Detecting grey level symmetry: The frequency domain approach

Yossi Gofman, Nahum Kiryati

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations


Applying symmetry detection algorithms to images after edge detection or segmentation is computationally attractive but potentially inadequate in demanding applications. In this paper a theoretical framework for refiectional symmetry analysis in grey level images is developed. The symmetry of a one dimensional function can be measured in the frequency domain as the fraction of its energy that resides in the symmetric Fourier basis functions. This intuitively appealing approach is extended to two dimensions. It is shown that the Radon transform is a convenient theoretical framework for grey level refiectional symmetry analysis. In particular, the projection-slice theorem unifies symmetry measurement in one and two dimensions and allows to measure refiectional symmetry in a 2-D function directly from its Fourier transform. Finite support computation requires windowing that can be interpreted in terms of the Gabor decomposition. Symmetry measurement in a natural image is demonstrated.

Original languageEnglish
Title of host publicationComputer Analysis of Images and Patterns - 6th International Conference, CAIP 1995, Proceedings
EditorsVaclav Hlavac, Radim Sara
PublisherSpringer Verlag
Number of pages6
ISBN (Print)3540602682, 9783540602682
StatePublished - 1995
Externally publishedYes
Event6th International Conference on Computer Analysis of Images and Patterns, CAIP 1995 - Prague, Czech Republic
Duration: 6 Sep 19958 Sep 1995

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference6th International Conference on Computer Analysis of Images and Patterns, CAIP 1995
Country/TerritoryCzech Republic


Dive into the research topics of 'Detecting grey level symmetry: The frequency domain approach'. Together they form a unique fingerprint.

Cite this