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Formulas for Photoshop blending modes

Posted: April 21st, 2010

Do you want to apply one of the Photoshop blending modes to two images but using a PixelMath-like tool? Here's a list of the current Photoshop blending modes and their equivalent PixelMath formula that I could find. While some of the formulas are precisely what Photoshop does, others are just an approximated guess. Also, blending modes that cannot be achieved by a straight PixelMath operation - such as Luminosity, Hue or Color - are excluded.

The formulas below assume the pixels in the image have a numeric range between 0 and 1, which is the default in PixInsight

In most cases, in order to mimic Photoshop's behavior, the option "Rescaled" in PixInsight's PixelMath should be checked, particularly those modes that could generate out-of-range values. Some other times, it doesn't matter, such as in the Darken and Lighten modes.

Blend mode	Commutativity	Formula	Addtl .info
Darken	commutative	min(Target,Blend)
Multiply	commutative	Target * Blend
Color Burn	non-commutative	1 - (1-Target) / Blend
Linear Burn	commutative	Target + Blend - 1
Lighten	commutative	max(Target,Blend)
Screen	commutative	1 - (1-Target) * (1-Blend)
Color Dodge	non-commutative	Target / (1-Blend)
Linear Dodge	commutative	Target + Blend
Overlay	non-commutative	(Target > 0.5) * (1 - (1-2(Target-0.5)) (1-Blend)) + (Target <= 0.5) * ((2Target) Blend)	A combination of multiply and screen.Also the same as Hard Light commuted
Soft Light	non-commutative	(Blend > 0.5) * (1 - (1-Target) * (1-(Blend-0.5))) + (Blend <= 0.5) * (Target * (Blend+0.5))	A combination of multiply and screen(The formula is only approximate)
Hard Light	non-commutative	(Blend > 0.5) * (1 - (1-Target) * (1-2(Blend-0.5))) + (Blend <= 0.5) (Target * (2*Blend))	A combination of multiply and screen. Also the same as Overlay commuted
Vivid Light	non-commutative	(Blend > 0.5) * (1 - (1-Target) / (2(Blend-0.5))) + (Blend <= 0.5) (Target / (1-2*Blend))	A combination of color burn and color dodge
Linear Light	non-commutative	(Blend > 0.5) * (Target + 2(Blend-0.5)) + (Blend <= 0.5) (Target + 2*Blend - 1)	A combination of linear burn and linear dodge
Pin Light	non-commutative	(Blend > 0.5) * (max(Target,2(Blend-0.5))) + (Blend <= 0.5) (min(Target,2*Blend)))	A combination of darken and lighten
Difference	commutative	\| Target - Blend \|
Exclusion	commutative	0.5 - 2(Target-0.5)(Blend-0.5)

:: 7 Comments

Comments

david (Contact, Page), February 23rd, 2011, 9:33

I tried the 'overlay' method in pixelmath, and even substituting '*' for 'x', and 0.5 for 1/2 it throws an error!

RBA (Contact, Page), February 23rd, 2011, 23:32

David, I should've made clear that the expressions aren't meant to be entered exactly as I indicated. Each software may have a different syntax depending on their particular PixelMath implementation.

For PixInsight, it would be something like this:

(($T > 0.5) * 1 - (1-2*($T-0.5)) * (1-BI)) ($T <= 0.5) * (2*$T) * BI

Where BI is the blending image.
Also note that all the expressions that use "if..." are approximate.

PSpeed42 (Contact, Page), February 3rd, 2014, 16:17

Hi, your chart is very useful.

However, I think that the Exclusion equation may not be correct. If I manually plug values into it then I get different results than one photoshop is displaying.

On the other hand, I've had good results with:
(source*(1-dest)) (dest*(1-source))

Hope it helps.

Royi (Contact, Page), May 16th, 2014, 5:19

They have some different math:
http://www.simplefilter.de/en/basics/mixmods.html

I'm wondering which Linear Light is more close to Photoshop's.

RBA (Contact, Page), May 16th, 2014, 18:14

Hello Royi,
You can always apply each of the formulas and calculate differences.

Sage (Contact, Page), May 23rd, 2014, 18:16

Royi, they are same. If you open brackets, you'll find out that condition is redudant.

Rob (Contact, Page), August 12th, 2014, 20:49

Thanks for this Site and this page of Formulas. A Links-Page would be a useful addition, Astrophotography is such an interesting subject.

Here is a Page of Workflows for Image Processing you may find helpful.

http://www.astrosurf.com/re/process.html

Thanks,
Rob

Low Light Videos
https://www.youtube.com/user/LowLightVideos

RBA (Contact, Page), August 31st, 2014, 11:12

Thank you Rob. On a side note, the processing workflow in the Astrosurf page you mentioned is a bit "old fashioned".

oyster (Contact, Page), April 10th, 2015, 3:23

as for Linear Light, your charts says "(Blend > 0.5) * (Target 2*(Blend-0.5))
(Blend

Vi (Contact, Page), August 14th, 2017, 12:31

The two Linear Light calculations mentioned in the comments are equivalent. In fact, the calculation shown in this page is unnecessary complicated, because Target 2*(Blend-0.5) is the same as Target 2*Blend -1. No case distinction necessary.

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