A signal processing approach to symmetry detection

• Published in: IEEE transactions on image processing Vol. 15; no. 8; pp. 2198 - 2207
• Main Authors: Keller, Y., Shkolnisky, Y.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01-08-2006; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Angular correlation; Applied sciences; Artificial Intelligence; Biomedical signal processing; Computer Graphics; Computer vision; Detection, estimation, filtering, equalization, prediction; Exact sciences and technology; Fourier transforms; Frequency estimation; Grid computing; Image analysis; Image Enhancement - methods; Image Interpretation, Computer-Assisted - methods; Image processing; Information Storage and Retrieval - methods; Information, signal and communications theory; Miscellaneous; Numerical Analysis, Computer-Assisted; Object detection; Pattern Recognition, Automated - methods; Rotational; Signal and communications theory; Signal processing; Signal processing algorithms; Signal Processing, Computer-Assisted; Signal representation. Spectral analysis; Signal, noise; Spectral analysis; Symmetry; Symmetry detection; Telecommunications and information theory; Image analysis; Fourier transformation; Spectrum analysis; Signal estimation; Signal processing; Two dimensional model; Algorithm; Signal analysis; Periodic signal
• ISSN: 1057-7149; 1941-0042
• DOI: 10.1109/TIP.2006.875227

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