3D Uncertain Implicit Surface Mapping Using GMM and GP

authored by: Qianqian Zou, Monika Sester
Abstract: In this letter, we address the challenge of constructing continuous 3D models that accurately represent uncertain surfaces, derived from noisy LiDAR data. Building upon our prior work, which utilized the Gaussian Process (GP) and Gaussian Mixture Model (GMM) for structured building models, we introduce a more generalized approach tailored for complex surfaces in urban scenes, where GMM Regression and GP with derivative observations are applied. A Hierarchical GMM (HGMM) is employed to optimize the number of GMM components and speed up the GMM training. With the prior map obtained from HGMM, GP inference is followed for the refinement of the final map. Our approach models the implicit surface of the geo-object and enables the inference of the regions that are not completely covered by measurements. The integration of GMM and GP yields well-calibrated uncertainties alongside the surface model, enhancing both accuracy and reliability. The proposed method is evaluated on real data collected by a mobile mapping system. Compared to the performance in mapping accuracy and uncertainty quantification of other state-of-the-art methods, the proposed method achieves lower RMSEs, higher log-likelihood and lower computational costs for the evaluated data.
Organisation(s): Institute of Cartography and Geoinformatics
Type: Article
Journal: IEEE Robotics and Automation Letters
Volume: 9
Pages: 10559-10566
No. of pages: 8
ISSN: 2377-3766
Publication date: 11.2024
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Control and Systems Engineering, Biomedical Engineering, Human-Computer Interaction, Mechanical Engineering, Computer Vision and Pattern Recognition, Computer Science Applications, Control and Optimization, Artificial Intelligence
Electronic version(s): https://doi.org/10.48550/arXiv.2403.07223 (Access: Open)
https://doi.org/10.1109/LRA.2024.3475873 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{02e487b80cb74dd096bc5e67a4b6f4e2,
title = "3D Uncertain Implicit Surface Mapping Using GMM and GP",
abstract = "In this letter, we address the challenge of constructing continuous 3D models that accurately represent uncertain surfaces, derived from noisy LiDAR data. Building upon our prior work, which utilized the Gaussian Process (GP) and Gaussian Mixture Model (GMM) for structured building models, we introduce a more generalized approach tailored for complex surfaces in urban scenes, where GMM Regression and GP with derivative observations are applied. A Hierarchical GMM (HGMM) is employed to optimize the number of GMM components and speed up the GMM training. With the prior map obtained from HGMM, GP inference is followed for the refinement of the final map. Our approach models the implicit surface of the geo-object and enables the inference of the regions that are not completely covered by measurements. The integration of GMM and GP yields well-calibrated uncertainties alongside the surface model, enhancing both accuracy and reliability. The proposed method is evaluated on real data collected by a mobile mapping system. Compared to the performance in mapping accuracy and uncertainty quantification of other state-of-the-art methods, the proposed method achieves lower RMSEs, higher log-likelihood and lower computational costs for the evaluated data.",
keywords = "laser-based, Mapping, probability and statistical methods, uncertainty representation",
author = "Qianqian Zou and Monika Sester",
note = "Publisher Copyright: {\textcopyright} 2024 IEEE.",
year = "2024",
month = nov,
doi = "10.48550/arXiv.2403.07223",
language = "English",
volume = "9",
pages = "10559--10566",
journal = "IEEE Robotics and Automation Letters",
issn = "2377-3766",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "11",
}