A General Solution of the Monge–Kantorovich Mass-Transfer Problem

Guerra, Pedro Jiménez; Rodrı́guez-Salinas, Baltasar

doi:10.1006/jmaa.1996.0330

Cited by 6 publications

(2 citation statements)

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“…The graph will be chosen as an optimal graph of an optimization problem to define. This formalism is known as the MongeKantorovich problem [10]. Let us give two measures µ and ν on two successive transversal cuts X and Y of R 2 , these measures are finite sums of atomic measures located on the centers of vessels:…”

Section: Construction Of Geometry Graph (G)mentioning

confidence: 99%

“…The second step deals with the graph construction which is developped in section 2. The construction of such a graph is based on a mass transfer problem called Monge-Kantorovich problem [10], by optimizing the cost of the transport of blood along the net of vessels. The mass of transport associated to blood flow, is evaluated with the surface of vessels on cuts.…”

Section: Introductionmentioning

confidence: 99%

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3D Reconstruction of blood vessels

Moussawi

Galusinski

Nguyen

2014

Engineering with Computers

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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 to connect the blood vessels between some widely spaced cuts in order 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 mass transfer problem Monge-Kantorovich [10] to model an optimized graph associated to 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 scanners data are available, a global reconstruction is proposed in a simple manner, without using the mass transfer problem.

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Section: Construction Of Geometry Graph (G)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%