About straight and premultiplied channels

Practical advice for developers
(from DVD-HQ.info)

This section is aimed mainly at software developers, but regular users should read it too, because it shows how simple it is to deal with these issues from a programming point of view.

It might sound a bit self-righteous to write an article telling Photoshop's or 3dsmax's programmers how to do their job but... well, someone has to, because it's pretty obvious they aren't going to get it right by themselves (both are up to version 9, and are still lacking basic alpha channel conversion abilities).

First, here are the formulas to convert between matted and non-matted alpha. They can deal with any matte colour and are easy to implement for any colour depth and in any language. The variables used in the formulas are:

Cm = Component (matted)

Cu = Component (unmatted)

Cb = Component (background / matte colour)

a = Alpha

amax = Maximum possible alpha value (ex., 1.0)

All values are assumed to vary between 0.0 and 1.0 (for 8-bit files this would be 0-255 and for 16-bit files it would be 0-65535; remember to divide by the scale if you use anything other than 0.0-1.0).

To convert from unmatted alpha to matted alpha:

Cm = ( Cu ∙ a ) + [ Cb ∙ ( amax - a ) ]

To convert from matted alpha to straight (unmatted) alpha:

If a = 0, then Cu = Cm

Else, Cu = [ Cm - Cb ∙ ( amax - a ) ] / a

The formulas should be applied once to each colour component (ex.: R, G and B) of each pixel.

Those formulas are enough to add support for alpha channel conversion (with any matte colour) to any application. The software can then either cache a "working format" version of the image (generally meaning a straight-alpha version) or it can perform the conversion whenever it needs to read a pixel's colour channel values. There is really no excuse for not including this basic ability in a professional-level application.

The second issue is how to determine the kind of alpha channel used by a file that the user has just imported. One solution is to simply ask the user, but that's a pretty poor solution; users have more important things to worry about. So let's look at how software can determine the type of alpha channel and, if it turns out to be a matted alpha channel, how it can determine the background colour.

First we look for a pixel that is 100% transparent (0% opaque). If one exists, store its RGB values. Look for another pixel that is 100% transparent. Compare its RGB values with the ones previously stored. Repeat until the end of the file. If all pixels with 0% opacity have the same RGB values, it's almost guaranteed that that colour is the one used for the matte (if indeed there is a matte). If the colour varies, there's a good chance that we're looking at a straight-alpha file, or that the file uses some sort of really weird encoding (like the background bitmap example given above).

Now, even if all 100% transparent pixels have exactly the same colour, the file might still use "straight" alpha, so it's time to take the "background" RGB values we found above, plug them into the matted / unmatted conversion formulas and see if they make sense.

No pixel can have less of the matte colour in its RGB values than its alpha value would allow. For example, a colour channel in a pixel that is only 10% opaque cannot deviate more than 10% from the same channel of the matte colour.

If this condition isn't met by every pixel in the file, then there is no matte. If it is met by every pixel in the file, there's a very good chance that there is a matte, using the background colour we determined earlier.

There are other ways to make these decisions, some of which are simpler, faster, and will also get it right most of the time (for example, the program might analyse only a few pixels, rather than every pixel in the image).

Software should perform these tests when a file is first imported, and use the results to pre-fill the source format (or "footage interpretation") settings. This means that, in 99% of cases, the user will only need to click "ok".

If the tests are inconclusive (ex., because there are no transparent pixels in the file), then the software should ask the user to make the choice.

In any case, the user should always be given the option to toggle the type of alpha channel (between straight and matted), to pick the matte colour (manually or from the image) or to have the software "guess" the alpha channel type and matte colour again. These options should be available at any moment; not just when the file is first imported. If the software uses working proxies, a change of source format settings would cause the file to be re-imported.

(end of quote from DVD-HQ.info © Rui del-Negro 2008)