Feature matching and heat flow in Centro-affine geometry

Peter J. Olver, Changzheng Qu, Yun Yang

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Article number093
Pages (from-to)1-22
Number of pages22
JournalSymmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume16
DOIs
StatePublished - 2020

Bibliographical note

Funding Information:
The authors thank the referees for their valuable comments and suggestions. C.Z. Qu is supported by the NSF-China grant-11631007 and grant-11971251. The work of.

Funding Information:
The authors thank the referees for their valuable comments and suggestions. C.Z. Qu is supported by the NSF-China grant-11631007 and grant-11971251.

Publisher Copyright:
© 2020, Institute of Mathematics. All rights reserved.

Keywords

  • Centro-affine geometry
  • Differential invariant
  • Edge matching
  • Equivariant moving frames
  • Heat flow
  • Inviscid Burgers’ equation

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