Generalized Maximum Likelihood Estimation for Perspective-n-Point Problem (2408.01945v1)

Abstract: The Perspective-n-Point (PnP) problem has been widely studied in the literature and applied in various vision-based pose estimation scenarios. However, existing methods ignore the anisotropy uncertainty of observations, as demonstrated in several real-world datasets in this paper. This oversight may lead to suboptimal and inaccurate estimation, particularly in the presence of noisy observations. To this end, we propose a generalized maximum likelihood PnP solver, named GMLPnP, that minimizes the determinant criterion by iterating the GLS procedure to estimate the pose and uncertainty simultaneously. Further, the proposed method is decoupled from the camera model. Results of synthetic and real experiments show that our method achieves better accuracy in common pose estimation scenarios, GMLPnP improves rotation/translation accuracy by 4.7%/2.0% on TUM-RGBD and 18.6%/18.4% on KITTI-360 dataset compared to the best baseline. It is more accurate under very noisy observations in a vision-based UAV localization task, outperforming the best baseline by 34.4% in translation estimation accuracy.

• The paper presents GMLPnP, a novel solver that integrates anisotropic uncertainty estimation with pose parameters to boost accuracy.
• It employs an iterative Generalized Least Squares procedure within a maximum likelihood framework for robust rotation and translation estimation.
• Empirical tests on synthetic and real-world datasets confirm significant gains, notably improving UAV localization and multi-camera adaptability.

Generalized Maximum Likelihood Estimation for Perspective-n-Point Problem

Introduction

The paper authored by Tian Zhan, Chunfeng Xu, Cheng Zhang, and Ke Zhu addresses a significant challenge in the field of vision-based pose estimation: the Perspective-n-Point (PnP) problem. Traditional approaches to this problem often overlook the anisotropic uncertainties inherent in real-world datasets, which can result in suboptimal and inaccurate estimations, especially under noisy conditions. The authors propose a novel solver, Generalized Maximum Likelihood PnP (GMLPnP), which aims to bridge this gap by incorporating and estimating uncertainties in the observations concurrently with the pose parameters. This approach is also designed to be independent of the camera model, making it versatile across different camera systems.

Problem Statement and Contribution

The PnP problem entails determining the 6-DoF pose from a set of $n$ 3D points and their corresponding 2D projections on an image. The standard assumption in many existing methods is that the observation noise is isotropic and Gaussian, which may not hold true in practical scenarios. The paper brings forth several key contributions:

1. Observation Uncertainty: The authors highlight that real-world data exhibit anisotropic uncertainties. These uncertainties, if unaccounted for, can lead to considerable inaccuracies.
2. Generalized Maximum Likelihood Approach: The proposed GMLPnP is grounded in maximum likelihood estimation, taking into account the anisotropic nature of observation uncertainties. This is achieved through an iterative Generalized Least Squares (GLS) procedure that estimates both the pose and the uncertainty parameters.
3. Decoupling from Camera Model: The GMLPnP method does not constrain the camera model, affording it greater versatility in applications involving different camera systems, such as fisheye and omnidirectional cameras.

Methodology

The GMLPnP approach involves the following steps:

1. Maximum Likelihood Estimation: The method minimizes a determinant criterion encapsulated within a maximum likelihood framework. When the noise covariance is known, the pose estimation is framed as a nonlinear optimization problem in object space.
2. Iterated GLS Procedure: For unknown noise covariance, the method iteratively refines the pose and covariance estimations. This iteration utilizes the residuals from the error function to update the covariance, converging towards the true values.

Empirical Evaluation

The efficacy of GMLPnP was evaluated through both synthetic and real-world experiments, benchmarked against several established PnP solvers. The key datasets used include:

1. Synthetic Data: The experiments showed that GMLPnP consistently outperformed other methods in terms of rotation and translation accuracy, especially in scenarios with high noise levels.
2. Real Datasets:
   • TUM-RGBD: GMLPnP outpaced other methods with a 4.7% improvement in rotation and 2.0% in translation accuracy.
   • KITTI-360: GMLPnP demonstrated significant gains of 18.6% in rotation and 18.4% in translation accuracy over the best baseline, emphasizing its robustness across different camera models.
3. UAV Localization: The paper extends the practical implications to vision-based UAV localization, where GMLPnP yielded a 29.7% overall improvement in translation accuracy, with a substantial 34.4% enhancement in elevation accuracy, compared to other techniques.

Implications and Future Directions

The practical implications of GMLPnP are extensive, particularly in fields requiring precise pose estimation under varying observational uncertainties, such as autonomous navigation, augmented reality, and robotics. By addressing anisotropic uncertainties and decoupling from camera models, the method enhances the robustness and applicability of vision-based pose estimation systems.

Future work may explore extending GMLPnP to multi-camera systems, both central and non-central, and integrating it with real-time systems where computational efficiency is crucial. Additionally, the method's adaptability to other forms of sensor fusion, such as combining visual data with LiDAR, could further broaden its applicability.

Conclusion

The GMLPnP solver proposed by Zhan et al. represents a significant stride in enhancing the accuracy and robustness of the PnP problem under anisotropic uncertainties. Through a generalized maximum likelihood framework, the method concurrently estimates pose and uncertainty, offering substantial improvements over conventional approaches. The empirical results underscore its potential for practical applications in diverse fields requiring precise vision-based pose estimations.