TEMPO: Feature-Endowed Teichm\"uller Extremal Mappings of Point Clouds

TL;DR

This paper introduces TEMPO, a novel method for computing Teichmüller extremal mappings on feature-rich point clouds, enabling accurate shape analysis and classification by preserving conformality distortions.

Contribution

The paper develops a discrete analogue of Teichmüller extremal mappings for point clouds and proposes TEMPO, a new algorithm for feature-endowed point cloud mapping.

Findings

Effective in recognizing and classifying point clouds

Introduces the Teichmüller metric for point cloud dissimilarity

Experimental results demonstrate high accuracy and robustness

Abstract

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.