This picture was taken in the SLAC 82-inch bubble chamber, filled with deuterium and exposed to a 12 GeV/c beam of positive kaons, .
The key feature that identifies the anti-omega is the neutral decaying particle (vee) to the left of the picture which is shown by measurement to come from the early decay of a charged particle (kink).
The vee is an anti-lambda which is recognizable because the anti-proton annihilates producing a characteristic 'star’.
After measurement, the whole event was uniquely fitted to the following hypothesis:
The original paper claims (click here) that only one of the lambda's decay in the bubble chamber. (One is left wondering about the vee at the top of the picture!)