Stability Analysis of Medial Axis Transform

Stability Analysis of Medial Axis Transform under Relative Hausdorff Distance

Medial axis transform (MAT) is a basic tool for shape analysis. But, in spite of its usefulness, it has some drawbacks, one of which is its instability under the boundary perturbation. To handle this problem in practical situations, various “pruning” methods have been proposed, which are usually heuristic in their nature and without sufficient error analyses. In this paper, we show that, althou...

One-Sided Stability of Medial Axis Transform

Computing a compact spline representation of the medial axis transform of a 2D shape

We present a full pipeline for computing the medial axis transform of an arbitrary 2D shape. The instability of the medial axis transform is overcome by a pruning algorithm guided by a user-defined Hausdorff distance threshold. The stable medial axis transform is then approximated by spline curves in 3D to produce a smooth and compact representation. These spline curves are computed by minimizi...

Robust skeletonization using the discrete lambda-medial axis

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...

Medial Axis Transformation based Skeletonzation of Image Patterns using Image Processing Techniques

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...