  The relations between oxygen abundance and disk surface brightness (OH-SB
relation) in the infrared W1 band are examined for a nearby late-type galaxies.
The oxygen abundances were presented in Paper I. The photometric
characteristics of the disks are inferred here using photometric maps from the
literature through bulge-disk decomposition. We find evidence that the OH - SB
relation is not unique but depends on the galactocentric distance r (taken as a
fraction of the optical radius R_25) and on the properties of a galaxy: the
disk scale length h and the morphological T-type. The parametric OH - SB
relation reproduces the observed data better than a simple, one-parameter
relation; the deviations resulting when using our parametric relation are
smaller by a factor of ~1.4 than that the simple relation. The influence of the
parameters on the OH - SB relation varies with galactocentric distance. The
influence of the T-type on the OH - SB relation is negligible at the centers of
galaxies and increases with galactocentric distance. In contrast, the influence
of the disk scale length on the OH -- SB relation is maximum at the centers of
galaxies and decreases with galactocentric distance, disappearing at the
optical edges of galaxies. Two-dimensional relations can be used to reproduce
the observed data at the optical edges of the disks and at the centers of the
disks. The disk scale length should be used as a second parameter in the OH -
SB relation at the center of the disk while the morphological T-type should be
used as a second parameter in the relation at optical edge of the disk. The
general properties of the abundance - surface brightness relations are similar
for the three considered bands B, K, and W1.
