Feature Matching and Heat Flow in Centro-Affine Geometry

Symmetry Integrability and Geometry-Methods and Applications

article

Peter J. Olver¹  Changzheng Qu²  Yun Yang³ 

[1] School of Mathematics, University of Minnesota;School of Mathematics and Statistics, Ningbo University;Department of Mathematics, Northeastern University

关键词: centro-affine geometry;    equivariant moving frames;    heat flow;    inviscid Burgers’ equation;    differential invariant;    edge matching 2020 Mathematics Subject Classification 53A15;    53A55;   

DOI  :  10.3842/SIGMA.2020.093

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown