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

School of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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
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

Publisher link

10.3842/SIGMA.2020.093

Find It

Find It at U of M Libraries

Cite this

@article{119b49b1d5224b5b9499a7ab355fd159,

title = "Feature matching and heat flow in Centro-affine geometry",

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",

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: {\textcopyright} 2020, Institute of Mathematics. All rights reserved.",

year = "2020",

doi = "10.3842/SIGMA.2020.093",

language = "English (US)",

volume = "16",

journal = "Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)",

issn = "1815-0659",

publisher = "Department of Applied Research, Institute of Mathematics of National Academy of Science of Ukraine",

}

TY - JOUR

T1 - Feature matching and heat flow in Centro-affine geometry

AU - Olver, Peter J.

AU - Qu, Changzheng

AU - Yang, Yun

N1 - 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.

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

KW - Centro-affine geometry

KW - Differential invariant

KW - Edge matching

KW - Equivariant moving frames

KW - Heat flow

KW - Inviscid Burgers’ equation

UR - http://www.scopus.com/inward/record.url?scp=85092406581&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85092406581&partnerID=8YFLogxK

U2 - 10.3842/SIGMA.2020.093

DO - 10.3842/SIGMA.2020.093

M3 - Article

AN - SCOPUS:85092406581

VL - 16

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

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

SN - 1815-0659

M1 - 093

ER -

Feature matching and heat flow in Centro-affine geometry

Abstract

Bibliographical note

Keywords

Publisher link

Find It

Other files and links

Fingerprint

Cite this