  Gamma-ray observations ranging from hundreds of MeV to tens of TeV are a
valuable tool for studying particle acceleration and diffusion within our
galaxy. Supernova remnants, pulsar wind nebulae, and star-forming regions are
the main particle accelerators in our local Galaxy. Constructing a coherent
physical picture of these astrophysical objects requires the ability to
distinguish extended regions of gamma-ray emission, the ability to analyze
small-scale spatial variation within these regions, and methods to synthesize
data from multiple observatories across multiple wavebands. Imaging Atmospheric
Cherenkov Telescopes (IACTs) provide fine angular resolution (<0.1 degree) for
gamma-rays above 100 GeV. Typical data reduction methods rely on source-free
regions in the field of view to estimate cosmic-ray background. This presents
difficulties for sources with unknown extent or those which encompass a large
portion of the IACT field of view (3.5 degrees for VERITAS).
Maximum-likelihood-based techniques are well-suited for analysis of fields with
multiple overlapping sources, diffuse background components, and combining data
from multiple observatories. Such methods also offer an alternative approach to
estimating the IACT cosmic-ray background and consequently an enhanced
sensitivity to largely extended sources. In this proceeding, we report on the
current status and performance of a maximum likelihood technique for the IACT
VERITAS. In particular, we focus on how our method framework employs a
dimension for gamma-hadron separation parameters in order to improve
sensitivity on extended sources.
