Reconstruction of coronary artery centrelines from x-ray rotational angiography using a probabilistic mixture model

Three-dimensional reconstructions of coronary arterial trees from X-ray rotational angiography (RA) images have the potential to compensate the limitations of RA due to projective imaging. Most of the existing model based reconstruction algorithms are either based on forward-projection of a 3D deformable model onto X-ray angiography images or back-projection of 2D information extracted from X-ray angiography images to 3D space for further processing. All of these methods have their shortcomings such as dependency on accurate 2D centerline segmentations. In this paper, the reconstruction is approached from a novel perspective, and is formulated as a probabilistic reconstruction method based on mixture model (MM) representation of point sets describing the coronary arteries. Specifically, it is assumed that the coronary arteries could be represented by a set of 3D points, whose spatial locations denote the Gaussian components in the MM. Additionally, an extra uniform distribution is incorporated in the mixture model to accommodate outliers (noise, over-segmentation etc.) in the 2D centerline segmentations. Treating the given 2D centreline segmentations as data points generated from MM, the 3D means, isotropic variance, and mixture weights of the Gaussian components are estimated by maximizing a likelihood function. Initial results from a phantom study show that the proposed method is able to handle outliers in 2D centreline segmentations, which indicates the potential of our formulation. Preliminary reconstruction results in the clinical data are also presented.