An Adaptive Hierarchical Approach to the Extraction of High Resolution Medial Surfaces

Abstract

We introduce a novel algorithm for medial surfaces extraction that is based on the density-corrected Hamiltonian analysis [20]. The approach extracts the skeleton directly from a triangulated mesh and adopts an adaptive octreebased approach in which only skeletal voxels are refined to a lower level of the hierarchy, resulting in robust and accurate skeletons at extremely high resolution. The quality of the extracted medial surfaces is confirmed by an extensive set of experiments.

An Unified Multiscale Framework for Planar, Surface, and Curve Skeletonization

“…Torsello and Rossi extend the TH density advection to extract 3D medial surfaces [54]. In their model, density advection stops when reaching the surface skeleton.…”

“…Torsello and Hancock correct this for a more accurate 2D skeleton detection by a momentum conservation principle ∇ · (ρ∇DT ∂ Ω ) = 0, where ρ is the mass density on the evolving boundary ∂ Ω [5]. Rossi and Torsello extend this idea to compute 3D surface skeletons [54]. However, this method does not compute curve skeletons and does not model the curve-surface skeleton relationship.…”

Feature preserving noise removal for binary voxel volumes using 3D surface skeletons

“…Advection method: Several methods compute 3D skeletons by contracting the surface ∂ in a vector field v that simulates advection of uniformly-spread mass from ∂ following a momentum conservation principle [54,65] . We use here the field v proposed in [54] , which has the desirable properties of being tangent to the skeleton surface and pointing towards its core.…”

Computing refined skeletal features from medial point clouds

“…Thinning is simple and fast, but can be sensitive to rigid Euclidean transformations. Field methods find S along singularities of DT ∂ or related fields [17,20,23,39,40,43,53] and can be efficiently implemented on GPUs [6,49] . Mesh methods use a surface sampling of ∂ only, which is cheaper and faster than the volumetric sampling of used by field and thinning methods.…”