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A Direct Semi-Exhaustive Search Method for Robust, Partial-to-Full Point Cloud Registration

Richard Cheng, Chavdar Papozov, Dan Helmick, Mark Tjersland

TL;DR

The paper tackles robust rigid point cloud registration without relying on correspondences, focusing on partial-to-full alignment. It introduces Direct Semi-Exhaustive Search (DSES), which for each rotation $R \in SO(3)$ computes an inlier-maximizing translation $t^*$ via a mode over translations $y_j - R x_i$, then evaluates a collection of candidate poses under a chosen $L_p$ norm. The method leverages GPU parallelism to achieve high reliability and generalization, demonstrating superior or competitive accuracy and recall on ModelNet40 and real-world robot pose estimation, with favorable behavior when the search space is well-constrained. Overall, DSES reframes registration as a parallelizable optimization over rotation space with mode-based translation estimation, offering a data-free alternative that maintains robustness to outliers and partial overlap while enabling flexible metric choices.

Abstract

Point cloud registration refers to the problem of finding the rigid transformation that aligns two given point clouds, and is crucial for many applications in robotics and computer vision. The main insight of this paper is that we can directly optimize the point cloud registration problem without correspondences by utilizing an algorithmically simple, yet computationally complex, semi-exhaustive search approach that is very well-suited for parallelization on modern GPUs. Our proposed algorithm, Direct Semi-Exhaustive Search (DSES), iterates over potential rotation matrices and efficiently computes the inlier-maximizing translation associated with each rotation. It then computes the optimal rigid transformation based on any desired distance metric by directly computing the error associated with each transformation candidate $\{R, t\}$. By leveraging the parallelism of modern GPUs, DSES outperforms state-of-the-art methods for partial-to-full point cloud registration on the simulated ModelNet40 benchmark and demonstrates high performance and robustness for pose estimation on a real-world robotics problem (https://youtu.be/q0q2-s2KSuA).

A Direct Semi-Exhaustive Search Method for Robust, Partial-to-Full Point Cloud Registration

TL;DR

The paper tackles robust rigid point cloud registration without relying on correspondences, focusing on partial-to-full alignment. It introduces Direct Semi-Exhaustive Search (DSES), which for each rotation computes an inlier-maximizing translation via a mode over translations , then evaluates a collection of candidate poses under a chosen norm. The method leverages GPU parallelism to achieve high reliability and generalization, demonstrating superior or competitive accuracy and recall on ModelNet40 and real-world robot pose estimation, with favorable behavior when the search space is well-constrained. Overall, DSES reframes registration as a parallelizable optimization over rotation space with mode-based translation estimation, offering a data-free alternative that maintains robustness to outliers and partial overlap while enabling flexible metric choices.

Abstract

Point cloud registration refers to the problem of finding the rigid transformation that aligns two given point clouds, and is crucial for many applications in robotics and computer vision. The main insight of this paper is that we can directly optimize the point cloud registration problem without correspondences by utilizing an algorithmically simple, yet computationally complex, semi-exhaustive search approach that is very well-suited for parallelization on modern GPUs. Our proposed algorithm, Direct Semi-Exhaustive Search (DSES), iterates over potential rotation matrices and efficiently computes the inlier-maximizing translation associated with each rotation. It then computes the optimal rigid transformation based on any desired distance metric by directly computing the error associated with each transformation candidate . By leveraging the parallelism of modern GPUs, DSES outperforms state-of-the-art methods for partial-to-full point cloud registration on the simulated ModelNet40 benchmark and demonstrates high performance and robustness for pose estimation on a real-world robotics problem (https://youtu.be/q0q2-s2KSuA).

Paper Structure

This paper contains 15 sections, 2 theorems, 11 equations, 4 figures, 3 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Classical Registration Methods
  4. Learning-based Registration Methods
  5. Problem Setup
  6. Our Method
  7. Pure Exhaustive Search
  8. Direct Semi-Exhaustive Search (DSES)
  9. Results
  10. ModelNet40 Experiments
  11. Real-World Robot Pose Estimation
  12. Conclusion
  13. Appendix
  14. Proof of Lemma 2
  15. Proof of Theorem 3

Key Result

Lemma 2

Suppose that no points within X are the same, and that no points within Y are the same. Then the optimal solution to eq:translation_optimization is

Figures (4)

  • Figure 1: Pictoral description of Algorithm \ref{['alg:boo']}.
  • Figure 2: (Top) Plot of computation time versus rotation range, given a translation range of $\pm0.2$m. (Bottom) Plot of computation time versus translation range, given a rotation range of $\pm45^\circ$.
  • Figure 3: Image of the robot described in Section \ref{['sec:tool_pose_correction']} picking up a jug from a grocery shelf, after using DSES to correct the gripper pose.
  • Figure 4: Reference arm tip point cloud (black) vs. observed arm tip point cloud (red) both (a) before pose alignment, (b) after pose alignment with DSES. While the pose delta is small, this difference impacts success of the resulting grasp.

Theorems & Definitions (3)

  • Remark 1
  • Lemma 2
  • Theorem 3