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Feature Matching and Heat Flow in Centro-Affine Geometry
Symmetry, integrability and geometry: methods and applications, Tome 16 (2020) Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     author = {Peter J. Olver and Changzheng Qu and Yun Yang},
     title = {Feature {Matching} and {Heat} {Flow} in {Centro-Affine} {Geometry}},
     journal = {Symmetry, integrability and geometry: methods and applications},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2020_16_a92/}
}
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Peter J. Olver; Changzheng Qu; Yun Yang. Feature Matching and Heat Flow in Centro-Affine Geometry. Symmetry, integrability and geometry: methods and applications, Tome 16 (2020). http://geodesic.mathdoc.fr/item/SIGMA_2020_16_a92/

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