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Efficient and Robust Absolute Pose Estimation via Gravity-Prior-Driven Transformation Decoupling and Pose Refinement

Hu Cao, Qianyi Yang, Xinyi Li, Jiong Liu, Yinlong Liu, Alois Knoll

arXiv:2609.00713v1cs.CV

TL;DR

Robust absolute pose estimation remains challenging because mismatched correspondences undermine existing gravity-aware solvers and accurate refinement is underdeveloped. The paper uses gravity-driven rotation-first decoupling, one-dimensional global voting, RANSAC translation, and dedicated refinement, with experiments reporting stronger performance and reduced SLAM drift.

  • Problem

    Gravity-aware pose estimation still needs robust handling of many mismatches and accurate refinement of solutions from selected inlier correspondences.

  • Method

    The method reduces 6-DoFs pose estimation to 1-DoF rotation plus 3-DoFs translation, using global voting, filtered-input RANSAC, and gravity-aware pose refinement.

  • Results

    The method outperforms existing SOTA approaches across synthetic and real-world evaluations and reduces trajectory drift in ORB-SLAM2 relocalization experiments.

  • Takeaways & Limitations

    The framework provides an efficient, robust, and high-precision solution for practical robotic and visual SLAM applications.

Abstract

from arXiv · show

Estimation of the absolute pose of an object is an essential task for various robotic applications. Recently, incorporating gravity direction as prior information has emerged as a popular approach to simplify absolute pose estimation. However, developing a robust and efficient algorithm to solve this challenging problem remains a difficult question due to large amounts of mismatches. In addition, obtaining an accurate pose solution from selected inlier correspondences with gravity prior is still a research gap. In this paper, we propose a novel transformation strategy that exploits geometric relations derived from the gravity prior. Through transformation decoupling, the original 6 degrees of freedom (DoF) absolute pose estimation problem is simplified into a 4-DoFs problem: 1-DoF for the rotation angle and 3-DoFs for translation, significantly improving the efficiency. For the 1-DoF rotation angle, we apply a one-dimensional global voting algorithm for optimal estimation. Once the optimal rotation is obtained, the mismatched correspondences are preliminarily filtered, and translation estimation, a linear problem, can be easily solved. Furthermore, to obtain accurate pose results, we introduce a novel pose refinement algorithm to enhance the accuracy of both rotation and translation. Extensive experiments on synthetic data and three publicly available real-world datasets (TUM RGB-D, ETH3D, and RobotCar) demonstrate that the proposed method achieves stronger performance compared to existing state-of-the-art (SOTA) approaches. To further validate our method, we integrated it into ORB-SLAM2. The results on the KITTI dataset show it effectively reduces drift and improves trajectory alignment during relocalization. The source code will be released upon acceptance.

I. INTRODUCTION

Absolute pose estimation from mismatched 2D-3D correspondences is difficult, while gravity priors offer a way to reduce problem dimensionality. The paper addresses robustness, efficiency, and gravity-aware pose refinement through a rotation-first framework.

  • Absolute pose estimation determines camera orientation and position relative to a 3D world from matched 2D-3D features.
  • Known gravity direction reduces the pose problem to a 4-DoFs formulation, but existing methods still struggle with outlier-contaminated inputs and efficient outlier removal.
  • Outliers arise from imperfect feature matching, partial overlap, and noisy data, and can produce seriously incorrect pose estimates.
  • Existing robust global methods become substantially more expensive as optimization dimensionality increases, motivating gravity-aware reduction from full 6-DoFs pose estimation.
  • The proposed framework reverses conventional translation-first decoupling by prioritizing rotation, then combines global voting, outlier filtering, RANSAC translation, and dedicated refinement.
  • Experiments on synthetic data, three real-world datasets, and SLAM integration report stronger performance than existing SOTA methods and reduced trajectory drift.

II. RELATED WORK

Prior work develops closed-form, learning-based, robust, decoupled, and gravity-aware solutions for PnP and absolute pose estimation. These approaches seek accuracy and robustness while reducing the cost of searching the full pose space.

  • Classical PnP methods include minimal P3P solutions, polynomial-root formulations, and EPnP, which estimates pose using four virtual control points.
  • Learning-based approaches model geometric dependencies with architectures such as geometry-aware transformers and frequency-aware state-space models.
  • RANSAC-based methods are widely used for outlier-contaminated correspondences, but their nondeterminism limits reliability as outlier rates increase.
  • Transformation decoupling separates rotation and translation into lower-dimensional subproblems, reducing the computational burden of global search.
  • Gravity-aware methods use known gravity direction to constrain absolute camera pose and construct geometric relations between corresponding points.
  • The PnP formulation uses 2D bearing vectors, 3D observations, scale factors, rotation R, and translation t to estimate camera pose.

IV. METHOD

The method uses gravity constraints to decouple absolute pose estimation into a one-dimensional rotation-angle problem followed by three-dimensional translation estimation. The resulting stages include rotation decoupling, global voting, translation estimation, and pose refinement.

  • IV. METHOD: The complete method comprises gravity-based rotation decoupling, one-dimensional global voting, RANSAC translation estimation, and pose refinement.Translation is estimated after rotationally filtering mismatched correspondences.
  • B. Decoupling Rotation with Gravity Prior: All gravity-consistent rotations are represented as two sequential steps involving a fixed alignment rotation and a rotation around the camera-frame gravity axis.The rotation around gc is parameterized by θ and computed using Rodrigues’ rotation formula.
  • B. Decoupling Rotation with Gravity Prior: Substituting the decoupled rotation into the correspondence model leaves θ as the only unknown rotational parameter before translation is estimated.The reformulated model is λ_i y_i = R(θ, gc)R0x_i + t.
  • B. Decoupling Rotation with Gravity Prior: Gravity constraints reduce the original PnP problem from 6 DoFs to 4 DoFs: one rotation angle and three translation parameters.The rotation angle lies in [-π, π], while translation remains in R3.

C. The Estimation of Rotation Angle

Rotation estimation uses pairwise 2D-3D constraints to reduce the gravity-constrained rotation search to the single angle θ. A one-dimensional voting procedure selects the most supported angle and helps identify likely inliers.

  • C. The Estimation of Rotation Angle: Pairwise 2D-3D correspondences yield a relational equation in which, under known gravity directions, only the rotation angle θ remains unknown.The pairwise terms are m_k = y_i × y_{i+1} and n_k = x_i − x_{i+1}.
  • C. The Estimation of Rotation Angle: The rotation angle is obtained by solving the corresponding trigonometric function using Rodrigues’ rotation formula.The formulation follows from the gravity-constrained rotation parameterization and pairwise relation.
  • C. The Estimation of Rotation Angle: Global voting divides [-π, π] into 360 intervals and selects θ* within the interval receiving the largest number of votes.For N correspondences, pairwise calculations are performed N(N−1)/2 times.
  • C. The Estimation of Rotation Angle: Pairwise correspondences that support the dominant angle are more likely to be inliers, enabling preliminary filtering of many outliers.The method does not guarantee that every remaining correspondence is an inlier.
  • C. The Estimation of Rotation Angle: After rotation estimation, translation is recovered from the filtered correspondences using RANSAC with least-squares translation fitting and an angular inlier threshold.The procedure samples two pairs, solves translation, counts inliers, and retains the translation with the highest count.

D. Translation Estimation

Translation estimation becomes a linear fitting problem once rotation is known, while pose refinement recomputes rotation and translation from initial inliers through constrained optimization. The refinement uses a hidden-variable resultant to solve the resulting conic intersection efficiently.

  • D. Translation Estimation: Given the estimated rotation, translation is estimated as a linear model-fitting problem using RANSAC on rotationally filtered correspondences.The goal is to align rotated and translated 3D points with their corresponding 2D bearing vectors.
  • D. Translation Estimation: For larger correspondence sets, the method formulates pose estimation as constrained least squares over rotation and translation.The gravity-aligned rotation uses x = cos(θ) and y = sin(θ), reducing the rotation representation to three unique elements.
  • D. Translation Estimation: The translation subproblem is a non-negative convex quadratic in unconstrained t, so its globally minimizing value can be computed for a fixed rotation.This value is obtained by differentiating the objective with respect to t and setting the derivative to zero.
  • D. Translation Estimation: The derivative condition forms a conic, and solving it with the circle constraint is equivalent to finding intersections of two conic curves.The paper uses a hidden-variable resultant instead of identifying all possible intersections geometrically.

A. Compared Methods

The experiments compare the proposed method with gravity-constrained, minimal-solver, and general PnP approaches, including both deterministic and RANSAC-based alternatives.

  • A. Compared Methods: BnB is evaluated as a 4-DoF gravity-prior method based on the Branch-and-Bound framework.The BnB method is from.
  • A. Compared Methods: The study includes Gao’s P3P and Ke’s AP3P embedded within RANSAC.Both are minimal pose solvers used as RANSAC-based baselines.
  • A. Compared Methods: The comparison also covers Sweeney’s and Kukelova’s P2P methods integrated with RANSAC.These baselines are denoted Swee and Kuke, respectively.
  • A. Compared Methods: Additional RANSAC-based baselines are SqPnP and EPnP.They are denoted Sqpnp and Epnp in the experiments.
  • A. Compared Methods: SupeRANSAC is included as a state-of-the-art RANSAC-like PnP comparison method.It is the PnP algorithm proposed by Barath.
  • A. Compared Methods: The comparison includes AaPnP, a camera-pose method that exploits specific real-world constraints.AaPnP is proposed by Roch et al.

B. Evaluation Metrics

The evaluation uses rotation error and translation error to compare pose-estimation methods.

  • Rotation error is measured by angle distance between the ground-truth and calculated rotations.The calculated rotation is represented by Rcal, and the metric uses the trace of a matrix.
  • Translation error evaluates the difference associated with the calculated translation vector.The calculated translation is represented by tcal.

C. Hardware Setting

Synthetic experiments evaluate robustness, accuracy, gravity-bias sensitivity, refinement, and runtime under controlled conditions. The method remains robust under corruption, while rotation estimation dominates runtime with quadratic growth in the number of correspondences.

  • Robustness to outliers: Under outlier rates from 0.1 to 0.8, the proposed method has significantly higher rotation and translation robustness than competing methods.Experiments use N=1000, noise σ=2.0, and 100 repetitions per scenario.
  • Robustness to noise: Within a reasonable noise range, the method maintains an almost 100% success rate for both rotation and translation estimation.Noise levels range from σ=0.5 to 4 with the outlier rate fixed at ω=0.5.
  • Heavily corrupted data: At ω=0.5 and σ=10.0, the method maintains a higher success rate than other methods under severe joint outlier and noise corruption.Each extreme-condition experiment is repeated 100 times.
  • Gravity-direction bias: As gravity-direction bias increases from 0.5° to 5°, both rotation and translation errors grow, with a higher likelihood of large errors.The biased-gravity experiments use N=1000, σ=1, and ω=0.5.
  • Pose refinement: Pose refinement improves the proposed method’s performance compared with using the method without refinement.This conclusion comes from the corresponding ablation experiment.
  • Runtime: R estimation dominates runtime because it processes N(N−1)/2 pair combinations, producing quadratic growth as input size increases.Unlike noise-sensitive BnB, runtime remains unaffected by noise level and outlier rate.
  • Runtime: Processing two pairs at a time enables parallel acceleration, and runtime decreases as the number of threads increases.The authors identify multithreading and GPU computation as possible acceleration techniques.

B. Real-World Data Experiments

Real-world experiments use matched image pairs and corresponding depth or point-cloud data from TUM RGB-D, ETH3D, and RobotCar. The method remains robust in complex scenes, although its runtime is longer than RANSAC-type methods for large inputs.

  • Datasets: The real-world evaluation uses approximately 100 image pairs from TUM RGB-D, ETH3D, and RobotCar, all providing ground-truth trajectories.The datasets contain depth maps or 3D point sets for constructing correspondences.
  • Data construction: 2D-3D correspondences are formed from image features such as ORB or SIFT, using bearing vectors from one image and 3D points from another.A 10- to 20-pixel search radius accounts for inaccuracies when retrieving corresponding 3D points.
  • Accuracy and robustness: The proposed method effectively estimates absolute camera pose when the vertical gravity direction is known and remains robust under substantial outlier contamination.The real-world results are reported for selected images from all three datasets.
  • Runtime: The method has longer runtime than RANSAC-type methods, especially for large input sizes, but supports acceleration through GPU processing or multithreading.Runtime comparisons are summarized across the real-world datasets.
  • Method behavior: The performance advantage is attributed to the joint effect of global-voting outlier filtering and refinement-based accuracy optimization.This combination is reported as making the method more suitable for practical applications.

C. Validation of ORB-SLAM2 integrated with our method on the KITTI dataset.

The proposed estimator replaces ORB-SLAM2’s original PnP solver and is evaluated on KITTI using absolute and relative pose errors. The integrated system shows improved trajectory accuracy, stability, and relocalization performance.

  • System integration: The integration replaces ORB-SLAM2’s original PnP solver with the proposed absolute pose estimator on the KITTI dataset.APE and RPE are used as the primary evaluation metrics.
  • Absolute pose error: For APE, the proposed method reduces RMSE from 16.40 to 9.36 and SSE from 361053.9 to 115607.3.Maximum error and standard deviation also decrease from 32.15 to 14.93 and from 6.5687 to 2.8524, respectively.
  • Relative pose error: For RPE, RMSE decreases from 0.176 to 0.159, while SSE, maximum error, and standard deviation also decline.The corresponding comparisons are 57.63 vs. 70.74, 3.64 vs. 4.58, and 0.1344 vs. 0.1550.
  • Trajectory alignment: The estimated trajectory closely aligns with the reference trajectory, with predominantly low errors and only minor deviations in challenging segments.The trajectory visualization uses solid blue for the estimate, dashed lines for the reference, and colors for error magnitude.
  • Relocalization: Relocalization tests show significant improvements in trajectory accuracy and relocalization performance after replacing the original solver with the full two-stage framework.The reported system-level result connects robust coarse estimation with high-precision refinement.

VII. DISCUSSION AND ANALYSIS

The method combines a coarse rotation-first estimation stage with a fine gravity-aware refinement stage. Experiments support the modules’ individual contributions, their synergy, and improved relocalization performance in SLAM.

  • C. Synergistic Effect of the Two-Stage Framework: KITTI Sequence 00 visualizations show drift-induced misalignment before relocalization and corrected trajectory alignment afterward.The estimated trajectory is compared with the point-cloud map before and after the relocalization event.
  • A. Contribution of the Coarse Estimation Stage: The coarse stage uses rotation-first decoupling and 1D global voting to improve outlier robustness and computational efficiency.The strategy exploits the low-dimensional gravity-constrained rotation space before translation estimation.
  • B. Contribution of the Fine Refinement Stage: The fine stage applies dedicated non-minimal refinement in the 4-DoFs gravity-constrained space to improve final pose accuracy.Controlled ablations report consistent gains in both rotation and translation accuracy.
  • C. Synergistic Effect of the Two-Stage Framework: The two stages mutually reinforce one another: coarse filtering supplies reliable inputs and initialization, while refinement exploits them for precise optimization.The full pipeline improves trajectory accuracy and relocalization performance beyond either stage alone.
  • Conclusion: The complete experiments validate each core module, superiority over strong baselines, and the rationale for the cascaded framework.The conclusion attributes the overall solution to rotation-first decoupling, robust voting and filtering, and dedicated high-precision refinement.
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