Q-MAT+: An error-controllable and feature-sensitive simplification algorithm for medial axis transform

Abstract

The medial axis transform (MAT), as an intrinsic shape representation, plays an important role in shape approximation, recognition and retrieval. Q-MAT is a state-of-the-art algorithm driven by quadratic error minimization to compute a geometrically precise, structurally concise, and compact representation of the MAT for 3D shapes. In this work we extend the technique to make it more robust, controllable, and name it Q-MAT+. Combining shape diameter function (SDF) and other mesh information, Q-MAT+ gets a more complete and accurate initial MAT than Q-MAT, even for extreme thin features, such as wires and sheets. Q-MAT+ could quickly remove insignificant branches while preserving significant ones to get a simple and faithful piecewise linear approximation of the MAT. Moreover, it performs the medial axis simplification with explicit maintenance and the control of Hausdorff error, which is not originally supported in Q-MAT. We further demonstrate the outstanding efficiency and accuracy of our method compared with other existing approaches for MAT generation and simplification.