A signal processing approach to symmetry detection

Yosi Keller, Yoel Shkolnisky

Research output: Contribution to journalArticlepeer-review

39 Scopus citations


We present an algorithm that detects rotational and reflectional symmetries of two-dimensional objects. Both symmetry types are effectively detected and analyzed using the angular correlation (AC), which measures the correlation between images in the angular direction. The AC is accurately computed using the pseudopolar Fourier transform, which rapidly computes the Fourier transform of an image on a near-polar grid. We prove that the AC of symmetric images is a periodic signal whose frequency is related to the order of the symmetry. This frequency is recovered via spectrum estimation, which is a proven technique in signal processing with a variety of efficient solutions. We also provide a novel approach for finding the center of symmetry and demonstrate the applicability of our scheme to the analysis of real images.

Original languageEnglish
Pages (from-to)2198-2207
Number of pages10
JournalIEEE Transactions on Image Processing
Issue number8
StatePublished - Aug 2006
Externally publishedYes

Bibliographical note

Funding Information:
Manuscript received January 30, 2005; revised August 23, 2005. This work was supported by a Grant from the Ministry of Science, Israel. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Ivan W. Selesnick. The authors are with theDepartment of Mathematics, Yale Universtiy, New Haven, CT 06520 USA. Digital Object Identifier 10.1109/TIP.2006.875227


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