Skeleton Marching-based Parallel Vascular Geometry Reconstruction Using Implicit Functions

Fast high-precision patient-specific vascular tissue and geometric structure reconstruction is an essential task for vascular tissue engineering and computer-aided minimally invasive vascular disease diagnosis and surgery.In this paper,we present an effective vascular geometry reconstruction technique by representing a highly complicated geometric structure of a vascular system as an implicit function.By implicit geometric modelling,we are able to reduce the complexity and level of difficulty of this geometric reconstruction task and turn it into a parallel process of reconstructing a set of simple short tubular-like vascular sections,thanks to the easy-blending nature of implicit geometries on combining implicitly modelled geometric forms.The basic idea behind our technique is to consider this extremely difficult task as a process of team exploration of an unknown environment like a cave.Based on this idea,we developed a parallel vascular modelling technique,called Skeleton Marching,for fast vascular geometric reconstruction.With the proposed technique,we first extract the vascular skeleton system from a given volumetric medical image.A set of sub-regions of a volumetric image containing a vascular segment is then identified by marching along the extracted skeleton tree.A localised segmentation method is then applied to each of these sub-image blocks to extract a point cloud from the surface of the short simple blood vessel segment contained in the image block.These small point clouds are then fitted with a set of implicit surfaces in a parallel manner.A high-precision geometric vascular tree is then reconstructed by blending together these simple tubular-shaped implicit surfaces using the shape-preserving blending operations.Experimental results show the time required for reconstructing a vascular system can be greatly reduced by the proposed parallel technique.