Painting marble?

[trenthamfamily.livejournal.com]

Is it possible to paint marble slabs? I have these ugly brown marble slabs that make up my shower and bathtub and countertop. It's swirled with tan... I don't like it. Anyways, instead of replacing the entire thing couldn't I lightly sand down the top to roughen it up a bit and then paint and seal it with something that could still let me use the shower and bathtub?

I imagine there has to be something out there. I'd like to get creative with the stencils and colors out there too.