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A signal processing approach to symmetry detection.

Yosi Keller1, Yoel Shkolnisky

  • 1Department of Mathematics, Yale Universtiy, New Haven, CT 06520, USA.

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|August 12, 2006
PubMed
Summary

We developed an algorithm to detect rotational and reflectional symmetries in 2D objects using angular correlation. This method efficiently analyzes image symmetries and identifies their centers.

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Area of Science:

  • Computer Vision
  • Image Processing
  • Signal Processing

Background:

  • Symmetry detection is crucial for analyzing 2D object structures.
  • Existing methods may lack efficiency or robustness for various symmetry types.

Purpose of the Study:

  • To present a novel algorithm for detecting both rotational and reflectional symmetries in 2D objects.
  • To leverage angular correlation and pseudopolar Fourier transform for accurate symmetry analysis.

Main Methods:

  • Utilizing angular correlation (AC) to measure image correlations in the angular direction.
  • Employing the pseudopolar Fourier transform for efficient AC computation.
  • Applying spectrum estimation to recover symmetry order from the AC signal.
  • Developing a new method for pinpointing the center of symmetry.

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Main Results:

  • The angular correlation (AC) of symmetric images is proven to be a periodic signal.
  • The frequency of the AC signal directly relates to the order of symmetry.
  • The algorithm accurately detects and analyzes rotational and reflectional symmetries.
  • The method's applicability to real-world images is demonstrated.

Conclusions:

  • The proposed algorithm offers an effective and efficient approach for 2D object symmetry detection.
  • The integration of pseudopolar Fourier transform and spectrum estimation enhances symmetry analysis.
  • The technique provides a robust tool for analyzing symmetries in various applications.