An algebraic approach to symmetry detection

Yosi Keller; Yoel Shkolnisky

doi:10.1109/icpr.2004.1334499

An algebraic approach to symmetry detection

Yosi Keller, Yoel Shkolnisky

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

23 Scopus citations

Abstract

We present an algorithm for detecting cyclic and dihedral symmetries of an object. Both symmetry types can be detected by the special patterns they generate in the object's Fourier transform. These patterns are effectively detected and analyzed using the "angular difference function" (ADF), which measures the difference in the angular content of images. The ADF is accurately computed by using the pseudo-polar Fourier transform, which rapidly computes the Fourier transform of an object on a near-polar grid. The algorithm detects all the axes of centered and non-centered symmetries. The proposed algorithm is algebraically accurate and uses no interpolations.

Original language	English
Title of host publication	Proceedings of the 17th International Conference on Pattern Recognition, ICPR 2004
Editors	J. Kittler, M. Petrou, M. Nixon
Pages	186-189
Number of pages	4
DOIs	https://doi.org/10.1109/icpr.2004.1334499
State	Published - 2004
Externally published	Yes
Event	Proceedings of the 17th International Conference on Pattern Recognition, ICPR 2004 - Cambridge, United Kingdom Duration: 23 Aug 2004 → 26 Aug 2004

Publication series

Name	Proceedings - International Conference on Pattern Recognition
Volume	3
ISSN (Print)	1051-4651

Conference

Conference	Proceedings of the 17th International Conference on Pattern Recognition, ICPR 2004
Country/Territory	United Kingdom
City	Cambridge
Period	23/08/04 → 26/08/04

Access to Document

10.1109/icpr.2004.1334499

Cite this

@inproceedings{dd4f45c8b04b4e3bb5c4007b4c30857b,

title = "An algebraic approach to symmetry detection",

abstract = "We present an algorithm for detecting cyclic and dihedral symmetries of an object. Both symmetry types can be detected by the special patterns they generate in the object's Fourier transform. These patterns are effectively detected and analyzed using the {"}angular difference function{"} (ADF), which measures the difference in the angular content of images. The ADF is accurately computed by using the pseudo-polar Fourier transform, which rapidly computes the Fourier transform of an object on a near-polar grid. The algorithm detects all the axes of centered and non-centered symmetries. The proposed algorithm is algebraically accurate and uses no interpolations.",

author = "Yosi Keller and Yoel Shkolnisky",

year = "2004",

doi = "10.1109/icpr.2004.1334499",

language = "אנגלית",

isbn = "0769521282",

series = "Proceedings - International Conference on Pattern Recognition",

pages = "186--189",

editor = "J. Kittler and M. Petrou and M. Nixon",

booktitle = "Proceedings of the 17th International Conference on Pattern Recognition, ICPR 2004",

note = "Proceedings of the 17th International Conference on Pattern Recognition, ICPR 2004 ; Conference date: 23-08-2004 Through 26-08-2004",

}

Keller, Y & Shkolnisky, Y 2004, An algebraic approach to symmetry detection. in J Kittler, M Petrou & M Nixon (eds), Proceedings of the 17th International Conference on Pattern Recognition, ICPR 2004. Proceedings - International Conference on Pattern Recognition, vol. 3, pp. 186-189, Proceedings of the 17th International Conference on Pattern Recognition, ICPR 2004, Cambridge, United Kingdom, 23/08/04. https://doi.org/10.1109/icpr.2004.1334499

An algebraic approach to symmetry detection. / Keller, Yosi; Shkolnisky, Yoel.
Proceedings of the 17th International Conference on Pattern Recognition, ICPR 2004. ed. / J. Kittler; M. Petrou; M. Nixon. 2004. p. 186-189 (Proceedings - International Conference on Pattern Recognition; Vol. 3).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - An algebraic approach to symmetry detection

AU - Keller, Yosi

AU - Shkolnisky, Yoel

PY - 2004

Y1 - 2004

N2 - We present an algorithm for detecting cyclic and dihedral symmetries of an object. Both symmetry types can be detected by the special patterns they generate in the object's Fourier transform. These patterns are effectively detected and analyzed using the "angular difference function" (ADF), which measures the difference in the angular content of images. The ADF is accurately computed by using the pseudo-polar Fourier transform, which rapidly computes the Fourier transform of an object on a near-polar grid. The algorithm detects all the axes of centered and non-centered symmetries. The proposed algorithm is algebraically accurate and uses no interpolations.

AB - We present an algorithm for detecting cyclic and dihedral symmetries of an object. Both symmetry types can be detected by the special patterns they generate in the object's Fourier transform. These patterns are effectively detected and analyzed using the "angular difference function" (ADF), which measures the difference in the angular content of images. The ADF is accurately computed by using the pseudo-polar Fourier transform, which rapidly computes the Fourier transform of an object on a near-polar grid. The algorithm detects all the axes of centered and non-centered symmetries. The proposed algorithm is algebraically accurate and uses no interpolations.

UR - http://www.scopus.com/inward/record.url?scp=10044264081&partnerID=8YFLogxK

U2 - 10.1109/icpr.2004.1334499

DO - 10.1109/icpr.2004.1334499

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

AN - SCOPUS:10044264081

SN - 0769521282

T3 - Proceedings - International Conference on Pattern Recognition

SP - 186

EP - 189

BT - Proceedings of the 17th International Conference on Pattern Recognition, ICPR 2004

A2 - Kittler, J.

A2 - Petrou, M.

A2 - Nixon, M.

T2 - Proceedings of the 17th International Conference on Pattern Recognition, ICPR 2004

Y2 - 23 August 2004 through 26 August 2004

ER -

An algebraic approach to symmetry detection

Abstract

Publication series

Conference

Access to Document

Other files and links

Fingerprint

Cite this