Metadata-Version: 2.4
Name: euclidean_hausdorff
Version: 1.3.2
Summary: quick approximation of the Gromov–Hausdorff distance restricted to Euclidean isometries
Project-URL: Homepage, https://github.com/bcecil2/euclidean_hausdorff
Project-URL: Issues, https://github.com/bcecil2/euclidean_hausdorff/issues
Author: Blake Cecil
Author-email: Vladyslav Oles <vlad.oles@proton.me>
License: The MIT License (MIT)
        
        Copyright (c) 2023 Vladyslav Oles (vlad.oles@proton.me), Blake Cecil
        
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License-File: LICENSE
Classifier: License :: OSI Approved :: MIT License
Classifier: Operating System :: OS Independent
Classifier: Programming Language :: Python :: 3
Requires-Python: >=3.9
Requires-Dist: numpy>=1.26.4
Requires-Dist: scipy>=1.12.0
Requires-Dist: sortedcontainers>=2.4.0
Description-Content-Type: text/markdown

# 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 Euclidean–Hausdorff distance (which itself is a relaxation and an upper bound of the Gromov–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.