Cosine-Pruned Medial Axis: A new method for isometric equivariant and noise-free medial axis extraction

TL;DR

The paper introduces CPMA, a novel medial axis pruning method that uses cosine transforms for noise robustness and isometric equivariance, providing stable and accurate medial axes even with contour noise.

Contribution

CPMA is a new medial axis pruning technique leveraging cosine transforms for noise robustness and isometric equivariance, improving stability and accuracy.

Findings

Achieves competitive results compared to state-of-the-art methods.

Provides stable medial axes under significant contour perturbations.

Demonstrates robustness to noise and transformations.

Abstract

We present the CPMA, a new method for medial axis pruning with noise robustness and equivariance to isometric transformations. Our method leverages the discrete cosine transform to create smooth versions of a shape $\Omega$. We use the smooth shapes to compute a score function $\scorefunction$ that filters out spurious branches from the medial axis. We extensively compare the CPMA with state-of-the-art pruning methods and highlight our method's noise robustness and isometric equivariance. We found that our pruning approach achieves competitive results and yields stable medial axes even in scenarios with significant contour perturbations.