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.
|Number of pages||10|
|Journal||IEEE Transactions on Image Processing|
|State||Published - Aug 2006|
Bibliographical noteFunding 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