The λ-medial axis was introduced in 2005 by Chazal and Lieutier as a new concept for computing the medial axis of a shape subject to filtering with a single parameter. These authors proved the stability of the λ-medial axis under small shape perturbations. In this paper, we introduce the definition of a discrete λ-medial axis (DLMA). We evaluate its stability and rotation invariance experimenta...

The popularity of medial axis in shape modeling and analysis comes from several of its well known fundamental properties. For example, medial axis captures the connectivity of the domain, has a lower dimension than the space itself, and is closely related to the distance function constructed over the same domain. We formally define the new concept of a medial zone of an n-dimensional semi-analy...

The medial axis of an image pattern is the loci of all inscribed disks that touch two or more boundary points without crossing any of the boundaries. The medial axis transform (MAT) is a powerful representation for objects with inherent symmetry or near-symmetry. The medial axis of 2-D image patterns provides a conceptual design base, with transition to a detailed design occurring when the radi...

The medial axis of an image pattern is the loci of all inscribed disks that touch two or more boundary points without crossing any of the boundaries. The medial axis transform (MAT) is a powerful representation for objects with inherent symmetry or nearsymmetry. The medial axis of 2-D image patterns provides a conceptual design base, with transition to a detailed design occurring when the radiu...

We present a new method for computing the medial axis of a given closed smooth curve or surface. It is based on an algorithm for approximating the signed distance function using polynomial splines over hierarchical T-meshes, which has recently been presented in [36]. Since the signed distance function is not differentiable along the medial axis, the hierarchical T-meshes is automatically refine...

The medial axis is an important shape descriptor first introduced by Blum [2] via a grassfire burning analogy. However, the medial axes are sensitive to boundary perturbations, which calls for global shape measures to identify meaningful parts of a medial axis. On the other hand, a more compact shape representation than the medial axis, such as a “center point”, is needed in various application...

In this paper, we present a novel method for medial axis approximation based on Constrained Centroidal Voronoi Diagram of discrete data (image, volume). The proposed approach is based on the shape boundary subsampling by a clustering approach which generates a Voronoi Diagram well suited for Medial Axis extraction. The resulting Voronoi Diagram is further filtered so as to capture the correct t...

A three-dimensional, medial-axis-based mesh generator is described. First the medial axis of the geometry to be meshed is constructed, then quad-dominant meshes on the medial surface are generated and extruded to the boundary at both sides of the medial surface. The resulting single cell layer is subdivided in direction normal to the boundary, yielding columns of hexahedral and three-sided pris...

We introduce the medial axis as a tool in the analysis of geometric structure of void space in porous media. The medial axis traces the fundamental geometry of the void pathways. We describe an algorithm for generating the medial axis of the void structure from digitized three dimensional images of porous media obtained from X ray CAT scans. The medial axis is constructed during an iterative er...

Medial axis Transform is sometimes used as an intermediate representation in algorithms for meshing or recognition of shapes from digitized data. This raises the question whether the Medial Axis captures fundamental topological invariants of the object. The (positive) answer has been known already in the case of smooth objects. The main result presented here is the homotopy equivalence of any b...