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I have read some about loop closure and I am somewhat confused.

Suppose we implement something like EKF slam using LIDAR and suppose loop closure is aided by computer vision based features so that if it re-visits a location, it can detect where it is.

What's not clear to me is how the map prior to loop closure is actually updated once proper loop closure is detected.

For example, this image shows the covariance matrix prior to vision based loop closure:

enter image description here

And after closure:

enter image description here

What is normally the actual process to modify the map once closure is detected so everything lines up? What kinds of fundamental assumptions are made to make it work? For example, in this case it appears you need to be confident that straight-looking walls are actually straight.

The images were pulled from this old SLAM paper:

http://www.robots.ox.ac.uk/~pnewman/papers/NewmanHoICRA05.pdf

I think the most interesting thing is actually back-propagating the probability of states given the closure constraint which it completely ignores.

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