TY - JOUR

T1 - 3D Uncertain Implicit Surface Mapping Using GMM and GP

AU - Zou, Qianqian

AU - Sester, Monika

N1 - Publisher Copyright: © 2024 IEEE.

PY - 2024/11/11

Y1 - 2024/11/11

N2 - 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.

AB - 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.

KW - laser-based

KW - Mapping

KW - probability and statistical methods

KW - uncertainty representation

UR - http://www.scopus.com/inward/record.url?scp=85207035754&partnerID=8YFLogxK

U2 - 10.48550/arXiv.2403.07223

DO - 10.48550/arXiv.2403.07223

M3 - Article

VL - 9

SP - 10559

EP - 10566

JO - IEEE Robotics and Automation Letters

JF - IEEE Robotics and Automation Letters

SN - 2377-3766

IS - 11

ER -