[How do you make an image truly monochromatic, with no translucency?]

Great!  Thanks!

[How do you make an image truly monochromatic, with no translucency?]

I have various images that need to be made monochromatic (icons for an app).  The original image has anti-aliasing, so there are lots of translucent pixels on the borders of the lines.  It is very, very difficult to tell the difference visually between a pixel that is completely transparent and one that is 99% transparent.  The only values I can use for pixels in the image are #00000000 (completely transparent) and #FFFFFFFF (fully opaque white).  Any pixels of any other value causes the image to be rejected.

 

Is there any effect I can apply or process I can go through to make all pixels that are mostly transparent become completely transparent, while pixels above a threshold become completely opaque white?