Assume we composite image B with opacity alphaB over image A with opacity alphaA, there’re two ways of calculating the alpha channel:

• Non-premultiplied alpha
• Premultiplied alpha

Non-premultiplied alpha

Composite Color:

• C = alphaB * B + (1 - alphaB) * alphaA * A

  where alphaB represents the appearance of semi-transparent B, and (1 - alphaB) represents what B lets through

Composite Alpha:

• alphaC = alphaB + (1 - alphaB) * alphaA

Premultiplied alpha

Premultiplied alpha means multiplying color by alpha first, and then compositing, where

• A’ = alphaA * (Ar, Ag, Ab, 1)

• B’ = alphaB * (Br, Bg, Bb, 1)

• C’ = B’ + (1 - alphaB) * A’

Final Color:

• C = C’ / alphaC’

Advantages of premultiplied alpha

1. Compositing operation treats all channels the same (color and a)
2. Fewer arithmetic operations for “over” operation
3. Closed under composition (repeated “over” operations)
4. Better representation for filtering (upsampling/downsampling) images with alpha channel
5. Fits naturally into rasterization pipeline (as homogeneous coordinates)

Closed: if taking two elements of the set and applying the operation on them always yields an element within that set

OpenGL Examples

Most Common:

glEnable(GL_BLEND);
glBlendFunc(GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA);

With premultiplied alpha

glBlendFunc(GL_ONE, GL_ONE_MINUS_SRC_ALPHA);