Contracting Medial Surfaces Isotropically for Fast Extraction of Centred Curve Skeletons

Abstract

Curve skeletons, which are a compact representation for three‐dimensional shapes, must be extracted such that they are high quality, centred and smooth. However, the centredness measurements in existing methods are expensive, lowering the extraction efficiency. Although some methods trade quality for acceleration, their generated low‐quality skeletons are not suitable for applications. In this paper, we present a method to quickly extract centred curve skeletons. It operates by contracting the medial surface isotropically to the locus of the centres of its maximal inscribed spheres, which are spheres that have their centres on the medial surface and cannot be further enlarged while remaining the boundary of their intersections with the medial surface composed of only the points on the sphere surfaces. Thus, the centred curve skeleton can be extracted conveniently. For fast extraction, we develop novel measures to quickly generate the medial surface and contract it layer by layer, with every layer contracted isotropically using spheres of equal radii to account for every part of the medial surface boundary. The experimental results show that we can stably extract curve skeletons with higher centredness and at much higher speeds than existing methods, even for noisy shapes.

Out‐of‐core Extraction of Curve Skeletons for Large Volumetric Models

“…Hence, for generating centered curve skeletons, many methods attempt to contract the medial surface of a 3D shape to leverage the centrality of the medial surface. They extract curve skeletons by removing the boundary of medial surfaces layer by layer [LB07,ABS11,CB16], using local contraction operators with carefully controlled directions and speeds [TJ12, LW17, LW18], or performing significance measurements on the medial surface [DS06, RvWT08, JST16, YSC*16]. Unfortunately, as these methods adopt an outside‐in evolution scheme, they are unavoidably sensitive to boundary perturbations and generally require tedious manual parameter adjustment to prune noisy branches.…”

“…For quantitative comparison, we use three evaluation metrics: the center deviation (CD), the contraction error (CE), and the number of skeleton nodes (vertices). The center deviation proposed in [LW17] measures the centrality of the skeleton by the center deviation on the cross-sections at the skeleton nodes. A smaller center deviation value indicates better centrality of the obtained skeleton.…”

“…The growing data size poses great challenges in memory and efficiency for existing methods to extract curve skeletons. Since most existing methods extract the curve skeleton by contracting the shape [PK98, ATC*08, ClO*10, LHW*13, QHL*20] or contracting the medial surface for results with better centrality [LB07, CB16, LW17,LW18,JST16,YSC*16, LWC20, CWL22], the model or the medial surface must be allocated to the random access memory (RAM). This means that the size of models that existing methods can handle is limited by the amount of memory space available.…”