  We present a continuous model for structural brain connectivity based on the
Poisson point process. The model treats each streamline curve in a tractography
as an observed event in connectome space, here a product space of cortical
white matter boundaries. We approximate the model parameter via kernel density
estimation. To deal with the heavy computational burden, we develop a fast
parameter estimation method by pre-computing associated Legendre products of
the data, leveraging properties of the spherical heat kernel. We show how our
approach can be used to assess the quality of cortical parcellations with
respect to connectivty. We further present empirical results that suggest the
discrete connectomes derived from our model have substantially higher
test-retest reliability compared to standard methods.
