Blend modes

Multiply blend mode multiplies the RGB channel numbers for each pixel from the top layer with the values for the corresponding pixel from the bottom layer. The result is always a darker picture; since each value is less than 1, their product will be less than either of the initial values.

${\displaystyle f(a,b)=ab}$, where a is the base layer value and b is the top layer value.

This mode is commutative: exchanging two layers does not change the result. If the two layers contain the same picture, multiply blend mode is equivalent to a quadratic curve, or gamma correction with γ=2. For image editing it is sometimes more convenient to simply go to the Curves dialog of the software, as it gives more flexibility in the shape of the curves. Or one can use Levels dialogue — the middle number is usually 1/γ, so one can just type 0.5.

If one layer contains a homogeneous color, for example the gray color (0.8, 0.8, 0.8), multiply blend mode is equivalent to a curve which is simply a straight line. This is also equivalent to using this gray value as opacity when doing “normal mode” blend with black bottom layer.

With Screen blend mode the values of the pixels in the two layers are inverted, multiplied, and then inverted again. This yields the opposite effect to multiply, and results in a brighter picture.

${\displaystyle f(a,b)=1-(1-a)(1-b)}$, where a is the base layer value and b is the top layer value.

This mode is symmetric: exchanging two layers does not change the result. If one layer contains a homogeneous gray, Screen blend mode is equivalent to using this gray value as opacity when doing “normal mode” blend with white top layer.

• 
  Example top layer
• 
  Example bottom layer
• 
  Multiply blend mode applied to the two example layers
• 
  Screen blend mode applied to the two example layers

Overlay combines Multiply and Screen blend modes.[3] The parts of the top layer where the base layer is light become lighter, the parts where the base layer is dark become darker. Areas where the top layer are mid grey are unaffected. An overlay with the same picture looks like an S-curve.

${\displaystyle f(a,b)={\begin{cases}2ab,&{\mbox{if }}a<0.5\\1-2(1-a)(1-b),&{\mbox{otherwise}}\end{cases}}}$

where a is the base layer value and b is the top layer value.

Depending on the value a of the base layer, one gets a linear interpolation between black (a=0), the top layer (a=0.5), and white (a=1).

Hard Light is also a combination of Multiply and Screen. Hard Light affects the blend layer's relationship to the base layer in the same way Overlay affects the base layer's relationship to the blend layer. The inverse relationship between Overlay and Hard Light makes them "commuted blend modes".

Comparison of soft light blend modes

Soft light is most closely related to Overlay and is only similar to Hard Light by name. Applying pure black or white does not result in pure black or white.

There are a variety of different methods of applying a soft light blend.[4] All the flavors produce the same result when the top layer is pure black; same for when the top layer is pure neutral gray. The Photoshop and illusions.hu flavors also produce the same result when the top layer is pure white (the differences between these two are in how one interpolates between these 3 results).

These three results coincide with gamma correction of the bottom layer with γ=2 (for top black), unchanged bottom layer (or, what is the same, γ=1) (for top neutral gray), and γ=0.5 (for top white).

The formula used by Photoshop as of 2012 has a discontinuity of local contrast, and other formulas correct it. Photoshop's formula is:[5]

${\displaystyle f_{photoshop}(a,b)={\begin{cases}2ab+a^{2}(1-2b),&{\mbox{if }}b<0.5\\2a(1-b)+{\sqrt {a}}(2b-1),&{\mbox{otherwise}}\end{cases}}}$

where a is the base layer value and b is the top layer value. Depending on b, one gets a linear interpolation between three gamma corrections: γ=2 (for b=0), γ=1 (for b=0.5), and γ=0.5 (for b=1).

Pegtop's formula[5] is smoother and corrects the discontinuity at b = 0.5:

${\displaystyle f_{pegtop}(a,b)=(1-2b)a^{2}+2ba}$.

This is a linear interpolation between Multiply (for a=0) and Screen (for a=1) blend modes. It can also be seen as a linear interpolation between the gamma correction with γ=2 (for b=0), and a certain tonal curve (for b=1). (The latter curve is equivalent to applying γ=2 to the negative of image.)

A third formula defined by illusions.hu[6] corrects the discontinuity in a different way, doing gamma correction with γ depending on b:

${\displaystyle f_{illusions.hu}(a,b)=a^{(2^{2(0.5-b)})}}$

For b=0, one still gets γ=2, for b=0.5 one gets γ=1, for b=1 one gets γ=0.5, but it is not a linear interpolation between these 3 images.

The formula specified by recent W3C drafts[2] for SVG and Canvas is mathematically equivalent to the Photoshop formula with a small variation where b≥0.5 and a≤0.25:

${\displaystyle f_{w3c}(a,b)={\begin{cases}a-(1-2b)\cdot a\cdot (1-a)&{\text{if }}b\leq 0.5\\a+(2b-1)\cdot (g_{w3c}(a)-a)&{\text{otherwise}}\end{cases}}}$

where

${\displaystyle g_{w3c}(a)={\begin{cases}((16a-12)\cdot a+4)\cdot a&{\text{if }}a\leq 0.25\\{\sqrt {a}}&{\text{otherwise}}\end{cases}}}$.

This is also the formula used by Cairo,[7] and in earlier PDF documentation.[8]

It is still a linear interpolation between 3 images for b=0, 0.5, 1. But now the image for b=1 is not γ=0.5, but the result of a tonal curve which differs from the curve of γ=0.5 for small values of a: while gamma correction with γ=0.5 may increase the value of a many times, this new curve limits the increase of a by coefficient 4.

This blend mode simply divides pixel values of one layer with the other, but it's useful for brightening photos if the color is on grey or less. It is also useful for removing a color tint from a photo. If you create a layer that is the color of the tint you wish to remove - such as a pale blue, for scenes that are too cool in color temperature - Divide mode will return that color to white in the resulting composite, as any value divided by itself equals 1.0 (white).

This blend mode simply adds pixel values of one layer with the other. In case of values above 1 (in the case of RGB), white is displayed. "Linear Dodge" produces the same visual result. Since this always produces the same or lighter colors than the input it is also known as 'plus lighter'. A variant subtracts 1 from all end values, with values below 0 becoming black; this mode is known as 'plus darker'.

This blend mode simply subtracts pixel values of one layer with the other. In case of negative values, black is displayed.

Difference subtracts the bottom layer from the top layer or the other way round, to always get a non-negative value. Blending with black produces no change, as values for all colors are 0. (The RGB value for black is (0,0,0).) Blending with white inverts the picture.

One of the main utilities for this is during the editing process, when it can be used to verify alignment of pictures with similar content. Exclusion is a very similar blend mode with lower contrast.

Darken Only creates a pixel that retains the smallest components of the foreground and background pixels. If the foreground pixel has the components ${\displaystyle (r_{1},g_{1},b_{1})}$, and the background has ${\displaystyle (r_{2},g_{2},b_{2})}$, the resultant pixel is

${\displaystyle [\min(r_{1},r_{2}),\min(g_{1},g_{2}),\min(b_{1},b_{2})]}$ [9]

Lighten Only has the opposite action of Darken Only. It selects the maximum of each component from the foreground and background pixels. The mathematical expression for Lighten Only is

${\displaystyle [\max(r_{1},r_{2}),\max(g_{1},g_{2}),\max(b_{1},b_{2})]}$ [9]