# euclidean-hausdorff Given the coordinates of 2- or 3-dimensional point clouds $A, B \subset \mathbb{R}^k$ (where $k \in \{2, 3\}$), estimates their Euclideanâ€“Hausdorff distance (which itself is a relaxation and an upper bound of the Gromovâ€“Hausdorff distance) $$d_\text{EH}(X, Y) = \inf_{T:E(k)} d_\text{H}(T(A), B),$$ where the infimum is taken over all $k$-dimensional Euclidean isometries and $d_\text{H}$ is the Hausdorff distance in $\mathbb{R}^k$. The distance is estimated from above by discretizing the compact feasible region (of the above minimization) into a search grid, whose vertices each represent a combination of some translation, rotation, and reflection.

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