# MathSciDoc: An Archive for Mathematician ∫

#### Geometric Modeling and Processingmathscidoc:1608.16075

ACM Transactions on Graphics, 35, (1), 8:1~8:16, 2015.12
The medial axis transform (MAT) is an important shape representation for shape approximation, shape recognition, and shape retrieval. Despite years of research, there is still a lack of effective methods for efficient, robust and accurate computation of the MAT. We present an efficient method, called {\em Q-MAT}, that uses quadratic error minimization to compute a structurally simple, geometrically accurate, and compact representation of the MAT. We introduce a new error metric for approximation and a new quantitative characterization of unstable branches of the MAT, and integrate them in an extension of the well-known quadric error metric (QEM) framework for mesh decimation. Q-MAT is fast, removes insignificant unstable branches effectively, and produces a simple and accurate piecewise linear approximation of the MAT. The method is thoroughly validated and compared with existing methods for MAT computation.
Medial axis, simplification, quadratic error metric, stability ratio, volume approximation
@inproceedings{pan2015q-mat:,
title={Q-MAT: Computing Medial Axis Transform By Quadratic Error Minimization},
author={Pan Li, Bin Wang, Feng Sun, Xiaohu Guo, Caiming Zhang, and Wenping Wang},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160826131943426890458},
booktitle={ACM Transactions on Graphics},
volume={35},
number={1},
pages={8:1~8:16},
year={2015},
}

Pan Li, Bin Wang, Feng Sun, Xiaohu Guo, Caiming Zhang, and Wenping Wang. Q-MAT: Computing Medial Axis Transform By Quadratic Error Minimization. 2015. Vol. 35. In ACM Transactions on Graphics. pp.8:1~8:16. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160826131943426890458.