  We present an extinction map of the inner $\sim$\SI{15}{\arcminute} by
{16}{\arcminute} of the Galactic Center (GC) with map `pixels' measuring
\SI{5}{\arcsecond} $\times$ \SI{5}{\arcsecond} using integrated light color
measurements in the near- and mid-infrared. We use a variant of the
Rayleigh-Jeans Color Excess (RJCE) method first described by Majewski et al.
(2011) as the basis of our work, although we have approached our problem with a
Bayesian mindset and dispensed with point-source photometry in favor of surface
photometry, turning the challenge of the extremely crowded field at the GC into
an advantage. Our results show that extinction at the GC is not inconsistent
with a single power law coefficient, $\beta=2.03\pm0.06$, and compare our
results with those using the Red Clump (RC) point-source photometry method of
extinction estimation. We find that our measurement of $\beta$ and its apparent
lack of spatial variation are in agreement with prior studies, despite the
bimodal distribution of values in our extinction map at the GC with peaks at
\num{5} and \SI{7.5}{mag}. This bimodal nature of extinction is likely due to
the InfraRed Dark Clouds that obscure portions of the inner GC field. We
present our extinction law and map and de-reddened NIR CMDs and color-color
diagram of the GC region using the point-source catalog of IR sources compiled
by DeWitt et al. (2010). The de-reddening is limited by the error in the
extinction measurement (typically \SI{0.6}{mag}), which is affected by the size
of our map pixels and is not fine-grained enough to separate out the multiple
stellar populations present toward the GC.
