# 3-D reconstruction of the coronary artery tree from multiple views of a rotational X-ray angiography

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## Abstract

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.

## Keywords

X-ray angiography 3-D reconstruction Coronary arteries Cardio-vascular disease Energy minimization Graph-cuts optimization## Notes

### Acknowledgments

The authors are thankful to Dr. Chenyang Xu, Dr. Guenter Lauritsch and Dr. Jan Boese for their generous support and enlightening discussions on this project, and are thankful to Prof. Patrick Serruys and Prof. Johannes Brachmann for providing the data in this study.

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