Anti-aliasing with fragment shaders and textures

I have a texture mapped object that I am putting through a fragment shader. The original texture mapped to the object is anti-aliased, but I think that the fragment shader only works on the pixel level. So in my case, if I have an anti-aliased line, half the pixel might be black and half of it white. My fragment shader should act on black pixels, but I only want to apply it to the part of the pixel that is actually black. Is that possible?

Textures do not have parts of texels. Textures don’t know if they’re “anti-aliased” or not. They’re just images. Half the texel can’t be black, because a texel can only be one color at a time. If the texel was created from half-black and half-white, it is now grey. And it doesn’t magically remember that it was created from half-black and half-white.

Unless you’re using a multisample texture, but accessing them requires texelFetch anyway.