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Many robotics applications require alignment and fusion of observationsobtained at multiple views to form a global model of the environment. Multi-waydata association methods provide a mechanism to improve alignment accuracy ofpairwise associations and ensure their consistency. However, existing methodsthat solve this computationally challenging problem are often too slow forreal-time applications. Furthermore, some of the existing techniques canviolate the cycle consistency principle, thus drastically reducing the fusionaccuracy. This work presents the CLEAR (Consistent Lifting, Embedding, andAlignment Rectification) algorithm to address these issues. By leveraginginsights from the multi-way matching and spectral graph clustering literature,CLEAR provides cycle consistent and accurate solutions in a computationallyefficient manner. Numerical experiments on both synthetic and real datasets arecarried out to demonstrate the scalability and superior performance of ouralgorithm in real-world problems. This algorithmic framework can providesignificant improvement in the accuracy and efficiency of existing discreteassignment problems, which traditionally use pairwise (but potentiallyinconsistent) correspondences. An implementation of CLEAR is made publiclyavailable online.

CLEAR: A Consistent Lifting, Embedding, and Alignment Rectification Algorithm for Multi-View Data Association