Variational Pruning of Medial Axes of Planar Shapes

Peter (Linxuan) Rong, Tao Ju

Eurographics Symposium on Geometry Processing 2023

Abstract

Medial axis (MA) is a classical shape descriptor in graphics and vision. The practical utility of MA, however, is hampered by its sensitivity to boundary noise. To prune unwanted branches from MA, many definitions of significance measures over MA have been proposed. However, pruning MA using these measures often comes at the cost of shrinking desirable MA branches and losing shape features at fine scales. We propose a novel significance measure that addresses these shortcomings. Our measure is derived from a variational pruning process, where the goal is to find a connected subset of MA that includes as many points that are as parallel to the shape boundary as possible. We formulate our measure both in the continuous and discrete settings, and present an efficient algorithm on a discrete MA. We demonstrate on many examples that our measure is not only resistant to boundary noise but also excels over existing measures in preventing MA shrinking and recovering features across scales.

Figures

_{Figure 1: Comparing our proposed significance measure, Vanishing Angle (VA), with two other global measures on the Seahorse (left: measures on the MA; right: pruned MAs at increasing thresholds; thresholds for VA are 30◦,45◦,60◦). Our measure is as effective as other measures in removing unwanted branches but results in less shrinkage of MA (see boxed regions). Figure 2: Comparing various local (OA and Circumradius) and global (ET, CR and VR) significance measures (top) and their respective pruned MAs (bottom) on the Chicken (left). For local measures, an erosion heuristic is used [SBTZ02] to ensure topology preservation. Boxes highlight spurious branches (OA), missing branches (Circumradius), and shrunken ends (ET and CR) on the pruned MA. VA pruning threshold is 50◦}