On the Addition and Comparison of Graphs Labeled with Stochastic Variables: Learnable Anatomical Catalogs

We provide an operator for the addition of a pair of graphs, labeled with continuous variables which are subject to stochastic variation. We also provide an operator for measuring dissimilarity between a pair of such graphs. We use such a representation and operators to model a collection of vascular anatomy which accounts for inter-individual variations in both branching structure and in vessel shape. The model may be incrementally acquired, and is thus a catalog of anatomy whose content may be learned. The model may be used in applications such as the reconstruction of vasculature in three-dimensions from x-ray images, which we briefly outline.