Extraction of local mirror-symmetric feature by odd-even decomposition

A mirror-symmetric feature extraction approach is proposed. When a point on the assumed symmetry axis is given, an arbitrary 1D signal is decomposed into a pair of odd and even components which maintain the information of absolute symmetry and dissymmetry, respectively. The average difference between the energy of the odd and even components reflects the degree of symmetry with regard to the given symmetry point. An objective function is obtained to search the most symmetric point in a 1D signal as an optimization process. The most likely mirror-symmetry axis is obtained from the set of symmetric points in all the rows in an image.