Feature Matching and Heat Flow in Centro-Affine Geometry
In this paper, we study the differential invariants and the invariant heat flow in centro-affine geometry, proving that the latter is equivalent to the inviscid Burgers' equation. Furthermore, we apply the centro-affine invariants to develop an invariant algorithm to match features of objects a...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2020 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2020
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211027 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Feature Matching and Heat Flow in Centro-Affine Geometry. Peter J. Olver, Changzheng Qu and Yun Yang. SIGMA 16 (2020), 093, 22 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859534299651375104 |
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| author | Olver, Peter J. Qu, Changzheng Yang, Yun |
| author_facet | Olver, Peter J. Qu, Changzheng Yang, Yun |
| citation_txt | Feature Matching and Heat Flow in Centro-Affine Geometry. Peter J. Olver, Changzheng Qu and Yun Yang. SIGMA 16 (2020), 093, 22 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In this paper, we study the differential invariants and the invariant heat flow in centro-affine geometry, proving that the latter is equivalent to the inviscid Burgers' equation. Furthermore, we apply the centro-affine invariants to develop an invariant algorithm to match features of objects appearing in images. We show that the resulting algorithm compares favorably with the widely applied scale-invariant feature transform (SIFT), speeded up robust features (SURF), and affine-SIFT (ASIFT) methods.
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| first_indexed | 2026-03-13T08:21:42Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211027 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-13T08:21:42Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Olver, Peter J. Qu, Changzheng Yang, Yun 2025-12-22T09:32:14Z 2020 Feature Matching and Heat Flow in Centro-Affine Geometry. Peter J. Olver, Changzheng Qu and Yun Yang. SIGMA 16 (2020), 093, 22 pages 1815-0659 2020 Mathematics Subject Classification: 53A15; 53A55 arXiv:2003.13842 https://nasplib.isofts.kiev.ua/handle/123456789/211027 https://doi.org/10.3842/SIGMA.2020.093 In this paper, we study the differential invariants and the invariant heat flow in centro-affine geometry, proving that the latter is equivalent to the inviscid Burgers' equation. Furthermore, we apply the centro-affine invariants to develop an invariant algorithm to match features of objects appearing in images. We show that the resulting algorithm compares favorably with the widely applied scale-invariant feature transform (SIFT), speeded up robust features (SURF), and affine-SIFT (ASIFT) methods. The authors thank the referees for their valuable comments and suggestions. The work of C.Z. Qu is supported by the NSF-China grant-11631007 and grant-11971251. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Feature Matching and Heat Flow in Centro-Affine Geometry Article published earlier |
| spellingShingle | Feature Matching and Heat Flow in Centro-Affine Geometry Olver, Peter J. Qu, Changzheng Yang, Yun |
| title | Feature Matching and Heat Flow in Centro-Affine Geometry |
| title_full | Feature Matching and Heat Flow in Centro-Affine Geometry |
| title_fullStr | Feature Matching and Heat Flow in Centro-Affine Geometry |
| title_full_unstemmed | Feature Matching and Heat Flow in Centro-Affine Geometry |
| title_short | Feature Matching and Heat Flow in Centro-Affine Geometry |
| title_sort | feature matching and heat flow in centro-affine geometry |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211027 |
| work_keys_str_mv | AT olverpeterj featurematchingandheatflowincentroaffinegeometry AT quchangzheng featurematchingandheatflowincentroaffinegeometry AT yangyun featurematchingandheatflowincentroaffinegeometry |