Multilevel Skeletonization Using Local Separators

TL;DR

A new, efficient algorithm for computing curve skeletons, based on local separators, which retains the high quality output, and applicability to any spatially embedded graph, while being orders of magnitude faster for all practical purposes.

Abstract

In this paper we give a new, efficient algorithm for computing curve skeletons, based on local separators. Our efficiency stems from a multilevel approach, where we solve small problems across levels of detail and combine these in order to quickly obtain a skeleton. We do this in a highly modular fashion, ensuring complete flexibility in adapting the algorithm for specific types of input or for otherwise targeting specific applications. Separator based skeletonization was first proposed by Bærentzen and Rotenberg in [ACM Tran. Graphics'21], showing high quality output at the cost of running times which become prohibitive for large inputs. Our new approach retains the high quality output, and applicability to any spatially embedded graph, while being orders of magnitude faster for all practical purposes. We test our skeletonization algorithm for efficiency and quality in practice, comparing it to local separator skeletonization on the University of Groningen Skeletonization Benchmark [Telea'16].

Figures (14)

• Figure 1: Shaded renders of triangle meshes and skeletons obtained by our algorithm.
• Figure 2: Visualisation of the three phases of the LSS algorithm. From left to right: A shaded render of the input, a number of computed minimal separators, a non-overlapping subset of the separators, and the resulting skeleton after extraction.
• Figure 3: Visualisation of the multilevel skeletonization approach. A solid cylinder with a handle is coarsened until it is of small size. A number of small local separators are found (shown in blue), and then projected back to the original input. Searching for small local separators again yields the separators around the handle (shown in red), but separators are too large at this level to be discovered around the cylinder. We combine the separators to obtain a general solution.
• Figure 4: A series of increasingly simplified approximations of neptune.ply, from the Groningen Skeletonization Benchmark, obtained through light edge matching contraction.
• Figure 5: A separator undergoing expansion as part of refinement. (A) shows an input, (B) a coarsened representation, (C) a computed separator denoted by red vertices, (D) the projected separator denoted by red vertices and the added vertices denoted by orange, (E) shows the separator obtained by minimising the thickened separator.