Interesting review of approaches to visually detect loop closings in robotics, and a novel, very efficient method that is independent on the image representation and based on not using the typical l2 norm (least squares), which leads to dense optimization problems

Yasir Latif, Guoquan Huang, John Leonard, José Neira, Sparse optimization for robust and efficient loop closing, Robotics and Autonomous Systems, Volume 93, July 2017, Pages 13-26, ISSN 0921-8890,DOI: 10.1016/j.robot.2017.03.016.

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, i.e., 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
ℓ 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.