Maximizing Survey Volume for Large-Area Multi-Epoch Surveys with Voronoi
  Tessellation
  The survey volume of a proper motion-limited sample is typically much smaller
than a magnitude-limited sample. This is because of the noisy astrometric
measurements from detectors that are not dedicated for astrometric missions. In
order to apply an empirical completeness correction, existing works limit the
survey depth to the shallower parts of the sky that hamper the maximum
potential of a survey. The number of epoch of measurement is a discrete
quantity that cannot be interpolated across the projected plane of observation,
so that the survey properties change in discrete steps across the sky. This
work proposes a method to dissect the survey into small parts with Voronoi
tessellation using candidate objects as generating points, such that each part
defines a `mini-survey' that has its own properties. Coupling with a maximum
volume density estimator, the new method is demonstrated to be unbiased and
recovered {\sim}20% more objects than the existing method in a mock catalogue
of a white dwarf-only solar neighbourhood with Pan--STARRS 1-like
characteristics. Towards the end of this work, we demonstrate one way to
increase the tessellation resolution with artificial generating points, which
would be useful for analysis of rare objects with small number counts.
