Modeling and hexahedral meshing of arterial networks from centerlines

Computational fluid dynamics (CFD) simulation provides valuable information on blood flow from the vascular geometry. However, it requires to extract accurate models of arteries from low resolution medical images, which remains challenging. Centerline-based representation is widely used to model large vascular networks with small vessels, as it enables manual editing and encodes the topological information. In this work, we propose an automatic method to generate an hexahedral mesh suitable for CFD directly from centerlines. The proposed method is an improvement of the state-of-the-art in terms of robustness, mesh quality and reproductibility. Both the modeling and meshing tasks are addressed. A new vessel model based on penalized splines is proposed to overcome the limitations inherent to the centerline representation, such as noise and sparsity. Bifurcations are reconstructed using a physiologically accurate parametric model that we extended to planar n-furcations. Finally, a volume mesh with structured, hexahedral and flow oriented cells is produced from the proposed vascular network model. The proposed method offers a better robustness and mesh quality than the state-of-the-art methods. As it combines both modeling and meshing techniques, it can be applied to edit the geometry and topology of vascular models effortlessly to study the impact on hemodynamics. We demonstrate the efficiency of our method by entirely meshing a dataset of 60 cerebral vascular networks. 92\% of the vessels and 83\% of the bifurcations where mesh without defects needing manual intervention, despite the challenging aspect of the input data. The source code will be released publicly.

Efficient Decomposition of Image and Mesh Graphs by Lifted Multicuts

Formulations of the Image Decomposition Problem as a Multicut Problem (MP) w.r.t. a superpixel graph have received considerable attention. In contrast, instances of the MP w.r.t. a pixel grid graph have received little attention, firstly, because the MP is NP-hard and instances w.r.t. a pixel grid graph are hard to solve in practice, and, secondly, due to the lack of long-range terms in the objective function of the MP. We propose a generalization of the MP with long-range terms (LMP). We design and implement two efficient algorithms (primal feasible heuristics) for the MP and LMP which allow us to study instances of both problems w.r.t. the pixel grid graphs of the images in the BSDS-500 benchmark. The decompositions we obtain do not differ significantly from the state of the art, suggesting that the LMP is a competitive formulation of the Image Decomposition Problem. To demonstrate the generality of the LMP, we apply it also to the Mesh Decomposition Problem posed by the Princeton benchmark, obtaining state-of-the-art decompositions.