Computing Multiscale Curve and Surface Skeletons of Genus 0 Shapes Using a Global Importance Measure

Abstract

We present a practical algorithm for computing robust, multiscale curve and surface skeletons of 3D objects. Based on a model which follows an advection principle, we assign to each point on the skeleton a part of the object surface, called the collapse. The size of the collapse is used as a uniform importance measure for the curve and surface skeleton, so that both can be simplified by imposing a single threshold on this intuitive measure. The simplified skeletons are connected by default, without special precautions, due to the monotonicity of the importance measure. The skeletons possess additional desirable properties: They are centered, robust to noise, hierarchical, and provide a natural skeleton-to-boundary mapping. We present a voxel-based algorithm that is straightforward to implement and simple to use. We illustrate our method on several realistic 3D objects.

MoleView: An Attribute and Structure-Based Semantic Lens for Large Element-Based Plots

“…12 shows a 3D skeleton, or medial axis, of a cow model. The skeleton is computed using the voxel-based method in [21]. Skeleton voxels are colored with their socalled importance with a blue-to-red rainbow colormap.…”

“…Skeleton importance can be used to simplify the object by pruning away less im- portant points. The skeletonization method in [21] conjectures, but does not rigorously prove or disprove, that the importance of skeleton points varies smoothly over small, connected, areas of the skeleton. We use our dual-layout lens to investigate this hypothesis.…”

Extended grassfire transform on medial axes of 2D shapes

“…measures have been proposed for identifying portions of the medial axis that depict prominent shape features, in 2D [15] and 3D [17], which can be classified into local or global ones [14,16]. Local measures rate a medial axis point by the boundary geometry in its immediate neighborhood, such as the angle formed by the medial axis point and its two closest boundary points [2,7,17,9] or the Euclidean distance between the two boundary points [1,6].…”

“…Ogniewicz and Ilg proposed several global measures with explicit mathematical definitions, which are based on measuring the length between the closest boundary points over the boundary curve (Potential Residue (PR)) [12]. The PR measure has been extended to evaluate 3D surface skeletons using lengths of geodesic curves on surfaces [5,14], and even further to evaluate 3D curve skeletons using approximated areas of geodesic patches [14].…”

Interactive skeletonization of intensity volumes

“…1(c) is generated from an inappropriate segmentation (b) using morphological thinning, which maintains the (noisy) topological structure of the segmentation. While methods that explicitly consider surface noise during skeletonization have been proposed [22], their results are still biased by the choice of the initial binary segmentation.…”