  Generating computational anatomical models of cerebrovascular networks is
vital for improving clinical practice and understanding brain oxygen transport.
This is achieved by extracting graph-based representations based on pre-mapping
of vascular structures. Recent graphing methods can provide smooth vessels
trajectories and well-connected vascular topology. However, they require
water-tight surface meshes as inputs. Furthermore, adding vessels radii
information on their graph compartments restricts their alignment along
vascular centerlines. Here, we propose a novel graphing scheme that works with
relaxed input requirements and intrinsically captures vessel radii information.
The proposed approach is based on deforming geometric graphs constructed within
vascular boundaries. Under a laplacian optimization framework, we assign
affinity weights on the initial geometry that drives its iterative contraction
toward vessels centerlines. We present a mechanism to decimate graph structure
at each run and a convergence criterion to stop the process. A refinement
technique is then introduced to obtain final vascular models. Our
implementation is available on https://github.com/Damseh/VascularGraph. We
benchmarked our results with that obtained using other efficient and
stateof-the-art graphing schemes, validating on both synthetic and real
angiograms acquired with different imaging modalities. The experiments indicate
that the proposed scheme produces the lowest geometric and topological error
rates on various angiograms. Furthermore, it surpasses other techniques in
providing representative models that capture all anatomical aspects of vascular
structures.
