Modeling the Topology of Cerebral Microvessels Via Geometric Graph Contraction

Studying the topology of cerebral microvessels has been shown to be essential for understanding the mechanisms underlying neurovascular coupling and brain microphysiology. One can derive topological models of these microvessels after labeling them based on their raw acquisitions from two-photon microscopy (TPM). However, adequate 3D mapping of cerebral microvasculature from TPM remains difficult due to the uneven intensities and shadowing effects. In this paper, we present a novel 2D/3D skeletonization solution to generate topological graph models of microvessels regardless of the quality of their binary maps. Our scheme first constructs a random initial graph encapsulated within the boundary of a binary mask. The vertices of the initial model are then iteratively contracted toward the centerline of microvessels by local connectivity-encoded gravitational forces. At each iteration, the model is decimated through vertices clustering and connectivity surgery processes. Lastly, a refinement algorithm is applied to convert the final decimated model into a curve skeleton. Synthetic angiograms and real TPM datasets are used for evaluation. By comparing against other efficient graphing schemes, we demonstrate that our solution performs better when applied to extract topological information from cerebral microvessel labels.