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Journal of Scientific Computing

Erschienen in:

15.05.2018

PCBC: Quasiconformality of Point Cloud Mappings

verfasst von: Tingwei Meng, Lok Ming Lui

Erschienen in: Journal of Scientific Computing | Ausgabe 1/2018

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Abstract

The study of surface mappings or deformations plays an important role for various applications in computer visions and graphics. An accurate and effective method to measure and control geometric distortions of the mapping is therefore necessary. Quasiconformality, which captures the local geometric distortion of a surface mapping, is a useful tool for this purpose. In discrete setting, surfaces are often represented by point clouds. Although quasiconformal theories are well developed in the continuous setting, the concept of quasiconformality on point clouds is still lacking. In this paper, we propose a geometric quantity, called the Point Cloud Beltrami Coefficient (PCBC), to measure quasiconformality of a point cloud mapping. Its ability to measure the local geometric distortion of a mapping is theoretically and numerically validated. Moreover, we propose an algorithm to solve for a point cloud mapping with a prescribed PCBC. Numerical experiments have been carried out on both synthetic and real point cloud data, which demonstrate the efficacy of the proposed algorithm.

Vorheriger Artikel Shock Regularization with Smoothness-Increasing Accuracy-Conserving Dirac-Delta Polynomial Kernels

Nächster Artikel A Linear Implicit Finite Difference Discretization of the Schrödinger–Hirota Equation

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Titel: PCBC: Quasiconformality of Point Cloud Mappings
verfasst von: Tingwei Meng
Lok Ming Lui
Publikationsdatum: 15.05.2018
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 1/2018
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-018-0724-8

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