Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 16 (2020), 093, 22 pages      arXiv:2003.13842      https://doi.org/10.3842/SIGMA.2020.093

Feature Matching and Heat Flow in Centro-Affine Geometry

Peter J. Olver a, Changzheng Qu b and Yun Yang c
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

Received April 02, 2020, in final form September 14, 2020; Published online September 29, 2020

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.

Key words: centro-affine geometry; equivariant moving frames; heat flow; inviscid Burgers' equation; differential invariant; edge matching.

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