Computing a Compact Spline Representation of the Medial Axis Transform of a 2D Shape

TL;DR

This paper introduces a practical pipeline for computing a stable, smooth, and compact spline-based representation of the medial axis transform of 2D shapes, overcoming instability issues through pruning and approximation techniques.

Contribution

It presents a novel method combining pruning and spline approximation to produce stable, smooth, and compact medial axis transforms for arbitrary 2D shapes.

Findings

Effective pruning yields stable medial axes.

Spline approximation produces smooth, compact representations.

Method is practical and yields faithful shape reconstructions.

Abstract

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 minimizing the approximation error between the input shape and the shape represented by the medial axis transform. Our results on various 2D shapes suggest that our method is practical and effective, and yields faithful and compact representations of medial axis transforms of 2D shapes.