gimp layer mode arithmetic

dinasset · **Posted:** Tue Feb 26, 2013 5:19 am **(#1)**

GIMP Version: 2.8.4
Operating System: Windows
OS Version: Win 7 32 bits
GIMP Experience: Beginner Level

To all Gimp experts chatting here.
I would like to understand a little bit the arithmetic behind the Gimp layer mode.
This morning I had a kind of surprise playing with Gimp layer modes in this context:
1 - create a new image transparent
2 - add a new layer on top transparent
3 - drawing/painting/filling with a picture the top layer
Quite obviously the image was displaying the top layer.
At this point I wanted to play by changing the "normal" with each of the other available modes, and - big surprise for me - ONLY with normal or dissolve I was seeing the picture, in ALL other modes I saw a transparent image (even with: multiply, overlay, etc.).
Because it looked very strange for my (limited) understanding of arithmetic, I made a try with another photo editor, Paint Shop Pro and results are completely different, in the sense that with EACH mode I was seeing the image, except for dodge which gave a black screen and burn which gave a white screen.
Well, I know that each photo editor implements a different arithmetic on layer modes, but - let me say - at least if "something" is added or overlaid to "nothing" then "something" should appear!
Could somebody of you experts tell me something about this behaviour of our friend Gimp?
Many thanks!!!

molly · **Joined:** Apr 07, 2010 **Posts:** 14182

I didn't think layer modes worked with a transparent below the dupe. The layer mode has nothing below it to subtract or add from.

dinasset · **Posted:** Tue Feb 26, 2013 5:45 am **(#3)**

Molly, as I said above with a "normal" human arithmetic if you add "something" to "nothing" you SHOULD get "something"....

garagecoder · **Posted:** Tue Feb 26, 2013 5:57 am **(#4)**

A blend in maths terms isn't always an add though (e.g. multiply anything by zero and you will get zero), but it will depend mainly on how gimp treats the alpha layer during a blend - hopefully somebody can explain.

rich2005 · **Joined:** Mar 04, 2011 **Posts:** 2425

Is it not explained here?
http://docs.gimp.org/2.8/en/gimp-concep ... modes.html

eg.

dinasset · **Posted:** Tue Feb 26, 2013 6:09 am **(#6)**

Well, if Gimp uses "multiply" to "overlay", then the result is understandable (x * 0 = 0); does Gimp use a multiply mechanism wherever, also when adding for instance?

ofnuts · **Joined:** Oct 25, 2010 **Posts:** 4739

dinasset wrote:

Molly, as I said above with a "normal" human arithmetic if you add "something" to "nothing" you SHOULD get "something"....

"Nothing" is (0,0,0) and is black

"Normal" mode (and dissolve) replace the alpha channel of the stack of layers below them. But in other modes, the arithmetic is performed on the RGB channels but the transparency of the layer stack below the "mode'd" channel is retained, so if the layer is transparent, there is nothing to see.

garagecoder · **Posted:** Tue Feb 26, 2013 6:26 am **(#8)**

ofnuts wrote:

dinasset wrote:

Molly, as I said above with a "normal" human arithmetic if you add "something" to "nothing" you SHOULD get "something"....

"Nothing" is (0,0,0) and is black

"Normal" mode (and dissolve) replace the alpha channel of the stack of layers below them. But in other modes, the arithmetic is performed on the RGB channels but the transparency of the layer stack below the "mode'd" channel is retained, so if the layer is transparent, there is nothing to see.

Aha that explains it then

Ronounours · **Joined:** Jan 03, 2011 **Posts:** 1656

ofnuts is perfectly right.
Actually, most of the documentation available on the web to describe formulas of blending modes are missing this important point : what to do with the alpha-channels of each layer and how to compute the alpha-channel of the resulting (blended) image.

ofnuts · **Joined:** Oct 25, 2010 **Posts:** 4739

Ronounours wrote:

ofnuts is perfectly right.
Actually, most of the documentation available on the web to describe formulas of blending modes are missing this important point : what to do with the alpha-channels of each layer and how to compute the alpha-channel of the resulting (blended) image.

What I have not quite figured out yet is how the blend mode formula (that assumes full opacity) is adapted when the mod'ed layer is partially transparent. Everyone knows that playing with the opacity slider for that layer tunes the amount of the blend mode effect...

dinasset · **Posted:** Tue Feb 26, 2013 7:47 am **(#11)**

based on the given info I removed the alpha channel from the top layer and results are ALL completely different!
Thanks to ofnuts and all other experts here (a poor gimp-er needs a sort of a master in gimp-science to understand this behaviour ... well this is the reason why gimp-chat exist!...

Ronounours · **Joined:** Jan 03, 2011 **Posts:** 1656

ofnuts wrote:

What I have not quite figured out yet is how the blend mode formula (that assumes full opacity) is adapted when the mod'ed layer is partially transparent. Everyone knows that playing with the opacity slider for that layer tunes the amount of the blend mode effect...

From what I understood (and implemented), in this case the blending operation is actually decomposed into two steps :
- First, the computation of the blended image, according to the selected mode (assuming full opacity).
- Second, the computation of the alpha blending between the base layer and the blended layer. And in that case, it is well known how to get the resulting alpha-channel, when the two layers to composite have alpha-channels too (accrding to http://en.wikipedia.org/wiki/Alpha_compositing).

ofnuts · **Joined:** Oct 25, 2010 **Posts:** 4739

Ronounours wrote:

ofnuts wrote:

What I have not quite figured out yet is how the blend mode formula (that assumes full opacity) is adapted when the mod'ed layer is partially transparent. Everyone knows that playing with the opacity slider for that layer tunes the amount of the blend mode effect...

From what I understood (and implemented), in this case the blending operation is actually decomposed into two steps :
- First, the computation of the blended image, according to the selected mode (assuming full opacity).
- Second, the computation of the alpha blending between the base layer and the blended layer. And in that case, it is well known how to get the resulting alpha-channel, when the two layers to composite have alpha-channels too (accrding to http://en.wikipedia.org/wiki/Alpha_compositing).

I still don't get it. AFAIK in normal mode a layer is composited with the image resulting of the compositing of the stack below it. So if you have, bottom to top, A,B,C,D: A is composed with B:

Code: Select all

RGBA(AB) = AlphaCompose(RGBA(A),RGBA(B))

then AB with C:

Code: Select all

RGBA(ABC) = AlphaCompose(RGA(AB),RGBA(C))

No mystery here. I assume that the actual opacity of a pixel is the product of the alpha value of the pixels and the general opacity of the layer (as set on the Opacity slider).

So if we add a layer M in one of the blend modes, assuming full opacity of M we have:

Code: Select all

RGB(ABCM) = Blend(RGB(ABC),RGB(M))
Alpha(ABCM) = Alpha(ABC)

where Blend() is one of the formulas, and there is no compositing... so what happens when A(M) isn't 100%? Is there, at least conceptually:

Code: Select all

# compute RGB image assuming full opacity, as above
RGB(ABCM) = Blend(RGB(ABC),RGB(M))
# Compute alpha channel for that image
A(ABCM) = A(M)*A(ABC)
# Compute final by composing original with blended image
RGBA(Final)= AlphaCompose(RGBA(ABC),RGBA(ABCM))

How far off am I?

Odinbc · **Posted:** Fri Mar 08, 2013 7:00 pm **(#14)**

5.6 The Blending Modes info at Grokking the Gimp is always worth a look.

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