Rule-Constrained Assignment for Cue-Ball Identification in Broadcast Snooker

Accurate cue-ball identification is essential for metric analysis of broadcast snooker. Existing systems evaluate each candidate independently against a fixed white prototype and reject candidates above an appearance threshold. Under broadcast conditions, illumination changes can make colored balls appear white, while intrusions from players and equipment can obscure the cue ball or introduce competing candidates. We formulate cue-ball identification as a rule-constrained assignment problem that jointly assigns detected candidates to the bounded snooker inventory: one cue ball, up to 15 reds, and six colors with known spots. The cue ball is selected by the incremental cost of assigning each candidate to the white slot, and the conventional appearance test follows as the one-slot case. On 419 hand-annotated shots, our method improves identity accuracy from 88.1% to 95.5%, and from 80.5% to 95.2% on held-out venues. Within CueLift, our metric state-recovery system, the assignment expands coverage from 36.2% to 55.4% over 6,241 scorable shots. Assigning an estimate to every shot in a separate evaluation on 2,529 shots preserves this advantage.