High-quality consistent meshing of multi-label datasets

In this paper, we extend some recent provably correct Delaunay-based meshing algorithms to the case of multi-label partitions, so that they can be applied to the generation of high-quality geometric models from labeled medical datasets. Our approach enforces watertight surface meshes free of self-intersections, and outputs surface and volume meshes of the different tissues which are consistent with each other, including at multiple junctions. Moreover, the abstraction of the tissue partition into an oracle that, given a point in space, answers which tissue it belongs to, makes our approach applicable to virtually any combination of data sources. Finally, our approach offers extensive control over the size and shape of mesh elements, through customizable quality criteria on triangular facets and on tetrahedra, which can be tuned independently for the different anatomical structures. Our numerical experiments demonstrate the effectiveness and flexibility of our approach for generating high-quality surface and volume meshes from real multi-label medical datasets.