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 @math -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.
It should be noted that in our previous conference publication @cite_29 , we have preliminarily shown that the proposed loop-closing framework is general and can employ most hand-crafted features. Recently, extended this sparse-optimization based framework to an incremental formulation allowing for the use of the previous solution of the sparse optimization to jump start the next one, while further extended it to a multi-step delayed detection of loops (instead of single-step detection as in our prior work @cite_29 ) in order to exploit the structured sparsity of the problem. In this paper, we present more detailed analysis and thorough performance evaluations, including new experiments using deep features and validations in challenging multiple-revisit scenarios, as well as new comparisons against the well-known nearest neighbour (NN) search.
@cite_29
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It is essential for a robot to be able to detect revisits or loop closures for long-term visual navigation. A key insight is that the loop-closing event inherently occurs sparsely, i.e., the image currently being taken matches with only a small subset (if any) of previous observations. Based on this observation, we formulate the problem of loop-closure detection as a sparse, convex 1-minimization problem. By leveraging on 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 global, 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 be close to each other when the corresponding images are visually similar. The proposed algorithm is validated extensively using public real-world datasets.