Cosine-Pruned Medial Axis: A New Method for Isometric Equivariant and Noise-Free Medial Axis Extraction

Abstract

We present the CPMA, a new method for medial axis pruning with noise robustness and equivariance to isometric transformations. The CPMA leverages the discrete cosine transform to create smooth versions of a shape $\Omega $ . We use the smooth shapes to compute a score function $\mathcal {F}_{\Omega }$ that filters out spurious branches from the medial axis of the original shape $\Omega $ . Our method generalizes to $n$ -dimensional shapes given the properties of the Discrete Cosine Transform. We extensively compare with state-of-the-art pruning methods to highlight the CPMA’s noise robustness and isometric equivariance. We conducted experiments using two 2D datasets — Kimia216 and Animal2000 — and one 3D dataset — the Groningen benchmark. We found that our pruning approach achieves competitive results and yields stable medial axes even in scenarios with significant contour perturbations.

Keywords

• Discrete cosine transform
• equivariance
• isometric transformation
• medial axis pruning
• morphological skeleton