coverage to alpha

[Eric Muller]

    On the one hand, we have a coverage map, i.e. for each pixel how
    much of it is covered by the outline.
    
    On the other hand, we are blending a foreground (text) color with a
    background color. So we need some alpha, and use it for a linear
    blending, in a linear colorspace.
    
    What is not clear to me is how to go from coverage to alpha.
    Identity is plausible, but there are also reasons to believe it is
    not:
    
    - things like White's
      illusion show that the perception works in strange ways
    
    - "One usually begins by assuming that nothing is known about the
    object world and then the diffraction limit outlines the range of
    object details that an image transfer allows to be gained and, by
    exclusion, those that it leaves undetermined. On the other hand, it
    might be known ahead of time that the ensemble of possible objects
    is restricted. Then distinctions can be made by concentrating on the
    expected differences and disregarding image aspects that might have
    arisen from sources known beforehand to be absent." (Optical
      superresolution and visual hyperacuity, Westheimer), which can
    explain how readers can perceive gray pixels differently (i.e.
    expecting black and white, and therefore perceiving gray as width)
    
    - may be the alpha should also depend on the foreground/background
    color
    
    - may be the alpha should also depend on the ppem. 
    
    I have not found much in the literature. Opinions, pointers? 
    
    Thanks,
    Eric.