CLIPPER: Robust Data Association without an Initial Guess

TL;DR

This paper addresses robust data association without a reliable initial guess by formulating a weighted consistency-graph problem called the densest edge-weighted clique (DEWC). It develops two practical relaxations: a convex semidefinite relaxation (MSRC-SDR) that can certify global optimality under a rank condition, and CLIPPER, a fast first-order algorithm that yields near-optimal solutions in milliseconds. The core contribution is a cohesive framework—DEWC, MSRC, and CLIPPER—along with empirical validation on point cloud registration datasets (e.g., Stanford Bunny, 3DMatch) showing superior precision and dramatic speed improvements in high-outlier regimes. The approach enables robust data association even when no informative initial guess is available, with potential applicability to a range of robotics perception problems beyond registration.

Abstract

Identifying correspondences in noisy data is a critically important step in estimation processes. When an informative initial estimation guess is available, the data association challenge is less acute; however, the existence of a high-quality initial guess is rare in most contexts. We explore graph-theoretic formulations for data association, which do not require an initial estimation guess. Existing graph-theoretic approaches optimize over unweighted graphs, discarding important consistency information encoded in weighted edges, and frequently attempt to solve NP-hard problems exactly. In contrast, we formulate a new optimization problem that fully leverages weighted graphs and seeks the densest edge-weighted clique. We introduce two relaxations to this problem: a convex semidefinite relaxation which we find to be empirically tight, and a fast first-order algorithm called CLIPPER which frequently arrives at nearly-optimal solutions in milliseconds. When evaluated on point cloud registration problems, our algorithms remain robust up to at least 95% outliers while existing algorithms begin breaking down at 80% outliers. Code is available at https://mit-acl.github.io/clipper.

Figures (4)

• Figure 1: Consistency graph construction example for point cloud registration. (a) Putative associations $u_1, \dots, u_5\in\mathcal{A}$ are given between red and blue point clouds. (b) The consistency graph $\mathcal{G}$ with vertices representing the associations and edges between two vertices indicating their geometric consistency. In the noiseless case, any two associations $u_i,u_j$ mapping points $p_i,p_j$ to $q_i,q_j$ are consistent if $\delta=0$, where $\delta\mathrel{:=}\|p_i-p_j\| - \|q_i-q_j\|$. The correct associations are colored green. (c) Edges of the consistency graph are weighted according to the pairwise consistency score function $s(\delta)$. If $\delta>\epsilon$ or if two associations start/end at the same point, the association pair is deemed inconsistent. (d) The affinity matrix $M$ is the numerical representation of the consistency graph $\mathcal{G}$.
• Figure 2: Point cloud registration in high-outlier/low-inlier regimes. The low registration error and high precision of DEWC* and MSRC-SDR* solutions arise by fully leveraging the weights of the consistency graph. CLIPPER relaxes these NP-hard problems and retains high precision and low registration error while being orders of magnitude faster. The low absolute difference of objective values compared to DEWC* indicates that CLIPPER frequently arrives at near-optimal solutions, while DS*, SM, SCGP fail in high outlier regimes due to the violation of the clique constraint (indicated by hash marks).
• Figure 3: Average registration error, precision, and recall of successful registrations ($t_\mathrm{err}\leq30cm$ and $R_\mathrm{err}\leq15\deg$) from the eight 3DMatch datasets. Not only does CLIPPER enable the most successful registrations (cf. Table \ref{['tbl:3dmatch']}), but it also produces the lowest registration error. This is due to its ability to achieve high precision, even in high outlier regimes. Because CLIPPER selects a high-precision set of correspondences, GNC does little to improve its performance.
• Figure 4: Scalability results. MSRC*, DEWC*, MSRC-SDR, and DS* had to be early stopped, indicated via the symbol .