How can I automatically get a (approximate) Lux value from overexposed and underexposed pictures?

Question

As you will soon understand, I am not a photographer. For research in a completely different field, I am interested in estimating, even with a large approximation, the brightness of the environment in a series of pictures.

I won't enter the lux vs illuminance vs luminance topic - let's say I am OK with anyone of these. So, as far as I understand:

EV to Lux

There are tables like this that, maybe with huge uncertainty, let you pass from EV to Lux, and you can get EV from exposure time and f-number. Fine!

1. What about ISO?

These tables work with ISO = 100. From my understanding, if I have ISO = 200, I just need to add 1 to my EV, thus looking at the row below. Is this correct?

2. What about pictures not exposed correctly?

If what I said in 1 is correct, I should be able to infer Lux by simply using ISO, exposure time and f-number. However, I could take two pictures, varying a single parameter between the two, and I would get two different Lux values even if the scene was the same.

For my application, I think another parameter should come into play, which might be the average brightness of the picture (the mean of all pixel values), that numerically stands between 0 and 255.

Automatically exposed pictures tend to have average values near 128. My wish is to take that into account, and, if my average value is, say, 150, add, say, 1 to the EV because the scene is presumably brighter.

Does this, approximately speaking, make any sense? Is there a relation between a single stop and the consequent variation in the average picture brightness?

Note: of course this logic breaks if the picture is very underexposed (has some 0s) or very overexposed (has 255s) because then you can't use the average brightness information. Let's say all pictures have average brightness between 80 and 200.

Answer 1

The good part is that the camera does measure brightness of the seen in terms of an EV value.

There are several different ways to do the measurement. Most of the modes calculate the result from a weighted average of the image. Some put more emphasis in the middle part (spot metering for example). If you know what mode was used and how the weights are distributed for that mode you know what pixel values contributed to the settings and thus the EV value.

The issue with that is that you do not know the distribution of weights over the image. This is proprietary information of the camera manufacturer. You could reverse engineer this information with a lot of testing, but that would be very time consuming and the results may only apply to the tested camera.

On top of that, there's no guarantee that the image taken has anything to do with a meter reading whatsoever. The measurement could be taken from subject matter that's not even part of the image. Or as you stated: the settings could be chosen manually. You could consider them arbitrary or random. This is why one could say that there's no "correct" exposure. Photography is an art after all. You could work yourself around that by taking the images under controlled circumstances so that you know that the settings used are based on a measurement of the actual subject matter.

On the other hand, settings for exposure compensation (that is, to deliberately move settings away from what was metered) are usually limited to plus minus 2 EV (3 on some models) This value indicates that the desirable exposure settings are usually in that range from the metered settings. Depending on what kind of approximation you are looking for, you could say that the used settings are the same as the metered settings with a maximum error of said plus minus 2 EV.

Dynamic range is limited and values clip. If the white clipping happens at value 255 depends on the bit depth of the data that the sensor produces. A lot of cameras produce more than 8 bit per channel. If you have an image that includes the sun or a reflection of it, those regions are usually blown out. The logic falls apart as you say. Finding a reasonable threshold for how many pixels are allowed to be blown out in an image to still apply the logic to it sounds like a tough statistical task.

And then there is flash. I take quite a few images with the meter of the camera blinking to signal underexposure. But that's not relevant to me in those situations, because I use a flash that compensates the darkness of the ambient light. The logic falls even more apart in this scenario.

conclusion

I don't think this makes sense in general, because there are too many things the influence the result, which makes the result itself somewhat arbitrary.

In a controlled environment, this could make sense though. Say for example an led in a box is photographed and the lux can be estimated from the photograph. A calibration with a lux meter would be helpful.

So much for the theory. The "correct" exposure that the metering modes are aiming for are an empirical value. It's what turned out to work for the average image. My suggestions would be to do the same. Take a few series of images along with a proper measurement from a lux meter of the scene. Then see if there's any correlation between the values.

Answer 2

The main part of this question comes down to How to calculate Lux from EV?, leaving only the problem of estimating the overexposure or underexposure.

It seems that you want to do at automatically. That's easy to answer: you can't, really, unless all of your images are of similar, known subjects. Otherwise, you would need a great deal of artificial intelligence to follow scene recognition. That's because there's no way to tell the difference between overexposure and a polar bear and a snowstorm, or underexposure and a black horse in a coal mine.

You say:

Automatically exposed pictures tend to have average values near 128.

And this is the crux of the problem. It is likely that many underexposed and overexposed pictures will also have this middle value. That's because while modern cameras attempt rudimentary scene understanding with matrix metering modes, they're often just guessing — and, here's the thing: it's when that guess is wrong that you're most likely to see underexposed or overexposed images. So, you can't just replicate that incorrect guess; that won't get you anywhere.

Does this, approximately speaking, make any sense? Is there a relation between a single stop and the consequent variation in the average picture brightness?

There is a relation, although the exact one will depend on your processing settings — but it's only a relation when you're starting from a known place. And if you had that, you wouldn't have this question in the first place.

Answer 3

You can't get any light information from the jpeg, the mapping is highly non trivial and depends on the RAW processing algorithm. No two pictures will use the same curve.

You could get light information from the RAW file, however. However you need the actual recorded values, you can't pass the file through a RAW processor, you need to parse the RAW file itself.