|You probably already know about 2D barcodes. Aren't they less alignment
|sensitive than the regular kind?

I don't know how the UPS "bullseye barcodes" work, but the PDF-814
barcodes which is used for the USPS's computer-printable postage (among
other things) is more sensitive to alignment than 1D barcodes.  With
the 1D barcodes, all that is required is for the sensor sweep to pass
through both ends of the code (and everything between) and if the code
is printed sufficiently tall it's possible to be 30+ degrees off and
still scan successfully (many supermarket scanners have three beams which
scan at 60-degree angles relative to each other so they can read any
barcode that's facing them regardless of orientation).  For PDF-814 codes
each "character" is 14 pixels long by three (identical) pixels high; to
and the scanner must see a character in its entirety to read it.

Note that it's not necessary for the beam to hit an entire row of char-
acters in a single pass; there are three sets of characters (with set 1
used on rows 0, 3, 6, etc.; set 2 used on rows 1, 4, 7, etc.; and set
3 used on rows 2, 5, 8, etc.) so the scanner can tell when the beam
crosses from one row to another; in addition the scanner can assemble
pieces of the code read on subsequent passes and can use ECC to fill in
any gaps.  As a result, it's usually not especially hard to make an item
scan with a PDF-814 barcode but it's not nearly as forgiving as, e.g.,
a UPC code.

That having been said, I think your best bets are either to have the
operator key in the Bingo balls or else digitize the TV picture (since
you already have a camera pointed at the ball) and the operator's going
to rotate the ball so it's visible to that camera).  Alternatively, if
the balls are placed on a grid after they're drawn (any ball on the grid
must have come from the cage regardless of keying errors, etc.) it may
be possible to simply have a switch in each of the 75 grid spots.