Correspondence-Free Pose Estimation with Patterns: A Unified Approach for Multi-Dimensional Vision

TL;DR

This work addresses 6D pose estimation without explicit point correspondences by introducing a unified, correspondence-free framework that treats point sets as patterns and employs independent feature functions to produce equations invariant to correspondence. The method generalizes to 3D-to-3D, 3D-to-2D, and 2D-to-2D scenarios by optimizing a set of aggregated, non-mappable equations $\frac{1}{N}\sum f_i(h(p_k,\theta)) = \frac{1}{N}\sum f_i(q_k)$, enabling pose recovery without explicit matches. It demonstrates robustness to noise, mismatches, and occlusions through simulations and real experiments, and offers a flexible initialization alternative or complement to feature-based pipelines. The approach broadens applicability to nonlinear perspective projections and potentially reduces reliance on reliable feature matching in challenging environments.

Abstract

6D pose estimation is a central problem in robot vision. Compared with pose estimation based on point correspondences or its robust versions, correspondence-free methods are often more flexible. However, existing correspondence-free methods often rely on feature representation alignment or end-to-end regression. For such a purpose, a new correspondence-free pose estimation method and its practical algorithms are proposed, whose key idea is the elimination of unknowns by process of addition to separate the pose estimation from correspondence. By taking the considered point sets as patterns, feature functions used to describe these patterns are introduced to establish a sufficient number of equations for optimization. The proposed method is applicable to nonlinear transformations such as perspective projection and can cover various pose estimations from 3D-to-3D points, 3D-to-2D points, and 2D-to-2D points. Experimental results on both simulation and actual data are presented to demonstrate the effectiveness of the proposed method.

Figures (7)

• Figure 1: Indoor experimental setup for correspondence-free pose estimation using wall patterns. The camera follows a trajectory while maintaining sufficient pattern visibility within its field of view.
• Figure 2: Reference points (the blue and red curves) in two pictures, where noisy reference points in the second picture with $b_{p}=0.02$ are represented in black points.
• Figure 3: The relation between the average runtime and the number of points correspondence.
• Figure 4: The match results through different feature extraction methods. (a) and (b) are the reference and subsequent frames which represent the images taken by a camera at different positions. The purple and green points in (c)-(f) are the extracted feature points based on different common feature extraction methods. The corresponding relationship between them is indicated by yellow lines.
• Figure 5: The registration results. Here (a) and Fig. \ref{['figcom']} (c)-(f) are generated by the MATLAB R2017b toolbox, Registration Estimator. There is a wrong registration in (a) and the green area indicated by the red arrow is the content beyond the field of the subsequent frame, just for the purpose of distinguishing. The green color shape has overlapped the purple one completely in (b).