Digital photography: how many actual iterations are there for a processed an image?


Each processing package has many options. Each slider has many stops. Each can be used in conjunction with any and all possible settings on every other filter. So every image you produce is one choice among a literally infinite set of iterations? Or not? I accidentally ask more questions than I meant to and some of S&R’s technically minded friends make your head hurt…

I was told there would be no math. – Chevy Chase as President Gerald Ford.

Sam Smith

A question for my photographer friends. If you run an image through a workflow of LightRoom, Photoshop, the Nik Suite and On1 Raw, how many specific iterations of a shot do you think are possible? As in, every possible combination and permutation all the filters and settings you could use or not use adds up to…?

I imagine the number is finite. I also imagine it’s really, really large.

Michael Pecaut Not sure i understand the question. Most of the settings in all of these programs are on sliders. So, infinite.

Sam Smith Maybe. It’s my assumption that underneath the hood the options are more discrete. It looks fluid to the user but mathematically it might not be?

If I’m wrong, then infinite may not be a bad answer.

Kinda interesting to consider that each photograph I post is literally one choice in an infinite universe. It hurts to think what that means for M-theory…

Michael Pecaut Yeah. As soon as i posted that, I wondered how many channels really exist in those sliders. It’s all digital, after all.

Michael Pecaut Even if you include all the presets in the camera itself. Now, if you are starting with a film camera, then the options are infinite because part of the processing is analog.

Sam Smith Right. Since it’s digital, I’m assuming this is a theoretically solvable math problem. And that the answer is technically finite, but for all practical purposes infinite.

Michael Pecaut i guess if you add all the weirdness associated with actually SEEING the image on a monitor…that might make it infinite. Colors and brightness may change in the monitor just because of temperature changes in the room or wear and tear on the circuits, etc. Not to mention the human eye itself.

Sam Smith Oh good lord. I can’t even think about that.

Cyndi Goetcheus Sarfan This thread is cracking me up. Is this what keeps you up at night Sam?! I am not sure I even understand the question posed but I am going infinite.

Sam Smith I have an enquiring mind.

Andrew Magalee Since they’re digital sliders, it’s definitely a finite number. All one would have to do to figure out the answer is find out how many steps each slider has in each program, then start multiplying.

It’s literally impossible for a computer to allow an infinite number of options. Even a program designed to repeatedly offer the option to cut a value in half will eventually run out of resources, even in a universe-sized computer.

Sam Smith Not a math guy, but this is what I thought, too. I lack the skills to compute it and the patience to assess the number of variables, although that part I probably could do if I had to. But even the number of variables is a big one.

Andrew Magalee The math is just multiplication. In theory, if there were a bunch of sliders with the same number of steps, you might use exponents to simplify the multiplication… but it’s all just steps times steps times steps times steps.

Sam Smith To the power of steps.

Evan Robinson Photoshop is effectively infinite because you can keep adding layers and each layer adds modifiers. I suspect there must be some absolute limit to the number of layers addable, but I expect it is quite large (e.g. not 8 bits but 16 or 32 bits).

Sam Smith I hadn’t even thought about the layers issue.

Evan Robinson You may perhaps have noticed that you have an artistic, perhaps even poetic, approach to life.

I, on the other hand, am an engineer.


Michael Pecaut Or moving things in the image.

Sam Smith I mean, cropping choices alone makes it damned near infinite.

Michael Pecaut I was assuming you didn’t change the image content. Like erasing blemishes.

Sam Smith Why would you assume that?

Michael Pecaut because if that were an option, then the answer is more than just the programs and then the answer is obviously infinite.

Sam Smith Okay, okay. Ignore cropping and blemish removal. Just the software settings.

Evan Robinson See my discussion of Photoshop, below. There are not nearly infinite outputs possible, regardless of the number of input sliders, layers, etc. because a bunch of the options must fold together to produce identical output.

Evan Robinson OK, here are some numbers for Lightroom.

In the develop module, excluding Lens Corrections, Transform, Effects, and Calibration, there are 51 sliders. Most of them have a range of -100 to 100, but there are exceptions. There is also the Tone Curve, which has 1000 possible points on the horizontal axis, each of which can have 1000 possible values on the vertical axis (for a total of … 1 MILLION possibilities). Multiplying all the possible ranges together, Excel comes up with 3.34×10^120 possibilities.

That excludes the Black & White options, which would be quite a bit smaller, as it would exclude 24 HSL sliders and the Vibrance and Saturation sliders in favor of 8 Black & White Mix sliders.

It also excludes any use of crop tools, heal or redeye tools, gradient tools, or brushing in effects over a localized portion of the image.

Regardless, it’s a lot.

Noodling with an idea for how to deal with Photoshop, I have a possible answer, but it is dependent upon your resolution. Fundamentally, Photoshop allows you to individually set the color value of each pixel in your image, so for an image of dimensions H x W pixels of D color depth, there are (H x W) pixels each of which has 2^D possible values, meaning that Photoshop has HW2^D possible outcomes.

For a 32 bpc (bits per color) RGB image in Photoshop (taken with my Nikon D850) that means (8256 * 5504) * 2^96 or 3.6 * 10^36 possibilities. In CMYK there would be more possibilities, like 1.55 * 10^46, because there are four inks instead of three phosphors.

Which tells you that a lot of the slider combinations in Lightroom overlap and produce identical output.

I trust Sam can now sleep tonight.

Sam Smith No. No he can’t.

That’s a big number. Now add to it four more packages in the workflow.

And yeah, you pretty much have to exclude stuff like cropping, etc. Healing probably does make it damned near infinite.

Evan Robinson Actually, I believe the Photoshop numbers show a distinct upper bound. It doesn’t matter how many sliders and controls you have, your output field is limited by the number of pixels you have and the number of color variations allowed in each pixel.

Sam Smith Hmmm. But you also have a humungous number of resolution options.

Evan Robinson Fundamentally, any cropped image is the same as the full resolution version, so I’m not gonna worry about that. And as for other tools, the Photoshop calculation essentially accounts for all possible pixel combinations, so all tools fold into that number.

Sam Smith Right. But you have to account for every possible resolution iteration. That adds to the equation.

Evan Robinson Again, gonna say it reduces it. Every pixel you take away removes 2^96 combinations. Every time you reduce a resolution by one, it adds 1 combination and removes N x 2^96 where N is the number of pixels removed. Net result of any crop is a loss of combinations (effectively, you are redoing the calculation at a smaller resolution).

Sam Smith Not sure this makes sense. The pixels will differ if the same image is at 72 dpi vs 300 dpi, right?

Evan Robinson Nope. The print size is just different.

Sam Smith Evan Robinson Huh? Image X – same image – rendered at 300 dpi vs 100 dpi has three pixels for every one. IE, each chunk is split into three, more of less.

Evan Robinson Image X, same image, at HxW pixels, has exactly the same pixels at 100dpi as 300dpi. The physical dimensions change, the pixels don/t

Evan Robinson: PPI Doesn’t Matter (and stop saying DPI)

Sam Smith Okay. Seems counterintuitive to me. But this would suggest the answer to my question is a lot simpler. Although, again, it seems like there can be fucktillions of ways of getting to the final point.

So I apparently asked two questions when I thought I was asking one.

Evan Robinson Yes. There are many ways to get to the same place. For example, imagine any Photoshop layer which reduces the output to full black. Most things you do after that will have no effect.

Andrew Magalee There’s no such thing as “near infinite.” Something’s either finite or infinite. Whatever monstrously huge finite number exists, there is always a larger finite number.

“Functionally infinite,” *might* be a more useful term if reaching the finite result were so large as to exceed the lifetime of the universe to reach.

But still, when dealing in digital mediums, the result must be finite by definition.

Michael Smith Image editing sounds like a pain. I’ll stick with audio and non-destructive editing and processing.

Sam Smith Well, there are ways of avoiding destruction.

Michael Pecaut Lightroom is non-destructive.

Sam Smith Some of the filters in On1 aren’t. Also my computer has an UNDO function… 🤣

Michael Smith I would think the answer then would be “infinite” given that you could recursively process a file as many times as you like. I hope this answer is as unhelpful as it feels.

Sam Smith That’s a point I hadn’t made yet. I actually have files that went into LR, then PS, then back out in to ACR, then back into PS and Nik Color Efex, then to On1, then back to Nik Analog Efex, then Color Efex, then On1 again, etc, as I tinker and noodle the minutiae.

Now, if the final output comes through PS – and it does – Evan has a point. How many options are there per pixel and how many pixels are there (and, if I’m right, how many resolution iterations are there)? In that frame, the answer may be way smaller and simpler. Just do pixel math.

Which is fun, because that would mean there are “functionally infinite” ways of arriving at a very finite final number.

Michael Smith I don’t know if that’s common for image processing but your workflow sounds messy to me. I do all of my processing inside of one program so that I can go back and tweak settings non-destructively. It’s also handy for applying those processes to another file so I can quickly render new tracks in styles I like.

Sam Smith There isn’t one program that does all I need to do. Frankly I wish I had a few more.

Evan Robinson It doesn’t matter if the final output is through Photoshop or not. Whatever tool you are using has the same basic limitation: number of pixels times number of colors possible per pixel. The Lightroom/Photoshop comparison just highlights how many control combinations must fold together into identical output.

Sam Smith So, in conclusion, how many actual output options are there? And we agree that the paths TO that number = … many?

Evan Robinson I’m gonna stick with the Photoshop numbers. There are, for any input image of dimensions HxW pixels in bit depth D and colors C, (HxW*2^(C*D)) possible output images of the same dimensions.

A black and white image has bit depth 2 and colors 1. An 8 bit greyscale image has bit depth 8 and colors 1. An RGB image has colors 3, a CMYK image has colors 4. And so on.

Specific calculations for my D850 are upstream somewhere if you want them.

In the case of both Lightroom and Photoshop, there are far more control combinations than there are output images. Many paths to the same image.

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