TEMPO: Feature-Endowed Teichmüller Extremal Mappings of Point Clouds

Abstract

In recent decades, the use of three-dimensional point clouds has been widespread in the computer industry. The development of techniques for 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 Teichmüller extremal mappings, which guarantees uniform conformality distortions on point cloud surfaces. Based on the discrete analogue, we propose a novel method called TEMPO for computing Teichmüller extremal mappings between feature-endowed point clouds. Using our proposed method, the Teichmüller 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.