Reconstructing vascular skeletons from x-ray angiograms

In this paper we present an approach for 3D reconstruction of vascular skeletons from x-ray angiograms at arbitrary angles. The key to this problem is solving the correspondence problem; that is, determine a mapping between points in each image pair. This paper describes, in some detail, the two main steps in our approach: (1) we determine vessels that correspond between images to obtain a `coarse grained' solution that acts to focus our next step; (2) we determine the correspondence between points in corresponding vessels, this gives a `fine grained' solution enabling the 3D shape of the vessel to be computed. We use a model of a collection of vasculature during the first step, use the second step relies only on general assumptions about space- curves. There are several novelties: images can be at arbitrary angles; generalization from the collection to include new vasculature; and weak dependence on the kind of image data. Results show the approach is efficient in time and space, accurate and reliable, and robust to noise.