Symmetry analysis for 2D images by using DCT coefficients

In this study, we proposed a new method to align symmetric signals by using symmetry property of discrete cosine transform (DCT), which is widely used in signal compression and pattern recognition. For the symmetric signals, the energy is concentrated in the even indexed DCT coefficients. Using this property, we defined a symmetry measure. In this measure, ratio of the energy in even indexed coefficients to total energy gives the symmetry value for the signal. When the symmetry values of the rotated image at different angles become maximum, it means that the image is aligned according to its symmetry axis. We use 2D face data in experimental studies, because of its well-known symmetric property. This symmetry measure can also be adapted to any dimensional signals. The proposed method is tested on texture and shape data of the 3D face which is taken from FRGC database. Using the proposed method which exploits face symmetry, it is shown that the alignment resolution better than 1° can be achieved.