| Name | euclidean-hausdorff JSON |
| Version |
1.3.1
JSON |
| download |
| home_page | None |
| Summary | quick approximation of the Gromov–Hausdorff distance restricted to Euclidean isometries |
| upload_time | 2024-10-31 07:11:48 |
| maintainer | None |
| docs_url | None |
| author | Blake Cecil |
| requires_python | >=3.9 |
| license | The MIT License (MIT) Copyright (c) 2023 Vladyslav Oles (vlad.oles@proton.me), Blake Cecil Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. |
| keywords |
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| VCS |
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| bugtrack_url |
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| requirements |
No requirements were recorded.
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| Travis-CI |
No Travis.
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| coveralls test coverage |
No coveralls.
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# 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.
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"description": "# euclidean-hausdorff\n\nGiven the coordinates of 2- or 3-dimensional point clouds $A, B \\subset \\mathbb{R}^k$ (where $k \\in \\{2, 3\\}$), estimates their Euclidean\u2013Hausdorff distance (which itself is a relaxation and an upper bound of the Gromov\u2013Hausdorff distance)\n\n$$d_\\text{EH}(X, Y) = \\inf_{T:E(k)} d_\\text{H}(T(A), B),$$\n\nwhere the infimum is taken over all $k$-dimensional Euclidean isometries and $d_\\text{H}$ is the Hausdorff distance in $\\mathbb{R}^k$.\n\nThe 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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