Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

3D Uncertain Implicit Surface Mapping using GMM and GP

Qianqian Zou, Monika Sester

TL;DR

This work introduces a more generalized approach tailored for complex surfaces in urban scenes, where GMM Regression and GP with derivative observations are applied, and integrates well-calibrated uncertainties alongside the surface model, enhancing both accuracy and reliability.

Abstract

In this study, we address the challenge of constructing continuous three-dimensional (3D) models that accurately represent uncertain surfaces, derived from noisy and incomplete LiDAR scanning 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 values and lower computational costs for the evaluated datasets.

3D Uncertain Implicit Surface Mapping using GMM and GP

TL;DR

This work introduces a more generalized approach tailored for complex surfaces in urban scenes, where GMM Regression and GP with derivative observations are applied, and integrates well-calibrated uncertainties alongside the surface model, enhancing both accuracy and reliability.

Abstract

In this study, we address the challenge of constructing continuous three-dimensional (3D) models that accurately represent uncertain surfaces, derived from noisy and incomplete LiDAR scanning 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 values and lower computational costs for the evaluated datasets.
Paper Structure (16 sections, 20 equations, 8 figures)

This paper contains 16 sections, 20 equations, 8 figures.

Table of Contents

  1. Introduction
  2. Map representation
  3. Gaussian Mixture Model
  4. Hierarchical Gaussian Mixture Models
  5. Gaussian Mixture Regression
  6. Gaussian Processes with HGMM priors
  7. Gaussian Processes
  8. GP Regression with Non-stationary Priors from HGMM
  9. GP with Derivative Observations
  10. Experiments and Evaluation
  11. Dataset
  12. Practical Implementation
  13. Surface reconstruction
  14. Evaluation
  15. Computation time comparison
  16. ...and 1 more sections

Figures (8)

  • Figure 1: Overall workflow.
  • Figure 2: Visualization of the error ellipsoids of Gaussian components in HGMM. (a) is the data. (b) shows four initial Gaussians, and they split into the next level in (c). The new components are checked by the principal curvature to see if they should be further split. (d) presents the final models.
  • Figure 3: Selected training points for GP: (a) shows 16 Gaussian components of GMM. (b) presents the differences between estimated signed distances and measured surface points. The green color indicates small errors as shown in the color bar. The points with large errors are selected for GP training in (c). (d) shows the GP inference results.
  • Figure 4: Urban point clouds in the LUCOOP dataset lucoop: colors are the labels of different Geo-objects.
  • Figure 5: Qualitative results extracted by the marching cubes algorithm: (a) surface of HGMM; (b) surface of GMMGP; (c) surface of the previous GMMGP2.5D. (d), (e) and (f) are the associated uncertainty (variance) of the HGMM/GMMGP/GMMGP2.5D surfaces; As shown by the color bars, redder colors indicate larger uncertainties and blue colors denote small uncertainties.
  • ...and 3 more figures