When evaluating the performance of a SLAM algorithm, quantifying the produced map quality is one of the most important criteria. Often, the produced map is compared with (1) a ground-truth map (which can be easily obtained in simulation) or (2) with another existing map that is considered accurate (in case of real world experiment where the ground-truth is not always available ).
Basically, grid maps are images, so image similarity measurement metrics can be used in this case. In this post, we consider three different metrics: Mean Square Error (MSE), K-nearest based normalized error (NE) and Structure Similarity Index (SSIM)