Coronary vessel cores from 3D imagery: a topological approach

摘要

We propose a simple method for reconstructing thin, low-contrast blood vessels from three-dimensional greyscaleimages. Our algorithm first extracts persistent maxima of the intensity on all axis-aligned two-dimensionalslices through the input volume. Those maxima tend to concentrate along one-dimensional intensity ridges, inparticular along blood vessels. Persistence (which can be viewed as a measure of robustness of a local maximumwith respect to perturbations of the data) allows to filter out the ‘unimportant’ maxima due to noise or inaccuracyin the input volume. We then build a minimum forest based on the persistent maxima that uses edges of lengthsmaller than a certain threshold. Because of the distribution of the robust maxima, the structure of this forestalready reflects the structure of the blood vessels. We apply three simple geometric filters to the forest in orderto improve its quality. The first filter removes short branches from the forest’s trees. The second filter addsedges, longer than the edge length threshold used earlier, that join what appears (based on geometric criteria)to be pieces of the same blood vessel to the forest. Such disconnected pieces often result from non-uniformity ofcontrast along a blood vessel. Finally, we let the user select the tree of interest by clicking near its root (pointfrom which blood would flow out into the tree). We compute the blood flow direction assuming that the tree isof the correct structure and cut it in places where the vessel’s geometry would force the blood flow direction tochange abruptly.