Affine Invariant Geometry for Non-rigid Shapes
Shape recognition deals with the study geometric structures. Modern surface processing methods can cope with non-rigidity—by measuring the lack of isometry, deal with similarity or scaling—by multiplying the Euclidean arc-length by the Gaussian curvature, and manage equi-affine transformations—by re...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer US
2016
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| Online Access: | http://hdl.handle.net/1721.1/103333 https://orcid.org/0000-0003-3254-2050 |
| _version_ | 1826200512076185600 |
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| author | Raviv, Dan Kimmel, Ron |
| author2 | Massachusetts Institute of Technology. Media Laboratory |
| author_facet | Massachusetts Institute of Technology. Media Laboratory Raviv, Dan Kimmel, Ron |
| author_sort | Raviv, Dan |
| collection | MIT |
| description | Shape recognition deals with the study geometric structures. Modern surface processing methods can cope with non-rigidity—by measuring the lack of isometry, deal with similarity or scaling—by multiplying the Euclidean arc-length by the Gaussian curvature, and manage equi-affine transformations—by resorting to the special affine arc-length definition in classical equi-affine differential geometry. Here, we propose a computational framework that is invariant to the full affine group of transformations (similarity and equi-affine). Thus, by construction, it can handle non-rigid shapes. Technically, we add the similarity invariant property to an equi-affine invariant one and establish an affine invariant pseudo-metric. As an example, we show how diffusion geometry can encapsulate the proposed measure to provide robust signatures and other analysis tools for affine invariant surface matching and comparison. |
| first_indexed | 2024-09-23T11:37:36Z |
| format | Article |
| id | mit-1721.1/103333 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T11:37:36Z |
| publishDate | 2016 |
| publisher | Springer US |
| record_format | dspace |
| spelling | mit-1721.1/1033332022-10-01T04:55:45Z Affine Invariant Geometry for Non-rigid Shapes Raviv, Dan Kimmel, Ron Massachusetts Institute of Technology. Media Laboratory Raviv, Dan Shape recognition deals with the study geometric structures. Modern surface processing methods can cope with non-rigidity—by measuring the lack of isometry, deal with similarity or scaling—by multiplying the Euclidean arc-length by the Gaussian curvature, and manage equi-affine transformations—by resorting to the special affine arc-length definition in classical equi-affine differential geometry. Here, we propose a computational framework that is invariant to the full affine group of transformations (similarity and equi-affine). Thus, by construction, it can handle non-rigid shapes. Technically, we add the similarity invariant property to an equi-affine invariant one and establish an affine invariant pseudo-metric. As an example, we show how diffusion geometry can encapsulate the proposed measure to provide robust signatures and other analysis tools for affine invariant surface matching and comparison. United States. Office of Naval Research (award N00014-12-1-0517) Israel Science Foundation (Grant Number 1031/120 2016-06-24T18:30:36Z 2016-06-24T18:30:36Z 2014-06 2012-02 2016-05-23T12:14:36Z Article http://purl.org/eprint/type/JournalArticle 0920-5691 1573-1405 http://hdl.handle.net/1721.1/103333 Raviv, Dan, and Ron Kimmel. “Affine Invariant Geometry for Non-Rigid Shapes.” Int J Comput Vis 111, no. 1 (June 14, 2014): 1–11. https://orcid.org/0000-0003-3254-2050 en http://dx.doi.org/10.1007/s11263-014-0728-2 International Journal of Computer Vision Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. Springer Science+Business Media New York application/pdf Springer US Springer US |
| spellingShingle | Raviv, Dan Kimmel, Ron Affine Invariant Geometry for Non-rigid Shapes |
| title | Affine Invariant Geometry for Non-rigid Shapes |
| title_full | Affine Invariant Geometry for Non-rigid Shapes |
| title_fullStr | Affine Invariant Geometry for Non-rigid Shapes |
| title_full_unstemmed | Affine Invariant Geometry for Non-rigid Shapes |
| title_short | Affine Invariant Geometry for Non-rigid Shapes |
| title_sort | affine invariant geometry for non rigid shapes |
| url | http://hdl.handle.net/1721.1/103333 https://orcid.org/0000-0003-3254-2050 |
| work_keys_str_mv | AT ravivdan affineinvariantgeometryfornonrigidshapes AT kimmelron affineinvariantgeometryfornonrigidshapes |