  We reconsider the issue of localization in open-closed B-twisted
Landau-Ginzburg models with arbitrary Calabi-Yau target. Through careful
analsysis of zero-mode reduction, we show that the closed model allows for a
one-parameter family of localization pictures, which generalize the standard
residue representation. The parameter $\lambda$ which indexes these pictures
measures the area of worldsheets with $S^2$ topology, with the residue
representation obtained in the limit of small area. In the boundary sector, we
find a double family of such pictures, depending on parameters $\lambda$ and
$\mu$ which measure the area and boundary length of worldsheets with disk
topology. We show that setting $\mu=0$ and varying $\lambda$ interpolates
between the localization picture of the B-model with a noncompact target space
and a certain residue representation proposed recently. This gives a complete
derivation of the boundary residue formula, starting from the explicit
construction of the boundary coupling. We also show that the various
localization pictures are related by a semigroup of homotopy equivalences.
