[cairo] Compositing strategies and pre-multiplied alpha

Bill Spitzak spitzak at d2.com
Thu Sep 22 14:45:31 PDT 2005

Mauricio Piacentini wrote:
> I need some help understanding the rationale behind using pre-multiplied
> alpha in a graphics API, and I understand this is used in Cairo image 
> surfaces, according to the docs.

If you were not premultiplying, compositing color C over B with alpha a 
would be done with "Ca+B(1-a)".

In premultiplied images, the C pixel is replaced with A = Ca and the 
math is changed to "A+B(1-a)". Substituting Ca for A will show that this 
is identical.

So mathematically there is no difference.

Advantages of premultiplied:

1. This is what almost all rendering and painting programs produce. 
Correctly producing a non-premultiplied image would require tracking a 
"coverage" for each pixel that is seperate from the "transparency". 
Premultiplied allows you to combine these values very early.

2. Premultiplied images look correct when the rgb channels are viewed. 
Non-premultiplied images will have noisy and bright pixels at any 
antialiased edges.

3. Premultipled images are more convienent for other operations such as 
adding to simulate a double exposure.

4. Premultiplied images allow "glow" where the color is greater than the 

5. Premultiplied over is available on Windows.

Advantages of non-premultiplied:

1. Supposedly this is what .png files are supposed to be, but everybody 
appears to be ignoring that.

2. The compositied result is always in the range 0-1, with no clamping 

3. An 8-bit image can antialias any 8-bit color accurately. A 
premultiplied image with 1/4 alpha, if added 4 times to get an opaque 
image, will only have 64 possible colors in 8 bits. This advantage is 
negated, however, because most implementations do not preserve 
intermediate results of more than 8 bits, thus the non-premultiplied 
version produces the same result.

I believe Cairo can do non-premultiplied, by setting the source pattern 
and the mask to the same image, then doing a copy operation. So you 
actually have both anyway.

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