A Region-growing GradNormal Algorithm for Geometrically and Topologically Accurate Mesh Extraction

With the prevalence of implicit shape processing and reconstruction, extracting a polygonal mesh of an isosurface from volume data, which plays an important role in these tasks, is receiving more and more attention. GradNormal, a recently proposed marching tetrahedra method, can effectively extract high-quality meshes from analytic functional shapes but suffers from detail loss and computational inefficiency issues. In this paper, we improve GradNormal from four aspects. First, we extend GradNormal from an analytic function to an arbitrary geometric domain equipped with the projection operation. Second, we select a seed tetrahedron and find only the tetrahedra intersecting the implicit surface, in a region-growing style, which helps save memory and accelerate calculation. Third, we invent a hierarchical tiling mechanism to enhance the recovery accuracy of the resulting mesh, unlike the uniform tiling used in GradNormal. Finally, we propose to accurately predict how the underlying surface goes through a tetrahedral element so that complicated topological structures such as thin plates and gaps can be well captured. Extensive experimental results on challenging shapes show that the improved GradNormal is able to quickly produce a feature-adapted triangle mesh that is more topologically and geometrically accurate than the state-of-the-art.