Flat, concave, convex, doesn't matter. All exactly the same swept volume. Have a close look at my diagram, imagine this is the shape made in the bore by the piston as it travels the length of its stroke. It is more easily thought about from the bottom of the stroke rising up. It is accurately measured with oil while the piston is at BDC. Then at TDC the remaining space is measured and minused to give the volume which is displaced by the piston in its upward travel. Compression ratio is just how much in volume is crammed into how little a space. Now this is affected by piston shape, but displacement is not.
EDIT- The three shapes I drew are just an example of three totally different cylinders (even though they're only 2d), which do you think has the greater volume?