GIMP Version: 2.8.4
Operating System: Windows
GIMP Experience: Beginner Level

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How could I know the algorithms for the blending modes in GIMP per pixel?

For example, if we discuss the "normal" blending mode. Here is what the help says:

"
Normal mode is the default layer mode. The layer on top covers the layers below it. If you want to see anything below the top layer when you use this mode, the layer must have some transparent areas.

The equation is:

Equation 8.2. Equation for layer mode “Normal”

E = M
"

I have made a test image with 1x1 size. I am testing with two layers. The end result per channel seems to be some sort of interpolation that depends on the alpha values of the layers, and it is not quite as simple as the above equation says. I usually want to understand what is happening when I am doing something, so it would be nice to know what is the real magic behind the scenes.

See this article for more information.
http://gimp-savvy.com/BOOK/index.html?node55.html

The entire HTML book tarball download link -
http://gimp-savvy.com/BOOK/TarDist/Grok ... 1.0.tar.gz

Thanks. Unfortunately, however, the article does not cover the information I am after, if I understood correctly.

For example, let's say that I have these layers:

Foreground: (Normal blending) R: 0 / G: 1 / B: 0 / A: 0.49
Background: (Normal blending) R: 0 / G: 0 / B: 1 / A: 0.84
Result: R: 0 / G: 0.54 / B: 0.46 / A: 0.92

The result is a mystery for me.

usually the background layer remain in normal mode at 100% opacity, are the layer(s) above that may have different mode and opacity.

I suppose is not a rule but vary mode and opacity of the BG layer doesn't seems give good result and for sure made the result less easy to predict ... if you modify BG transparency there is nothing behind that may transpare

About the formula were a couple of discussions in the gmic group on flickr on merging mode , with links to the sources of algorithms used.

Gmic may be more interesting because has more modes supported, instead gimp has still a couple of serius bugs in the color modes (mainly "Soft Light" and "Overlay" give always the identical result but where also discussion on the color mode, compared with the PS color mode )

The equations that are given in the GIMP Users Manual presume an opacity of 100% for the pixels of both layers. The resulting pixel's value, taking into account opacity(or alpha), is the linear interpolation between the lower layer (I) and the result of the given formula.

So for Normal mode, the actual equation is E= α*M + (1-α)*I . Where α is the opacity of the pixel (normalized to fall within the range 0..1).

For Hard Light, where the given equation is E=(2*M*I)/256 for when M's value is < 128, the actual equation is E=(α*2*M*I)/256 + (1-α)*I . When M's value is >128, the formula is E=α*(255 - ((255-I)*(255-(2*(M-128))))/256) + (1-α)*I .

Thanks saulgoode, this seems to be what I am looking for.

Does this equation concern the calculation of a color channel? If so, is 'a' the alpha channel value of the upper or lower layer, or of the end result?

According to my calculations, the result pixel's alpha channel value seems to be: resultA = upperA + (1 - upperA) * lowerA. (values being 0-1, not 0-255)

My test calculations with what results gimp gives me are not matching the equation. Could you possibly give me an example with values, using for example the green channel in the example of post #3, please? I would like to understand this.

5.6 The Blending Modes at Grokking the Gimp is not exactly what your looking for but does contain useful information on the topic.

Yes and in practice is needed to be able to modify the opacity of the layer above and that make the calculation more complex .

But from your example on merging the channels i believe you want modify also the opacity and mode of the BG layer and that in most of cases doesn't make much sense and anyway add even more complexities to the calculation :

I believe without much good reasons because i can't see reasons to modify mode and transparency of the BG layer , merging mode is almost meaningless for the BG layer because , as example Lighten Only, Darken Only, Multiply, all are supposed to be used with a layer below and have no any sense with nothing below, that is always the case for the BG layer that for definition has no layer below it

Gimp uses the standard algorithm: http://en.wikipedia.org/wiki/Alpha_compositing

However, if I understand correctly a couple of exchanges I have seen on the developer's list, it all depends whether you are working in direct light on in gamma-corrected light. As I understand it, 8-bit Gimp always work in gamma-corrected light(*), so what really happens is that the RGB value are gamma-uncorrected to go back to direct light, then the compositing is computed, and then the gamma-correction is applied on the result, so you don't get exactly what the straightforward computation gives you. If you need more info there is a full source tarball awaiting you

(*) IIRC the discussion was about the possibility to drop the gamma-correction when working in high-precision in the future versions.

Thanks. This should help me understand the issue.

PhotoComix: Yeah, I think the lower layer's blend mode does not affect it, unless there are layers underneath that.

In practice affect a lot (you may try and see ) but creates only problems

It happened to me, by changing layers position to move as BG layer one with low opacity and different mode and never that had interesting effect ,
merge suppose something BELOW to be merged with , if there is nothing as always in case of the BG layer is even possible presume for usability (and/or to no crash the programs with impossible calculation when moving layers ) a imaginary layer filled with transparency , white or the BG color below the BG layer