TEASER: Fast and Certifiable Point Cloud Registration (2001.07715v2)

Abstract: We propose the first fast and certifiable algorithm for the registration of two sets of 3D points in the presence of large amounts of outlier correspondences. We first reformulate the registration problem using a Truncated Least Squares (TLS) cost that is insensitive to a large fraction of spurious correspondences. Then, we provide a general graph-theoretic framework to decouple scale, rotation, and translation estimation, which allows solving in cascade for the three transformations. Despite the fact that each subproblem is still non-convex and combinatorial in nature, we show that (i) TLS scale and (component-wise) translation estimation can be solved in polynomial time via adaptive voting, (ii) TLS rotation estimation can be relaxed to a semidefinite program (SDP) and the relaxation is tight, even in the presence of extreme outlier rates, and (iii) the graph-theoretic framework allows drastic pruning of outliers by finding the maximum clique. We name the resulting algorithm TEASER (Truncated least squares Estimation And SEmidefinite Relaxation). While solving large SDP relaxations is typically slow, we develop a second fast and certifiable algorithm, named TEASER++, that uses graduated non-convexity to solve the rotation subproblem and leverages Douglas-Rachford Splitting to efficiently certify global optimality. For both algorithms, we provide theoretical bounds on the estimation errors, which are the first of their kind for robust registration problems. Moreover, we test their performance on standard, object detection, and the 3DMatch benchmarks, and show that (i) both algorithms dominate the state of the art and are robust to more than 99% outliers, (ii) TEASER++ can run in milliseconds, and (iii) TEASER++ is so robust it can also solve problems without correspondences, where it largely outperforms ICP and it is more accurate than Go-ICP while being orders of magnitude faster.

• The paper introduces TEASER, a certifiable approach that decouples registration into distinct scale, rotation, and translation estimation tasks.
• It employs truncated least squares and convex semidefinite programming relaxation to achieve global optimality even with extreme outlier contamination.
• The TEASER++ implementation demonstrates real-time efficiency and sets a new standard for robust 3D registration in robotics and computer vision.

Essay on "TEASER: Fast and Certifiable Point Cloud Registration"

The paper "TEASER: Fast and Certifiable Point Cloud Registration" addresses a fundamental problem in robotics and computer vision: the alignment of two sets of 3D points, or point cloud registration, in the presence of significant outlier correspondences. The authors introduce TEASER, a fast and certifiable solution capable of handling extreme outlier rates that often arise in real-world applications.

Approach and Contributions

The work presents a novel methodology combining Truncated Least Squares (TLS) estimation with semidefinite programming (SDP) relaxation to achieve certifiably global optimality. The algorithm decouples the complex, non-convex registration problem into manageable subproblems: scale, rotation, and translation estimation. Each subproblem is tackled using distinct techniques:

1. Robust Scale Estimation: The authors introduce Translation and Rotation Invariant Measurements (TRIMs) to make the scale estimation invariant to these transformations. The estimation problem is then efficiently solved using an adaptive voting scheme analogous to histogram voting but optimized for robustness to outliers.
2. Robust Rotation Estimation: Employing a quaternion parameterization, the problem is transformed into a Quadratically Constrained Quadratic Program (QCQP), which is subsequently relaxed into a convex SDP. This tight relaxation permits the certification of global optimality for the estimated rotation, even in the presence of severe outlier contamination.
3. Robust Translation Estimation: Translation estimation is performed using a component-wise TLS approach, greatly simplifying the problem while retaining robustness to outliers.

A key component of the TEASER pipeline is the Maximum Clique Inlier Selection (MCIS) framework, which uses graph-theoretic structures to prune outliers effectively by identifying cliques that correspond to consistent inlier sets.

Numerical Results

The paper provides strong numerical evidence for TEASER's robustness and efficiency. It consistently outperforms classical and contemporary methods such as RANSAC, Fast Global Registration, and Guaranteed Outlier Removal, particularly under high outlier rates exceeding 90%. Notably, TEASER++—the optimized implementation—achieves real-time performance, solving registration tasks in milliseconds while maintaining robustness against outlier ratios above 99%.

Theoretical Implications

The work lays a foundation for certifiable perception in robotics, offering guarantees about the optimality of solutions. Theoretical analysis presents bounds on the estimation errors for each subproblem, making TEASER the first approach in robust registration to provide such theoretical performance guarantees.

Practical Implications and Future Directions

The release of TEASER++ as an open-source library provides a practical tool for robotics and computer vision practitioners requiring robust and reliable registration even in challenging environments. The contributions extend beyond point cloud registration, pointing towards applications in motion estimation, object localization, and 3D reconstruction.

Future work could explore certifiable algorithms for broader perception tasks. Additionally, integration with deep learning methods could enhance robustness to descriptor mismatch and improve outlier rejection capabilities.

The paper marks a significant step in point cloud registration, offering robust performance without sacrificing computational efficiency, setting a new standard for 3D registration tasks in both theory and practice.