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, $beta=2.03pm0.06$, 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 um{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.
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