sensors. That image covers 1.2 (4.9/4.2) times as many sensor elements on the D500 sensor as on the D810 sensor.  If I print the D500 and the D810 images at 300 dpi, the printed objects are 1.2 times larger (not 1.5). But I can print the D500 image at 360 dpi instead of 300 dpi, so that the printed images are the same size for both formats (360/300 = 1.2).  I cannot quite manage it at 24 x 36, which at 360 dpi is 21.6MP, but if I am allowed to adjust print resolution (and you just try and stop me  ) there is no sensor "enlargement" except at the most extreme print sizes.  For the D5, which has 6.4 micron pixel pitch, I would have to print at 450 dpi instead of 360 dpi to eliminate enlargement (6.4/4.2 = 1.5).   

[David H. Hartman]

No.  The D500 has 20MP.  At 300 dpi, 8 x 10 is 5.4MP, 12 x 18 is 9MP, 24 x 36 is 18MP.  Because I have spare pixels, I can print all those sizes at identical resolution: there is no "enlargement" of the DX image as output size increases until I exceed 24 x 36.  It was different when a D2 only had 4MP: then printing larger was the same as enlarging a negative, because except for tiny prints the only way to print bigger was to lower dpi.   

A D810 has 36MP and a D500 has 20MP, so the sensor elements are slightly smaller on the D500 (pixel pitch 4.2 microns vs 4.9).  Suppose I have the same lens on both: the same object is imaged the same size on both sensors. That image covers 1.2 (4.9/4.2) times as many sensor elements on the D500 sensor as on the D810 sensor.  If I print the D500 and the D810 images at 300 dpi, the printed objects are 1.2 times larger (not 1.5). But I can print the D500 image at 360 dpi instead of 300 dpi, so that the printed images are the same size for both formats (360/300 = 1.2).  I cannot quite manage it at 24 x 36, which at 360 dpi is 21.6MP, but if I am allowed to adjust print resolution (and you just try and stop me  ) there is no sensor "enlargement" except at the most extreme print sizes.  For the D5, which has 6.4 micron pixel pitch, I would have to print at 450 dpi instead of 360 dpi to eliminate enlargement (6.4/4.2 = 1.5).   

36 x 10 = 360
24 x 15 = 360

[I too tired write and hoped the above conveyed what I was thinking. My previous post may have been ambiguous.]