In recent decades, the use of 3D point clouds has been widespread in computer industry. The development of techniques in analyzing point clouds is increasingly important. In particular, mapping of point clouds has been a challenging problem. In this paper, we develop a discrete analogue of the Teichm\"{u}ller extremal mappings, which guarantee uniform conformality distortions, on point cloud surfaces. Based on the discrete analogue, we propose a novel method called TEMPO for computing Teichm\"{u}ller extremal mappings between feature-endowed point clouds. Using our proposed method, the Teichm\"{u}ller metric is introduced for evaluating the dissimilarity of point clouds. Consequently, our algorithm enables accurate recognition and classification of point clouds. Experimental results demonstrate the effectiveness of our proposed method.
@article{arxiv.1511.06624,
title = {TEMPO: Feature-Endowed Teichm\"uller Extremal Mappings of Point Clouds},
author = {Ting Wei Meng and Gary Pui-Tung Choi and Lok Ming Lui},
journal= {arXiv preprint arXiv:1511.06624},
year = {2020}
}