  The structural network of the brain, or structural connectome, can be
represented by fiber bundles generated by a variety of tractography methods.
While such methods give qualitative insights into brain structure, there is
controversy over whether they can provide quantitative information, especially
at the population level. In order to enable population-level statistical
analysis of the structural connectome, we propose representing a connectome as
a Riemannian metric, which is a point on an infinite-dimensional manifold. We
equip this manifold with the Ebin metric, a natural metric structure for this
space, to get a Riemannian manifold along with its associated geometric
properties. We then use this Riemannian framework to apply object-oriented
statistical analysis to define an atlas as the Fr\'echet mean of a population
of Riemannian metrics. This formulation ties into the existing framework for
diffeomorphic construction of image atlases, allowing us to construct a
multimodal atlas by simultaneously integrating complementary white matter
structure details from DWMRI and cortical details from T1-weighted MRI. We
illustrate our framework with 2D data examples of connectome registration and
atlas formation. Finally, we build an example 3D multimodal atlas using T1
images and connectomes derived from diffusion tensors estimated from a subset
of subjects from the Human Connectome Project.
