"Connectability" matters too: completion theories need to be complete.

Kogo and Wagemans provide an intriguing way of assigning a polarity value to closed edges in fragmented images (solving the border ownership problem), but their model lacks generality and disregards connectability as a relevant aspect of visual completion. The lack of generality depends on considering concave disk sectors (pacmen) as the main inducers of illusory contours. Connectability is crucial for defining the occurrence, the salience and the shape of completed contours. A complete theory of completion should integrate border ownership and connectability, rather than emphasizing one aspect over the other.