It looks like the frame is no different in the back than many bikes not designed for cantilever brakes. You don't have a cable stop bridge between the rear seat stays, so you'd have to use a seat post-mounted cable hanger. Google for "seat post cable hanger" and you'll see examples of what you'd need for that. It appears that you have a cable stop on the non-drive side of the top tube, underneath. You'd need to run a length of outer housing from this cable stop to your seat post cable hanger to get the inner cable up and on top of the brake area, so it travels in a straight line down the center of the seat stay area.

Edit: it looks like BikeForums filters out Red Dit URLs. Google for "2012 giant escape r3" to see a picture of what I'm seeing.