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Symmetry, Integrability and Geometry: Methods and Applications, 2020, Volume 16, 093, 22 pp.
DOI: https://doi.org/10.3842/SIGMA.2020.093 (Mi sigma1630) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Feature Matching and Heat Flow in Centro-Affine Geometry

Peter J. Olvera, Changzheng Qub, Yun Yangc

a School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA
b School of Mathematics and Statistics, Ningbo University, Ningbo 315211, P.R. China
c Department of Mathematics, Northeastern University, Shenyang, 110819, P.R. China
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DOI: https://doi.org/10.3842/SIGMA.2020.093
Abstract: 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.
Keywords: centro-affine geometry, equivariant moving frames, heat flow, inviscid Burgers' equation, differential invariant, edge matching.
Funding agency Grant number
National Natural Science Foundation of China 11631007
11971251
The work of C.Z. Qu is supported by the NSF-China grant-11631007 and grant-11971251.
Received: April 2, 2020; in final form September 14, 2020; Published online September 29, 2020
Bibliographic databases:
Document Type: Article
MSC: 53A15, 53A55
Language: English
Citation: Peter J. Olver, Changzheng Qu, Yun Yang, “Feature Matching and Heat Flow in Centro-Affine Geometry”, SIGMA, 16 (2020), 093, 22 pp.
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
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