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14 April 2005 Automated 3D reconstruction of coronary artery tree based on stochastic branch and bound
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The paper discusses a new method for reconstructing vessel trees from biplane X-Ray projections. The used method reconstructs corresponding points in less than a second and is thus ideally suited for interventional procedures where time is essential. Biplane reconstruction is a two-fold problem: find corresponding points in both images and reconstruct the vessel segments between successive corresponding points in 3D. In this paper we solve the first problem using a new branch and bound technique based on Bayesian networks. With epipolar geometry we assign each of the vessel bifurcation/crossing/endpoint in one image a set of corresponding points in the second image. Starting with the vessel of largest diameter as root node we successively build up a tree of all possible solutions. Branches are cut according to probabilistic conditions (branch&bound based global search for the best solution). Each node is thus a possible partial tree for which we assign a conditional probability that the assignment of corresponding points is correct. The probability is the joint probability of having the correct topology, connectivity, tree and segment shape, characteristics of bifurcations. The respective probabilities for each bifurcation are measured from CTA data of real patients and the probability of the node is computed via a Bayesian network. If the assigned probability is too small, the branch is pruned. Further, for performance reasons we use A*-search where the most probable solution gets favored. All corresponding points are found in less then one second and both, topology and vessel crossings, are identified correctly. This method is thus by orders of magnitude faster than competing ones. This approach is therefore focused on both an automatic and robust method for 3D biplane reconstruction on one hand and an interactive method on the other hand. Further, it can be trained on a typical set of patients in order to obtain as reliable information as possible about the 3D vascular tree.
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Patrick Buhler, Philipp Rebholz, and Jurgen Hesser "Automated 3D reconstruction of coronary artery tree based on stochastic branch and bound", Proc. SPIE 5746, Medical Imaging 2005: Physiology, Function, and Structure from Medical Images, (14 April 2005);

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