 # 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) * ((2*Target) * 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)

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

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