Segmentation of lung vessel trees by global optimization Pieter Bruyninckx and Dirk Loeckx and Dirk Vandermeulen and Paul Suetens Medical Image Computing (ESAT/PSI), Faculty of Engineering, Katholieke Universiteit Leuven, University Hospital Gasthuisberg, Herestraat 49 bus 7003, B-3000 Leuven, Belgium ABSTRACT We present a novel method for lung vessel tree segmentation. The method combines image information and a high-level physiological model, stating that the vasculature is organized such that the whole organ is perfused using minimal effort. The method consists of three consecutive steps. First, a limited set of possible bifurcation locations is determined. Subsequently, individual vessel segments of varying diameters are constructed between each two bifurcation locations. This way, a graph is constructed consisting of each bifurcation location candidate as vertices and vessel segments as edges. Finally, the overall vessel tree is found by selecting the subset of these segments that perfuses the whole organ, while minimizing an energy function. This energy function contains a data term, a volume term and a bifurcation term. The data term measures how well the selected vessel segments fit to the image data, the volume term measures the total amount of blood in the vasculature, and the bifurcation term models the physiological fit of the diameters of the in- and outgoing vessels in each bifurcation. The selection of the optimal subset of vessel segments into a single vessel tree is an NP-hard combinatorial optimization problem that is solved here with an ant colony optimization approach. The bifurcation detection as well as the segmentation method have been validated on lung CT images with manually segmented arteries and veins. Keywords: Segmentation, Lung vessels, tree like structure, global optimization, ant colony optimization 1. INTRODUCTION Vessel trees in the liver and the lungs are fractal like structures that minimize a certain energy while delivering blood to the whole organ. 1–3 Murray was the first to analytically derive the rules that apply to a bifurcation that delivers blood in the most efficient way from one source to multiple target locations. Given a certain radius for the incoming vessel, this resulted in minimizing the total volume of all vessel segments while the radii of the vessel segments obey a certain rule, which is also known as Murray’s law. This law has been confirmed later on, by analyzing the amount, radius and depth of the vessels in the small intestine of a dog. 4 This physiological knowledge has already successfully been applied to generate in silico phantoms using constrained constructive optimization, a technique that iteratively adds branches to the tree while minimizing the local energy of the newly created subtree. 5–7 The segmentation of lung vessel trees is a challenging problem, because these vessels are complex branch- ing structures, that consist of an intertwining arterial and venous tree. The main application for lung vessel segmentation is the diagnosis of pulmonary embolism, which is a common pathology for which treatment signif- icantly improves the patient’s health. 8 The segmentation of lung vessel trees is also useful for minimizing the amount of false positives when performing nodule detection. Also the separation of the arteries and the veins, which is a side-effect of the segmentation, is useful to help the radiologist by accelerating the reading and image interpretation process. Moreover the resulting trees can be used to separate the different lung lobes. At first sight the segmentation of tree like structures seems to be an extension of the segmentation of individual vessels, for which numerous algorithms exist. 9 A classic approach to find a vessel between two locations is by applying a minimum cost path (MCP) algorithm. Li et al. have proposed such a method that also incorporates the radius of the vessel, which results in an elegant method that delivers an accurate centerline as well as the radius of the vessel. 10 For any segmentation problem it is important to have an adequate model of the structure Corresponding author: Pieter.Bruyninckx@uz.kuleuven.ac.be Medical Imaging 2009: Image Processing, edited by Josien P. W. Pluim, Benoit M. Dawant, Proc. of SPIE Vol. 7259, 725912 · © 2009 SPIE CCC code: 1605-7422/09/$18 · doi: 10.1117/12.811570 Proc. of SPIE Vol. 7259 725912-1