Render out pixels on edge of mesh

I have a procedural mesh with a material. I would like to render out a pixel if more than half its “area” is over the edge of the procedural mesh. If less than half its area is over the edge, I want to draw the full pixel.

Here is an image that shows my current situation:


Note how pixels get cut off along the procedural mesh. I would like them to either be fully drawn or not there at all. Are there any options/strategies I could try?