  Kirilov et al (2019) develop a metric, called Panoptic Quality (PQ), to
evaluate image segmentation methods. The metric is based on a confusion table,
and compares a predicted to a ground truth segmentation. The only non
straightforward part in this comparison is to align the segments in the two
segmentations. A metric only works well if that alignment is a partial
bijection. Kirilov et al (2019) list 3 desirable properties for a definition of
alignment: it should be simple, interpretable and effectively computable. There
are many definitions guaranteeing a partial bijection and these 3 properties.
We present the weakest: one that is both sufficient and necessary to guarantee
that the alignment is a partial bijection. This new condition is effectively
computable and natural. It simply says that the number of correctly predicted
elements (in image segmentation, the pixels) should be larger than the number
of missed, and larger than the number of spurious elements. This is strictly
weaker than the proposal in Kirilov et al (2019). In formulas, instead of |TP|>
|FN\textbar| + |FP|, the weaker condition requires that |TP|> |FN| and |TP| >
|FP|. We evaluate the new alignment condition theoretically and empirically.
