Sparse Optimization for Robust and Efficient Loop Closing
This addresses the need for robust and efficient loop closing in long-term visual navigation for robots, representing an incremental improvement over existing methods.
The paper tackles the problem of loop-closure detection in robot navigation by formulating it as a sparse convex optimization problem, enabling real-time operation without offline dictionary learning and achieving efficient matching with a unique globally optimal decision.
It is essential for a robot to be able to detect revisits or loop closures for long-term visual navigation.A key insight explored in this work is that the loop-closing event inherently occurs sparsely, that is, the image currently being taken matches with only a small subset (if any) of previous images. Based on this observation, we formulate the problem of loop-closure detection as a sparse, convex $\ell_1$-minimization problem. By leveraging fast convex optimization techniques, we are able to efficiently find loop closures, thus enabling real-time robot navigation. This novel formulation requires no offline dictionary learning, as required by most existing approaches, and thus allows online incremental operation. Our approach ensures a unique hypothesis by choosing only a single globally optimal match when making a loop-closure decision. Furthermore, the proposed formulation enjoys a flexible representation with no restriction imposed on how images should be represented, while requiring only that the representations are "close" to each other when the corresponding images are visually similar. The proposed algorithm is validated extensively using real-world datasets.