  We present a new method to extract the three-dimensional electron density
profile and density compression ratio of shock fronts associated with Coronal
Mass Ejections (CMEs) observed in white light coronagraph images. We
demonstrate the method with two examples of fast halo CMEs ($\sim$ 2000 km
s$^{-1}$) observed on 2011 March 7 and 2014 February 25. Our method uses the
ellipsoid model to derive the three-dimensional (3D) geometry and kinematics of
the fronts. The density profiles of the sheaths are modeled with
double-Gaussian functions with four free parameters and the electrons are
distributed within thin shells behind the front. The modeled densities are
integrated along the lines of sight to be compared with the observed brightness
in COR2-A, and a $\chi^2$ approach is used to obtain the optimal parameters for
the Gaussian profiles. The upstream densities are obtained from both the
inversion of the brightness in a pre-event image and an empirical model. Then
the density ratio and Alfv\'{e}nic Mach number are derived. We find that the
density compression peaks around the CME nose, and decreases at larger position
angles. The behavior is consistent with a driven shock at the nose and a
freely-propagating shock wave at the CME flanks. Interestingly, we find that
the supercritical region extends over a large area of the shock and last longer
(several tens of minutes) than past reports. It follows that CME shocks are
capable of accelerating energetic particles in the corona over extended spatial
and temporal scales and are likely responsible for the wide longitudinal
distribution of these particles in the inner heliosphere. Our results also
demonstrate the power of multi-viewpoint coronagraphic observations and forward
modeling in remotely deriving key shock properties in an otherwise inaccessible
regime.
