If you're ok with helping the computer out a bit, you could put a very small matrix bar code (think QR Code) on top of each piece. Since there are 6 chess pieces and 2 colors, you could have a code for each piece in just a 2x2 matrix (4 dots / bits).
Otherwise, it seems like it may be very difficult, as I'm not even sure of what some of the black on black pieces are myself (bottom right).
If you want only to modify the chessmen and not the board then I'm sure some transponder could be fitted and the table could have 3 receivers removably fixed to it that could triangulate their positions.
If it has to be camera based but you're going to modify them men could you just give them all different coloured hats.
It make me think it would be easier to recognize a domino game than a chessboard!
The other option, although a magnitude harder, would be to take two (or maybe three) images from a lower angle on two different sides and use that to determine the silhouette of the pieces.