Cosine-Pruned Medial Axis: A new method for isometric equivariant and noise-free medial axis extraction
This method addresses the problem of extracting stable and noise-free medial axes for shape analysis, which is relevant for computer vision and graphics applications.
The paper introduces Cosine-Pruned Medial Axis (CPMA), a new method for extracting medial axes that are robust to noise and equivariant to isometric transformations. It uses discrete cosine transform to smooth shapes and compute a score function to filter spurious branches, achieving competitive results and stable medial axes even with significant contour perturbations.
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 $Ω$. 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.