Channel mapping and matrices

[Mike in Rancho]

As of this week, I finally have a fully-complete 7x2 EFW. This now has me thinking about NB mapping in ST again, since I will soon do it with my own data.

I know ST is unique (and keeps us within guardrails) with the compose and color, split parallel luminance and chrominance, plus the pre-fab matrices, but I was still wondering if anyone knows a resource for a better understanding of what is going on with these techniques. Nuts and bolts sort of. I've looked about but haven't found much yet.

I believe in other solutions this is generally, though probably not identically, available via channel pixel math equations. I read them but I can't say I always understand them. Or perhaps more so - I am often skeptical when they are posted. But that could be because I don't understand them yet.

For example, in one case a greater than 1.0 multiplier of Ha was fed into the R channel, with the OIII subtracted from it. I'm baffled, but it is giving me a "red flag" feeling. Could be the obvious of creating a hole in the Ha to stick the OIII through?

In any event, I notice in the matrix list that all the mapping adds (are they actual addition functions?) add up to 100% for each of the R, G, and B channels as mapped into by the S, H, and O components. This of course seems unlikely to be coincidental, and so must have some good cause. I was thinking perhaps clipping prevention, but then again if these are linear functions that probably isn't a concern (other than star cores?).

Anyway, since we can't go beyond the presets I know we also probably can't go astray in ST with "wrong" pixel math, and that the mapping just dictates the three hues we will be working with for our relative emission concentrations. Those I can look at the formulas and get a good sense of what the colors will be.

But I'm still curious and want to understand what I read out there in the wild (not a how to but more of a why, and what is and isn't ethical). If anyone knows any good tutorials...

[admin]

As of this week, I finally have a fully-complete 7x2 EFW. This now has me thinking about NB mapping in ST again, since I will soon do it with my own data.

Congrats!!

I know ST is unique (and keeps us within guardrails) with the compose and color, split parallel luminance and chrominance, plus the pre-fab matrices, but I was still wondering if anyone knows a resource for a better understanding of what is going on with these techniques. Nuts and bolts sort of. I've looked about but haven't found much yet.

I believe in other solutions this is generally, though probably not identically, available via channel pixel math equations. I read them but I can't say I always understand them. Or perhaps more so - I am often skeptical when they are posted. But that could be because I don't understand them yet.

For example, in one case a greater than 1.0 multiplier of Ha was fed into the R channel, with the OIII subtracted from it. I'm baffled, but it is giving me a "red flag" feeling. Could be the obvious of creating a hole in the Ha to stick the OIII through?

This would give me a red flag feeling as well. Mostly from signal processing point of view as it opens up clipping scenarios (e.g. what if a Ha multiplier > 1.0 was fed into R and there was no O-III in that area to pull it down from above 1.0? Unless some sort of normalization is applied afterwards...). Plus it makes things rather intuitive for someone trying to figure out what is going on in an area. Hue creation from tristimulus values doesn't really call for (or work with) subtraction, unless perhaps some sort of out-of-gamut color space is being targeted (which doesn't really make sense in this context IMO).

In any event, I notice in the matrix list that all the mapping adds (are they actual addition functions?) add up to 100% for each of the R, G, and B channels as mapped into by the S, H, and O components. This of course seems unlikely to be coincidental, and so must have some good cause. I was thinking perhaps clipping prevention, but then again if these are linear functions that probably isn't a concern (other than star cores?).

Anyway, since we can't go beyond the presets I know we also probably can't go astray in ST with "wrong" pixel math, and that the mapping just dictates the three hues we will be working with for our relative emission concentrations. Those I can look at the formulas and get a good sense of what the colors will be.

But I'm still curious and want to understand what I read out there in the wild (not a how to but more of a why, and what is and isn't ethical). If anyone knows any good tutorials...

It really is (almost) as simple as following the assignment laid out in the Matrix parameter options.
Let's take, for example "SHO 40SII+60Ha,70Ha+30OIII,100OIII"

What is happening internally is;

• The assumption is made that your data was imported as SHO:RGB in the compose module (e.g. as it says on the butttons at the top in that module).
• Therefore, ST assumes that S-II currently purely lives in the red channel, Ha currently purely lives in the green channel and O-III currently purely lives in the blue channel.
• The Color module then scales the R, G and B channels (aka the S-II, Ha and O-III signal respectively) by the multipliers defined by Red/Green/Blue Bias Reduce/Increase. In other words, by modifying those Red/Green/Blue Bias controls, you are directly throttling the pure S-II, Ha and O-III signals before any remapping is done. Note that the S-II, Ha and O-III signals are normalized after the multiplication so that no channel will ever exceed 1.0 (or in other words, if I, say, massively pull on the green slider, the other channels really just "shrink" by the weighted inverse). For example RGB 0.6:12:3 would become 0.05:1.0:0.25 after normalization. This is now your input signal for the remapping.
• Finally, the remapping is performed. In the case of our example "SHO 40SII+60Ha,70Ha+30OIII,100OIII", the remapping becomes;
  • Rnew = 0.4*Rbiased + 0.6*Gbiased
  • Gnew = 0.7*Gbiased + 0.3*Bbiased
  • Bnew = 1.0*Bbiased

In the case of StarTools that is not entirely the end of the story, however, as, only the resultant coloring is used. The brightness component is unceremoniously thrown away, while the separate brightness/luminance from the (parallel-processed) detail/luminance dataset is adopted instead. How exactly the luminance is integrated with the coloring is dependent on the chose LRGB Method Emulation (see docs or in-app help item).

The remapping, however, is quite transparent and you can, for example, calculate from the mapping equation what hue a pure S-II, Ha or O-III signal will have. For example, a pure Ha signal (1.0) in our example would yield;
R = 0.4 * 0 + 0.6 * 1.0 = 0.6
G = 0.7 * 1.0 + 0.3 * 0 = 0.7
B = 0

You can plug that into, say an online RGB to HSL converter (multiply by 255 as this one expects an 8-bit value for each R, G and B value). For the resultant RGB 153, 179, 0, you will get a Hue of 69 degrees, which looks like this. In other applications (e.g. PixInsight), many (not all) people would now freak out because that's green! (ew!) They would now likely resort to tweaking the equation (in essence picking another hue for Ha), or resorting to SCNR/green killing tools (selectively modifying pixels above a threshold of green), rather than do the logical/"correct" thing and tweaking the input signal. In StarTools this is as easy as chaining the Green Bias Reduce/Increase to a point where that yucky green is overwhelmed by the other S-II and O-III signal.

So you get something nicely balanced like this even though Ha is (of course) dominant;

StarTools_2838.jpg (215.04 KiB) Viewed 3243 times

That smidgen of green dominance at 9 o'clock is enough to let the viewer know that that area is indeed strongly Ha dominant compared to other areas.
Crucially, the input signal is just attenuated (or boosted) in relation to the other three signals, but is not harmed in any other way that is either destructive, unpredictable or non-replicable across other datasets/objects/gear. The holy grail of color rendering for documentary photographical purposes is;

• to be able to get comparable coloring across different objects with comparable emissions

and

• to be able to replicate comparable coloring by different people with different gear, however with comparable filters

Narrowband imaging is really no exception. Sure, you have leeway in the hues, but the way these hues behave and the story they tell about the same object should be consistent.

To make a long story short, it's not so much about the pixel math / compositing equation - it just establishes the hue (which is best kept as simple and predictable as possible to aid the viewer seeing the three different emissions). The important bit is the throttling of the input signal to the equation to get draw the viewer's attention to a specific feature/emission via color.

Hope this helps!

[Mike in Rancho]

Thanks Ivo! Super helpful. I will have to bookmark this for re-reading and further digesting.

I must admit I had previously been thinking "linearly" that the mapping was done first, followed by the bias, and that ST just figured it all out mathematically how to still know what Ha, S2, and O3 were. I mean, that's usually the sequence I do it in the workflow - pick a matrix, throttle what's needed. But of course, far easier for ST to just maintain the original R, G, and B files (of course assuming proper compositing), apply the bias settings, then whatever matrix is selected, and throw that up on the screen.

Well, that clears up that big misunderstanding of mine.

I'm actually pretty fine with "yucky" green, or purple, or magenta, even for stars, since I know what they mean in narrowband based on what I've set up ST to do. Thus, my bias throttling, almost always of Ha, is designed just to pull back that dominance, globally (correct?), in order to reveal the other emissions.

The online converter worked as you indicated. But, I also found I could readily do the same thing in GIMP's color selection. Putting the same RGB numbers in from your example generated a very yucky green! GIMP seems to allow RGB input of either 0-100 or 0-255, and once input will also pop up values for HSV or LCH. The HSV translation seemed to match the HSL translation. Very cool way to check out the "pure" emission blends, though obviously not yet affected by luminance or LRGB emulation.

Honestly I can't dig up that post with the (to me) unusual multiplier and subtraction anymore, so just assuming it was some method to poke OIII through the Ha. Perhaps misplaced though, as to documentary value or maybe even effectiveness. The other I ran across (strange ~ symbols, channel multiplying like Ha*SII, and exponents!) I was actually able to dig up a source for, which was for "dynamic" narrowband combining. After reading through that I believe it is just more "art." As you imply, the transparent and tried-and-true simplicity is probably that way for good reason.

Anyway, the impetus of all this (over)thinking on my part is our current monthly target of the Wizard Nebula - a fairly small target that seemed like a good candidate for SHO. Except the OIII turned out to be particularly weak and not well separated, spatially, from the Ha. My integration is short and so has very poor SNR, but I took my Ha and SII early in the month and they seemed reasonable. Once my OIII filter finally arrived, well, it sure didn't pick up much. Other than a giant halo on a mag 5 star, but that's another story.

Irony of ironies considering your comments, I looked tonight and a fellow user had helpfully downloaded, modified, and uploaded a version of my posted test image after running some kind of de-purple/de-magenta process. Well, I did warn everyone that purple stars were coming. Probably figured I was upset about it.

[admin]

I'm actually pretty fine with "yucky" green, or purple, or magenta, even for stars, since I know what they mean in narrowband based on what I've set up ST to do. Thus, my bias throttling, almost always of Ha, is designed just to pull back that dominance, globally (correct?), in order to reveal the other emissions.

That's exactly how I prefer to process images too.
That's the thing; a light touch is all that is needed. There are just so many myths and misconceptions on how narrowband coloring works.

Honestly I can't dig up that post with the (to me) unusual multiplier and subtraction anymore, so just assuming it was some method to poke OIII through the Ha. Perhaps misplaced though, as to documentary value or maybe even effectiveness. The other I ran across (strange ~ symbols, channel multiplying like Ha*SII, and exponents!) I was actually able to dig up a source for, which was for "dynamic" narrowband combining. After reading through that I believe it is just more "art." As you imply, the transparent and tried-and-true simplicity is probably that way for good reason.

I have seen these too. Particularly multiplication and exponents (gamma correction) are incredibly misguided.

Irony of ironies considering your comments, I looked tonight and a fellow user had helpfully downloaded, modified, and uploaded a version of my posted test image after running some kind of de-purple/de-magenta process. Well, I did warn everyone that purple stars were coming. Probably figured I was upset about it.

Another one of those misconceptions; people tend to dislike purple stars because it is reminiscent of visual spectrum chromatic aberration found in cheap(er) achromats. Of course, the real reason is that stars emit relatively little in the Ha band versus the other bands...

[Mike in Rancho]

Uh oh. Well I'm not sure my channel throttling tends to be light touch.

Granted there must be a target element involved. This current target, the Wizard (which frankly I am tired of and so unlikely to amass more integration, even though I really need it) is even more Ha-dominant/OIII-weak than many other targets, which themselves are often Ha dominant. The OIII is there, just well-hidden. And of course it has the worst SNR and noise of the bunch, so emphasizing it relative to the Ha mucks up the whole image. But, the target is what the target is, so I won't resort to trickery.

I may look to upload the SHO files for linking, to see what anyone here might be able to make of them, and what a reasonable throttling would be such that a pretty but still legit info balance is achieved.

I've also been trying to think of the best ways to explain these images, colors, and any throttling that was utilized. Making a pure emission key from the mapping RGB as you described above could be one good part of that. But how to explain the global throttling?

Ivo, I believe you described the channel bias sliders before as a simple linear domain multiplier, for increase, or 1/x inverse, for reduce. Now also taking into account the possible normalization mentioned above. I'm wondering whether it makes a difference that the bias occurs in linear, rather than stretched after AutoDev? Simplest example: If my green (Ha) reduce was 2.0, it is thus linearly multiplied by 1/2 -- can I say that my final image has globally throttled the Hydrogen Alpha by 50% (or one-half) in order to reveal more relative OIII and SII? If the bias reduce was 3.0, then my throttling is to 1/3 (or in other words a reduction of 67%)? Or does the stretch throw that all out the window?