Generalized symmetry transformation with Gaussian phase weight function

• Published in: Optical review (Tokyo, Japan) Japan), 2012-03, Vol.19 (2), p.58-63
• Main Authors: Lee, Hee-Yul, Kim, Tae-Hun, Jeon, Joon-Hyung, Choi, Il, Park, Kil-Houm
• Format: Article
• Language: English
• Subjects: Atomic; Lasers; Microwaves; Molecular; Optical and Plasma Physics; Optical Devices; Optics; Photonics; Physics; Physics and Astronomy; Quantum Optics; Regular Paper; RF and Optical Engineering
• ISSN: 1340-6000; 1349-9432
• DOI: 10.1007/s10043-012-0013-y

The generalized symmetry transformation (GST) is a symmetry operator detecting objects by using edge gradient directions. Conventional GST uses the cosine function to define the phase weight function (PWF), which represents the symmetry of two gradient directions. The cosine function of PWF leads to a good performance in detecting symmetrical objects. However, the weights of gradient pairs, which are considered to be asymmetrical, are relatively high, so side effects appear near the symmetry pick regions. (Note that side effects disturb the multiple object detection.) In this paper, we use the Gaussian function in calculating the symmetric weights of gradient pairs. The Gaussian function can suppress the weights of less symmetric gradient pairs. In addition, the symmetry for elliptically shaped objects can be more emphasized by controlling the width of the Gaussian function. The proposed GST is evaluated through experiments on synthetic images, which include various bright and dark plane figures, and on real images, which requires the detection of elliptical shapes.