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29 April 2005 Coronary vessel cores from 3D imagery: a topological approach
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We propose a simple method for reconstructing thin, low-contrast blood vessels from three-dimensional greyscale images. Our algorithm first extracts persistent maxima of the intensity on all axis-aligned two-dimensional slices through the input volume. Those maxima tend to concentrate along one-dimensional intensity ridges, in particular along blood vessels. Persistence (which can be viewed as a measure of robustness of a local maximum with respect to perturbations of the data) allows to filter out the `unimportant' maxima due to noise or inaccuracy in the input volume. We then build a minimum forest based on the persistent maxima that uses edges of length smaller than a certain threshold. Because of the distribution of the robust maxima, the structure of this forest already reflects the structure of the blood vessels. We apply three simple geometric filters to the forest in order to improve its quality. The first filter removes short branches from the forest's trees. The second filter adds edges, 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 of contrast along a blood vessel. Finally, we let the user select the tree of interest by clicking near its root (point from which blood would flow out into the tree). We compute the blood flow direction assuming that the tree is of the correct structure and cut it in places where the vessel's geometry would force the blood flow direction to change abruptly. Experiments on clinical CT scans show that our technique can be a useful tool for segmentation of thin and low contrast blood vessels. In particular, we successfully applied it to extract coronary arteries from heart CT scans. Volumetric 3D models of blood vessels can be obtained from the graph described above by adaptive thresholding.
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Andrzej Szymczak, Allen Tannenbaum, and Konstantin Mischaikow "Coronary vessel cores from 3D imagery: a topological approach", Proc. SPIE 5747, Medical Imaging 2005: Image Processing, (29 April 2005);

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