The filling-in theory of brightness perception has gained much attenti
on recently owing to the success of vision models. However, the theory
and its instantiations have suffered from incorrectly dealing with tr
ansitive brightness relations. This paper describes an advance in the
filling-in theory that overcomes the problem. The advance is incorpora
ted into the BCS/FCS neural network model, which allows it, for the fi
rst time, to account for all of Arend's test stimuli for assessing bri
ghtness perception models. The theory also suggests a new teleology fo
r parallel ON- and OFF-channels.