Geodesic voting methods: overview, extensions and application to blood vessel segmentation

This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae, and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand, or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. In this article we present new methods to segment thin tree structures, which are, for example, present in microglia extensions and cardiac or neuronal blood vessels. Many authors have used minimal cost paths, or geodesics relative to a local weighting potential P, to find a vessel pathway between two end points. We use a set of such geodesic paths to find a tubular tree structure with minimal interaction. Recently, we have introduced a set of methods called geodesic voting. In this article, we review all these methods and present some extensions. We also adapt these methods to the segmentation of complex tree structures in a noisy medium and apply them to the segmentation of blood vessels in 2D and 3D. 1. Introduction In this article we present novel methods for the segmentation of tree structures. These methods are based on minimal paths and can be applied to extract numerous structures, such as microglia extensions, neurovascular structures, blood vessels and pulmonary trees. There are many studies dedicated to the extraction of vascular or airway trees. For a review of such methods, see Kirbas and Quek (2004), Lesage et al. Among the approaches used to segment such tree structures, we consider the following three models, classified according to their method for extracting the tubular aspect of the tree: centreline-based models, surface models and 4D curve models. The first category focuses on directly extracting the centrelines of the tubular tree (Lorigo et al. 2001; Swift et al. 2002). After extracting the centrelines, a second process can be used to segment the lumen of the tree (see Bouix et al. 2005). The second category directly extracts the surface of the vessel. These approaches include explicit and implicit surface models. The former models …