  We exploit ionization-parameter mapping as a powerful tool to measure the
optical depth of star-forming HII regions. Our simulations using the
photoionization code CLOUDY and our new, SURFBRIGHT surface brightness
simulator demonstrate that this technique can directly diagnose most
density-bounded, optically thin nebulae using spatially resolved emission line
data. We apply this method to the Large and Small Magellanic Clouds, using the
data from the Magellanic Clouds Emission Line Survey. We generate new HII
region catalogs based on photoionization criteria set by the observed
ionization structure in the [SII]/[OIII] ratio and Ha surface brightness. The
luminosity functions from these catalogs generally agree with those from
Ha-only surveys. We then use ionization-parameter mapping to crudely classify
all the nebulae into optically thick vs optically thin categories, yielding
fundamental new insights into Lyman continuum radiation transfer. We find that
in both galaxies, the frequency of optically thin objects correlates with Ha
luminosity, and that the numbers of these objects dominate above log L\geq37.0.
The frequencies of optically thin objects are 40% and 33% in the LMC and SMC,
respectively. Similarly, the frequency of optically thick regions correlates
with H I column density, with optically thin objects dominating at the lowest
N(HI). The integrated escape luminosity of ionizing radiation is dominated by
the largest regions, and corresponds to luminosity-weighted, ionizing escape
fractions from the H II region population of \geq0.42 and \geq0.40 in the LMC
and SMC, respectively. These values correspond to global galactic escape
fractions of 4% and 11%, respectively. This is sufficient to power the
ionization rate of the observed diffuse ionized gas in both galaxies. Our
results suggest the possibility of significant galactic escape fractions of
Lyman continuum radiation.
