Alpha Compositing - Description

Description

To store matte information, the concept of an alpha channel was introduced by Alvy Ray Smith in the late 1970s, and fully developed in a 1984 paper by Thomas Porter and Tom Duff. In a 2D image element, which stores a color for each pixel, additional data is stored in the alpha channel with a value between 0 and 1. A value of 0 means that the pixel does not have any coverage information and is transparent; i.e. there was no color contribution from any geometry because the geometry did not overlap this pixel. A value of 1 means that the pixel is opaque because the geometry completely overlapped the pixel.

If an alpha channel is used in an image, it is common to also multiply the color by the alpha value, to save on additional multiplications during compositing. This is usually referred to as premultiplied alpha.

Assuming that the pixel color is expressed using straight (non-premultiplied) RGBA tuples, a pixel value of (0.0, 0.5, 0.0, 0.5) implies a pixel which has 50% of the maximum green intensity and 50% opacity. If the color were fully green, its RGBA would be (0, 1, 0, 0.5).

However, if this pixel uses premultiplied alpha, all of the RGB values (0, 1, 0) are multiplied by 0.5 and then the alpha is appended to the end to yield (0, 0.5, 0, 0.5). In this case, the 0.5 value for the G channel actually indicates 100% green intensity (with 50% opacity). For this reason, knowing whether a file uses premultiplied or straight alpha is essential to correctly process or composite it.

Premultiplied alpha has some practical advantages over normal alpha blending because premultiplied alpha blending is associative and linear interpolation gives better results, although premultiplication can cause a loss of precision and, in extreme cases, a noticeable loss of quality.

With the existence of an alpha channel, it is possible to express compositing image operations, using a compositing algebra. For example, given two image elements A and B, the most common compositing operation is to combine the images such that A appears in the foreground and B appears in the background. This can be expressed as A over B. In addition to over, Porter and Duff defined the compositing operators in, held out by (usually abbreviated out), atop, and xor (and the reverse operators rover, rin, rout, and ratop) from a consideration of choices in blending the colors of two pixels when their coverage is, conceptually, overlaid orthogonally:

The over operator is, in effect, the normal painting operation (see Painter's algorithm). The in operator is the alpha compositing equivalent of clipping.

As an example, the over operator can be accomplished by applying the following formula to each pixel value:

where is the result of the operation, is the color of the pixel in element A, is the color of the pixel in element B, and and are the alpha of the pixels in elements A and B respectively. If it is assumed that all color values are premultiplied by their alpha values, we can rewrite the equation for output color as:

and resulting alpha channel value is

However, this operation may not be appropriate for all applications, since it is not associative. The associative version of this operation is very similar; simply take the newly computed color value and divide it by its new alpha value, as follows:

Image editing applications that allow merging of layers generally prefer this second approach.