  Functional magnetic resonance imaging (fMRI) functional connectivity between
brain regions is often computed using parcellations defined by functional or
structural atlases. Typically, some kind of voxel averaging is performed to
obtain a single temporal correlation estimate per region pair. However, several
estimators can be defined for this task, with various assumptions and degrees
of robustness to local noise, global noise, and region size.
  In this paper, we systematically present and study the properties of 9
different functional connectivity estimators taking into account the spatial
structure of fMRI data, based on a simple fMRI data spatial model. These
include 3 existing estimators and 6 novel estimators. We demonstrate the
empirical properties of the estimators using synthetic, animal, and human data,
in terms of graph structure, repeatability and reproducibility,
discriminability, dependence on region size, as well as local and global noise
robustness.
  We prove analytically the link between regional intra-correlation and
inter-region correlation, and show that the choice of estimator has a strong
influence on inter-correlation values.
