  We present an empirical relation between the cold gas surface density
($\Sigma_{\rm gas}$) and the optical extinction (${\rm A_V}$) in a sample of
103 galaxies from the Extragalactic Database for Galaxy Evolution (EDGE)
survey. This survey provides CARMA interferometric CO observations for 126
galaxies included in the Calar Alto Legacy Integral Field Area (CALIFA) survey.
The matched, spatially resolved nature of these data sets allows us to derive
the $\Sigma_{\rm gas}$-${\rm A_V}$ relation on global, radial, and kpc (spaxel)
scales. We determine ${\rm A_V}$ from the Balmer decrement
(H$\alpha$/H$\beta$). We find that the best fit for this relation is
$\Sigma_{\rm gas} ({\rm M_\odot pc^{-2}})\sim~26~\times~ {\rm A_V}({\rm mag})$,
and that it does not depend on the spatial scale used for the fit. However, the
scatter in the fits increases as we probe smaller spatial scales, reflecting
the complex relative spatial distributions of stars, gas, and dust. We
investigate the $\Sigma_{\rm gas}$/ ${\rm A_V}$ ratio on radial and spaxel
scales as a function of ${\rm EW(H\alpha)}$. We find that at larger values of
${\rm EW(H\alpha)}$ (i.e., actively star-forming regions) this ratio tend to
converge to the value expected for dust-star mixed geometries ($\sim$ 30
$\mathrm{M_{\odot} \,pc^{-2}\,mag^{-1}}$). On radial scales, we do not find a
significant relation between the $\Sigma_{\rm gas}$/${\rm A_V}$ ratio and the
ionized gas metallicity. We contrast our estimates of $\Sigma_{\rm gas}$ using
${\rm A_V}$ with compilations in the literature of the gas fraction on global
and radial scales as well as with well known scaling relations such as the
radial star-formation law and the $\Sigma_{\rm gas}$-$\Sigma_*$ relation. These
tests show that optical extinction is a reliable proxy for estimating
$\Sigma_{\rm gas}$ in the absence of direct sub/millimeter observations of the
cold gas.
