Feature matching and heat flow in Centro-affine geometry

Peter J. Olver; Changzheng Qu; Yun Yang

doi:10.3842/SIGMA.2020.093

Feature matching and heat flow in Centro-affine geometry

Peter J. Olver, Changzheng Qu, Yun Yang

Mathematics

Research output: Contribution to journal › Article › peer-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 language	English (US)
Article number	093
Pages (from-to)	1-22
Number of pages	22
Journal	Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume	16
DOIs	https://doi.org/10.3842/SIGMA.2020.093
State	Published - 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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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{\textquoteright} 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, Differential invariant, Edge matching, Equivariant moving frames, Heat flow, Inviscid Burgers{\textquoteright} equation",

author = "Olver, {Peter J.} and Changzheng Qu and Yun Yang",

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language = "English (US)",

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Feature matching and heat flow in Centro-affine geometry

Abstract

Bibliographical note

Keywords

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