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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
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.
Received: April 2, 2020; in final form September 14, 2020; Published online September 29, 2020
Citation:
Peter J. Olver, Changzheng Qu, Yun Yang, “Feature Matching and Heat Flow in Centro-Affine Geometry”, SIGMA, 16 (2020), 093, 22 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1630 https://www.mathnet.ru/eng/sigma/v16/p93
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