hal-01002127
https://univ-tln.hal.science/hal-01002127
https://univ-tln.hal.science/hal-01002127/document
https://univ-tln.hal.science/hal-01002127/file/papier.pdf
doi:10.1007/s00366-014-0398-3
[UNIV-TLN] Université de Toulon
[INSMI] CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions
[IMATH] Institut de mathématiques de Toulon
[TDS-MACS] Réseau de recherche en Théorie des Systèmes Distribués, Modélisation, Analyse et Contrôle des Systèmes
[ANR] ANR
3D Reconstruction of Blood Vessels
Al Moussawi, Ali
Galusinski, Cedric
Nguyen, Christian
[MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA]
[MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP]
ART
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 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.
2014-12-14
2014-06-05
en
Engineering with computers