Abstract
The aim of this paper is to achieve the 3D reconstruction of blood vessels from a limited number of 2D transversal cuts obtained from scanners. This is motivated by the fact that data can be missing. The difficulty of this work is in connecting the blood vessels between some widely spaced cuts to produce the graph corresponding to the network of vessels. We identify the vessels on each transversal cut as a mass to be transported along a graph which allows to determine the bifurcation points of vessels. Specifically, we are interested in branching transportation Brasco et al. (SIAM J Math Anal 43(2):1023---1040, 2011) to model an optimized graph associated with the network of vessels. At this stage, we are able to reconstruct a 3D level set function by using the 2D level set functions given by the transversal cuts and the graph information. When the whole scanner data are available, a global reconstruction is proposed in a simple manner, without using the mass transfer problem.
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