Vessel geometry modeling and segmentation using convolution surfaces and an implicit medial axis

In the context of vessel tree structures segmentation with implicit deformable models, we propose to exploit convolution surfaces to introduce a novel variational formulation, robust to bifurcations, tangential vessels and aneurysms. Vessels are represented by an implicit function resulting from the convolution of the centerlines of the vessels, modeled as a second implicit function, with localized kernels of continuously-varying scales. The advantages of this coupled representation are twofold. First, it allows for a joint determination of the vessels centerlines and radii, with a single model relevant for segmentation and visualization tasks. Second, it allows us to define a new shape constraint on the implicit function representing the centerlines, to enforce the tubular shape of the segmented objects. The algorithm has been evaluated on the segmentation of the portal veins in 20 CT-scans of the liver from the 3D-IRCADb-01 database, achieving an average recovery of 73% of the trees with fast computational times.