premultiplying

Premultiplying, or premultiplied alpha, is a technique used in digital image compositing in which the color channels are stored already multiplied by the alpha transparency. This contrasts with straight (unassociated) alpha, where the RGB channels are stored independently of the alpha value.

In a pixel with alpha A in the range [0, 1], the premultiplied color channels are R' = R × A, G' = G × A, and B' = B × A. The stored pixel is then represented as (R', G', B', A). When compositing a foreground (source) image over a background (destination), the typical equation with premultiplied colors is C_out = C_src + (1 − A_src) × C_dst and A_out = A_src + (1 − A_src) × A_dst. Because the source RGB values are already multiplied by its alpha, the blending operation requires fewer multiplications.

Conversions between representations are straightforward. To convert from straight to premultiplied, multiply the RGB channels by the alpha. To convert back, if A > 0, R = R'/A, G = G'/A, B = B'/A; if A == 0, the color can be set to zero. Storage may use 0–1 floating-point values or 0–255 integers; rounding in the integer case can introduce small color errors.

Formats and usage: premultiplied alpha is common in graphics pipelines, GPUs, and video compositing because it can simplify blending and reduce edge artifacts during filtering. Some image formats (or pipelines) store premultiplied data, while others store straight alpha and convert as needed. Users should be aware of the representation when performing edits or format conversions to avoid color distortions.