How do I stop projector showing through surfaces?

I'm using a series of projectors to project render textures around my environment. It works great, except the projection displays on all surfaces it passes through, and not just the first it comes to (as a light would). How can I occlude the projections behind the first surface? Note that I can't simply choose to ignore those surfaces, since other projectors may need to use them.

My first thought was to take a depth texture from the point of the view of the projector and somehow use that to filter the projected texture, but not really sure if I'm going in the right direction with that... Any ideas?