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.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.