Topology-graph Directed Separating Boundary Surfaces Approximation of Nonmanifold Neuroanatomical Structures: Application to Mouse Brain Olfactory Bulb

Boundary surface approximation of 3-D neuroanatomical regions from sparse 2-D images (e.g., mouse brain olfactory bulb structures from a 2-D brain atlas) has proven to be difficult due to the presence of abutting, shared boundary surfaces that are not handled by traditional boundary-representation data structures and surfaces-from-contours algorithms. We describe a data structure and an algorithm to reconstruct separating surfaces among multiple regions from sparse cross-sectional contours. We define a topology graph for each region, that describes the topological skeleton of the region´s boundary surface and that shows between which contours the surface patches should be generated. We provide a graph-directed triangulation algorithm to reconstruct surface patches between contours. We combine our graph-directed triangulation algorithm together with a piecewise parametric curve fitting technique to ensure that abutting or shared surface patches are precisely coincident. We show that our method overcomes limitations in 1) traditional contours-from-surfaces algorithms that assume binary, not multiple, regionalization of space, and in 2) few existing separating surfaces algorithms that assume conversion of input into a regular volumetric grid, which is not possible with sparse interplanar resolution.