Published July 21, 2021
| Version v1
Conference paper
A reduced parallel transport equation on Lie Groups with a left-invariant metric
Creators
Contributors
Others:
- Université Côte d'Azur (UCA)
- E-Patient : Images, données & mOdèles pour la médeciNe numériquE (EPIONE) ; Inria Sophia Antipolis - Méditerranée (CRISAM) ; Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)
- The authors have received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (grant agreement G-Statistics N° 786854). It was also supported by the French government through the 3IA Côte d'Azur Investments ANR-19-P3IA-0002 managed by the National Research Agency.
- ANR-19-P3IA-0002,3IA@cote d'azur,3IA Côte d'Azur(2019)
- European Project: 786854,H2020 Pilier ERC,ERC AdG(2018)
Description
This paper presents a derivation of the parallel transport equation expressed in the Lie algebra of a Lie group endowed with a left-invariant metric.The use of this equation is exemplified on the group of rigid body motions SE(3), using basic numerical integration schemes, and compared to the pole ladder algorithm. This results in a stable and efficient implementation of parallel transport. The implementation leverages the python package geomstats and is available online.
Abstract
International audienceAdditional details
Identifiers
- URL
- https://hal.inria.fr/hal-03154318
- URN
- urn:oai:HAL:hal-03154318v2
Origin repository
- Origin repository
- UNICA