Variational Pruning of Medial Axes of Planar Shapes

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.

Automated summary

The medial axis (MA) is a well-known shape descriptor in graphics and vision, but it is sensitive to boundary noise. Existing significance measures for pruning MA often lead to the shrinking of desired branches and the loss of fine-scale shape features. We propose a novel significance measure derived from a variational pruning process, which aims to preserve points parallel to the shape boundary. Our measure is formulated in both continuous and discrete settings, and an efficient algorithm is presented for the discrete MA. Experimental results show that our measure is resistant to boundary noise, prevents MA shrinking, and recovers features across scales.