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To present an efficient and robust method for 3-D reconstruction of the coronary artery tree from multiple ECG-gated views of an X-ray angiography. 2-D coronary artery centerlines are extracted automatically from X-ray projection images using an enhanced multi-scale analysis. For the difficult data with low vessel contrast, a semi-automatic tool based on fast marching method is implemented to allow manual correction of automatically-extracted 2-D centerlines. First, we formulate the 3-D symbolic reconstruction of coronary arteries from multiple views as an energy minimization problem incorporating a soft epipolar line constraint and a smoothness term evaluated in 3-D. The proposed formulation results in the robustness of the reconstruction to the imperfectness in 2-D centerline extraction, as well as the reconstructed coronary artery tree being inherently smooth in 3-D. We further propose to solve the energy minimization problem using α-expansion moves of Graph Cuts, a powerful optimization technique that yields a local minimum in a strong sense at a relatively low computational complexity. We show experimental results on a synthetic coronary phantom, a porcine data set and 11 patient data sets. For the coronary phantom, results obtained using different number of views are presented. 3-D reconstruction error evaluated by the mean plus one standard deviation is below one millimeter when 4 or more views are used. For real data, reconstruction using 4 to 5 views and 256 depth labels averaged around 12 s on a computer with 2.13 GHz Intel Pentium M and achieves a mean 2-D back-projection error of 1.18 mm (ranging from 0.84 to 1.71 mm) in 12 cases. The accuracy for multi-view reconstruction of the coronary artery tree as reported from the phantom and patient studies is promising, and the efficiency is significantly improved compared to other approaches reported in the literature, which range from a few to tens of minutes. Visually good and smooth reconstruction is demonstrated.

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This paper addresses reconstruction of a temporally deforming 3D coronary vessel tree, i.e., 4D reconstruction from a sequence of angiographic X-ray images acquired by a rotating C-arm. Our algorithm starts from a 3D coronary tree that was reconstructed from images of one cardiac phase. Driven by gradient vector flow (GVF) fields, the method then estimates deformation such that projections of deformed models align with X-ray images of corresponding cardiac phases. To allow robust tracking of the coronary tree, the deformation estimation is regularized by smoothness and cyclic deformation constraints. Extensive qualitative and quantitative tests on clinical data sets suggest that our algorithm reconstructs accurate 4D coronary trees and regularized estimation significantly improves robustness. Our experiments also suggest that a hierarchy of deformation models with increasing complexities are desirable when input data are noisy or when the quality of the 3D model is low.