Recovering the HII region size statistics from 21-cm tomography
  We introduce a novel technique, called "granulometry", to characterize and
recover the mean size and the size distribution of HII regions from 21-cm
tomography. The technique is easy to implement, but places the previously not
very well defined concept of morphology on a firm mathematical foundation. The
size distribution of the cold spots in 21-cm tomography can be used as a direct
tracer of the underlying probability distribution of HII region sizes. We
explore the capability of the method using large-scale reionization simulations
and mock observational data cubes while considering capabilities of SKA1-low
and a future extension to SKA2. We show that the technique allows the recovery
of the HII region size distribution with a moderate signal-to-noise ratio from
wide-field imaging ($\rm SNR\lesssim3$), for which the statistical uncertainty
is sample variance dominated. We address the observational requirements on the
angular resolution, the field-of-view, and the thermal noise limit for a
successful measurement. To achieve a full scientific return from 21-cm
tomography and to exploit a synergy with 21-cm power spectra, we suggest an
observing strategy using wide-field imaging (several tens of square degrees) by
an interferometric mosaicking/multi-beam observation with additional
intermediate baselines (~2-4 km).
