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What is the definition of loop closure in Graph Slam?

Ref: Graph Slam

The theory of Graph Slam define here but I think there is no hints about loop closure. I give this reference for review purpose.

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The GraphSLAM algorithm from the paper you linked does not have a loop closure mechanism in the sense of a dedicated procedure for finding correspondences between landmarks observed at different nodes separated by an arbitrary distance/time interval. GraphSLAM effectively tests every non-corresponding pair of features/landmarks in turn to look for new correspondences.

If it seems inefficient, note that it is an offline SLAM algorithm: its purpose is to estimate the posterior probability over the entire path along with the map, instead of just the current pose. Offline algorithms are typically less concerned with computational or memory constraints as they can sometimes run on more powerful computers and can take longer to run.

The paper also notes just above the algorithm (Table 10) that "The inner loop of this algorithm can be made more efficient by selective probing of feature pairs m_j, m_k, [...]". Such a 'selective probing' would - at least naively - be done using some form of nearest neighbour search to test 'close' features before 'far' features for correspondence. It still wouldn't be a dedicated procedure so I wouldn't call it 'Loop closure', but it gets closer to the idea.

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