CLIPPER: A Graph-Theoretic Framework for Robust Data Association (2011.10202v2)

Abstract: We present CLIPPER (Consistent LInking, Pruning, and Pairwise Error Rectification), a framework for robust data association in the presence of noise and outliers. We formulate the problem in a graph-theoretic framework using the notion of geometric consistency. State-of-the-art techniques that use this framework utilize either combinatorial optimization techniques that do not scale well to large-sized problems, or use heuristic approximations that yield low accuracy in high-noise, high-outlier regimes. In contrast, CLIPPER uses a relaxation of the combinatorial problem and returns solutions that are guaranteed to correspond to the optima of the original problem. Low time complexity is achieved with an efficient projected gradient ascent approach. Experiments indicate that CLIPPER maintains a consistently low runtime of 15 ms where exact methods can require up to 24 s at their peak, even on small-sized problems with 200 associations. When evaluated on noisy point cloud registration problems, CLIPPER achieves 100% precision and 98% recall in 90% outlier regimes while competing algorithms begin degrading by 70% outliers. In an instance of associating noisy points of the Stanford Bunny with 990 outlier associations and only 10 inlier associations, CLIPPER successfully returns 8 inlier associations with 100% precision in 138 ms. Code is available at https://mit-acl.github.io/clipper.

• The paper introduces CLIPPER, a graph-theoretic method that robustly addresses data association challenges in high-noise and high-outlier robotic environments.
• Its methodology relaxes the combinatorial problem into a continuous optimization solved via a projected gradient ascent to efficiently extract the densest subgraph.
• Empirical results demonstrate 100% precision in scenarios with up to 90% outliers and processing times around 15 ms, outperforming conventional algorithms.

Understanding CLIPPER: A Graph-Theoretic Framework for Robust Data Association

The paper presents CLIPPER (Consistent LInking, Pruning, and Pairwise Error Rectification), a novel approach for solving data association problems in environments rife with noise and outliers. This method is grounded in a graph-theoretic framework that hinges on the geometric consistency of associations, addressing the limitations inherent in contemporary techniques that struggle to balance scalability and accuracy in adverse conditions.

Problem and Context

Data association, a pertinent challenge in robotics, involves matching correspondences between sets of objects derived from sensory data, such as point clouds, in an unstructured and noisy environment. Traditional methods, grounded in linear assignment algorithms like the Hungarian or auction algorithms, are ill-equipped to maintain resilience under high noise and outlier conditions. CLIPPER aims to offer a robust alternative by utilizing the geometric relationships in the data sets within a graph-theoretic model.

Technical Formulation

CLIPPER leverages a graph representation where vertices signify potential associations and edges denote geometric consistency. The core objective is to identify the densest subgraph of these associations, which translates to finding the set of correspondences least affected by noise and outliers. The traditional maximum clique problem (MCP) is inadequately equipped for such scenarios, especially when one needs to consider weighted graphs where degrees of consistency vary.

Methodology

The framework structures the problem as an optimization challenge, relaxing the constraints via a continuous formulation suited for weighted graphs. This approach avoids NP-hard complexity in its entirety while converging efficiently on a solution that scales with problem size. The use of a projected gradient ascent algorithm permits low computational overhead, securing real-time performance across various problem dimensions and densities.

CLIPPER’s process can be outlined in two primary phases:

1. Solving the Relaxed Optimization: By relaxing the hard combinatorial problem into a continuous domain, CLIPPER utilizes projected gradient ascent to rapidly converge upon a plausible solution.
2. Extracting the Densest Subgraph: The final stage involves interpreting the relaxed solution to effectively determine the subset of associations forming the densest subgraph, thus actualizing the optimal correspondences.

Numerical Results and Implications

The authors report convincingly on CLIPPER’s performance, demonstrating its efficiency in synthetic data association scenarios compared to leading edge algorithms like PMC and the methods by Leordeanu and Belachew. Of particular note, CLIPPER maintains 100% precision even in regimes encountering 90% outliers, a precision threshold unmet by many competitors at similar outlier levels.

Additionally, its computational efficiency, operating consistently around 15 ms, allows it to be readily deployed in applications where decisions must be made on the fly, such as in simultaneous localization and mapping (SLAM) or in multi-object tracking. This positions CLIPPER as a flexible tool adaptable to a diverse set of robotic perception problems, simplifying the construction of consistency graphs from different data types such as lines, planes, and point clouds.

Future Directions

While CLIPPER effectively balances precision and runtime trade-offs across various scenarios, further work might explore its application across broader domains or integrate additional geometric priors to further enhance robustness under even steeper noise and outlier conditions. Future research could also investigate tighter integration with machine learning methods for learning association priors dynamically from data, potentially enhancing its scope and applicability in evolving environments.

In summary, CLIPPER advances the field of robust data association by providing a scalable, precise, and computationally agile framework that adapitates to the challenges posed by high-noise environments, making it an advantageous alternative for researchers looking to implement resilient robotic systems.