  A simple optical to mid-IR color selection, R-[24] > 14, i.e. f_nu(24) /
f_nu(R) > 1000, identifies highly dust obscured galaxies (DOGs) with typical
redshifts of z~2 +/- 0.5. Extreme mid-IR luminosities (L_{IR} > 10^{12-14})
suggest that DOGs are powered by a combination of AGN and star formation,
possibly driven by mergers. In an effort to compare their photometric
properties with their rest frame optical morphologies, we obtained high spatial
resolution (0.05 -0.1") Keck Adaptive Optics (AO) K'-band images of 15 DOGs.
The images reveal a wide range of morphologies, including: small exponential
disks (8 of 15), small ellipticals (4 of 15), and unresolved sources (2 of 15).
One particularly diffuse source could not be classified because of low signal
to noise ratio. We find a statistically significant correlation between galaxy
concentration and mid-IR luminosity, with the most luminous DOGs exhibiting
higher concentration and smaller physical size. DOGs with high concentration
also tend to have spectral energy distributions (SEDs) suggestive of AGN
activity. Thus central AGN light may be biasing the morphologies of the more
luminous DOGs to higher concentration. Conversely, more diffuse DOGs tend to
show an SED shape suggestive of star formation. Two of fifteen in the sample
show multiple resolved components with separations of ~1 kpc, circumstantial
evidence for ongoing mergers.
