On the addition and comparison of graphs labeled with stochastic variables: Learnable anatomical catalogs

Research output: Contribution to journalArticle

Abstract

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.
Original languageEnglish
Pages (from-to)43-58
Number of pages16
JournalJournal of Combinatorial Optimization
Volume5
Issue number1
DOIs
Publication statusPublished - 1 Mar 2001

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Anatomy
Graph in graph theory
Operator
Continuous Variables
Dissimilarity
Vessel
Three-dimension
Branching
Model
X rays

Cite this

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abstract = "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.",
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