The medial axis is a classical representation of digital objects widely used in many applications. However, such a set of balls may not be optimal: subsets of the medial axis may exist without changing the reversivility of the input shape representation. In this article, we first prove that finding a minimum medial axis is an NP-hard problem for the Euclidean distance. Then, we compare two algo...

We present the CPMA, a new method for medial axis pruning with noise robustness and equivariance to isometric transformations. The CPMA leverages discrete cosine transform create smooth versions of shape $\Omega $ . use shapes compute score function $\mathcal {F}_{\Omega }$ that filters out spurious branches from original Our generalizes $n$ -dimensional given properties Discrete Cosine Transfo...

Medial axes and skeletons are notoriously sensitive to contour irregularities. This lack of stability is a serious problem for applications in e.g. shape analysis and recognition. In 2005, Chazal and Lieutier introduced the λ-medial axis as a new concept for computing the medial axis of a shape subject to single parameter filtering. The λ-medial axis is stable under small shape perturbations, a...

We propose an Euclidean medial axis filtering method which generates subsets of Euclidean medial axis were filtering rate is controlled by one parameter. The method is inspired by Miklos’, Giesen’s and Pauly’s scale axis method which preserves important features of an input object from shape understanding point of view even if they are at different scales. Our method overcomes the most importan...

It is shown that a convex medial axis polyhedron has two distinct edge unfoldings: cuttings along edges that unfold the surface to a simple planar polygon. One of these unfoldings is a generalization of the point source unfolding, and is easily established to avoid overlap. The other is a novel unfolding that requires a more complex argument to establish nonoverlap, and might generalize.