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.

A 3D fully parallel surface-thinning algorithm

“…As a result, the ''skeleton'' produced generally includes false segments that must be removed by a pruning step [43,44]. Note that incorporated regularization/pruning has also been proposed [40].…”

Image-based vessel-by-vessel analysis for red blood cell and plasma dynamics with automatic segmentation

“…First, artery and vein images were thinned in the longitudinal direction of the vessel tree. Then, the thinned vessels were segmented with a part-type segmentation method for articulated voxel shapes (Reniers et al, 2008) with modifications for two-dimensional images.…”

“…To determine the branching pattern of the vessel, a geodesicness measure (γ) was computed at each pixel on the vessel segments except for the junctions and endpoints (Reniers et al, 2008). For example, if the target segment vessels had a high geodesicness measure (e.g., γ = nearly 1), those vessels were judged as running in parallel to the vessel wall and thus defined as a single segment.…”

Patch‐type Segmentation of Voxel Shapes using Simplified Surface Skeletons

“…Section 2 presents related work. In Section 3, we discuss preliminaries, including the computation of multiscale skeletons [RVT08] which is a key component of our segmentation approach. In Section 4, we discuss the core of our approach.…”