Characterizing Protoclusters and Protogroups at z $\sim$ 2.5 Using
  Ly$\alpha$ Tomography
  Ly-$\alpha$ tomography surveys have begun to produce three-dimensional (3D)
maps of the intergalactic medium (IGM) opacity at $z \sim 2.5$ with Mpc
resolution. These surveys provide an exciting new way to discover and
characterize high-redshift overdensities, including the progenitors of today's
massive groups and clusters of galaxies, known as protogroups and
protoclusters. We use the IllustrisTNG-$300$ hydrodynamical simulation to build
mock maps that realistically mimic those observed in the Ly-$\alpha$
Tomographic IMACS Survey (LATIS). We introduce a novel method for delineating
the boundaries of structures detected in 3D Ly-$\alpha$ flux maps by applying
the watershed algorithm. We provide estimators for the dark matter masses of
these structures (at $z\sim2.5$), their descendant halo masses at $z=0$, and
the corresponding uncertainties. We also investigate the completeness of this
method for the detection of protogroups and protoclusters. Compared to earlier
work, we apply and characterize our method over a wider mass range that extends
to massive protogroups. We also assess the widely used fluctuating
Gunn-Peterson approximation (FGPA) applied to dark-matter-only simulations; we
conclude while it is adequate for estimating the Ly-$\alpha$ absorption signal
from moderate-to-massive protoclusters ($ \gtrsim 10^{14.2} M_{\odot}$), it
artificially merges a minority of lower-mass structures with more massive
neighbors. Our methods will be applied to current and future
Ly-$\alpha$~tomography surveys to create catalogs of overdensities and study
environment-dependent galaxy evolution in the Cosmic~Noon~era.
