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:

Blend mode	Commutativity	Formula	Addtl .info
Darken	commutative	R = min(Target,Blend)
Multiply	commutative	R = Target x Blend
Color Burn	non-commutative	R = 1 - (1-Target) / Blend
Linear Burn	commutative	R = Target + Blend - 1
Lighten	commutative	R = max(Target,Blend)
Screen	commutative	R = 1 - (1-Target) x (1-Blend)
Color Dodge	non-commutative	R = Target / (1-Blend)
Linear Dodge	commutative	R = Target + Blend
Overlay	non-commutative	if (Target > ½) R = 1 - (1-2x(Target-½)) x (1-Blend) if (Target <= ½) R = (2xTarget) x Blend	A combination of multiply and screen.Also the same as Hard Light commuted
Soft Light	non-commutative	if (Blend > ½) R = 1 - (1-Target) x (1-(Blend-½)) if (Blend <= ½) R = Target x (Blend+½)	A combination of multiply and screen(The formula is only approximate)
Hard Light	non-commutative	if (Blend > ½) R = 1 - (1-Target) x (1-2x(Blend-½)) if (Blend <= ½) R = Target x (2xBlend)	A combination of multiply and screen. Also the same as Overlay commuted
Vivid Light	non-commutative	if (Blend > ½) R = 1 - (1-Target) / (2x(Blend-½)) if (Blend <= ½) R = Target / (1-2xBlend)	A combination of color burn and color dodge
Linear Light	non-commutative	if (Blend > ½) R = Target + 2x(Blend-½) if (Blend <= ½) R = Target + 2xBlend - 1	A combination of linear burn and linear dodge
Pin Light	non-commutative	if (Blend > ½) R = max(Target,2x(Blend-½)) if (Blend <= ½) R = min(Target,2xBlend))	A combination of darken and lighten
Difference	commutative	R = \| Target - Blend \|
Exclusion	commutative	R = ½ - 2x(Target-½)x(Blend-½)

:: 2 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.

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Formulas for Photoshop blending modes

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