Variational Pruning of Medial Axes of Planar Shapes

Rong, Peter; Ju, Tao

Variational Pruning of Medial Axes of Planar Shapes

Files

v42i5_06_14902.pdf (6.53 MB)

Date

2023

Authors

Rong, Peter
Ju, Tao

Publisher

The Eurographics Association and John Wiley & Sons Ltd.

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.

CCS Concepts: Computing methodologies -> Shape analysis

        @article{10.1111:cgf.14902
,
journal = {Computer Graphics Forum},
title = {{Variational Pruning of Medial Axes of Planar Shapes
}},
author = {Rong, Peter and 
Ju, Tao
},
year = {2023
},
publisher = {The Eurographics Association and John Wiley & Sons Ltd.
},
ISSN = {1467-8659
},
DOI = {10.1111/cgf.14902
}
}