Pattern Recognition by detection of local symmetries

The symmetries in a neighbourhood of a gray value image are modelled by conjugate harmonic function pairs. These are shown to be a suitable curve linear coordinate pair, in which the model represents a neighbourhood. In this representation the image parts, which are symmetric with respect to the chosen function pair, have iso-gray value curves which are simple lines or parallel line patterns. The detection is modelled in the special Fourier domain corresponding to the new variables by minimizing an error function. It is shown that the minimization process or detection of these patterns can be carried out for the whole image entirely in the spatial domain by convolutions. What will be defined as the partial derivative image is the image which takes part in the convolution. The convolution kernel is complex valued, as are the partial derivative image and the result. The magnitudes of the result are shown to correspond to a well defined certainty measure, while the orientation is the least square estimate of an orientation in the Fourier transform corresponding to the harmonic coordinates. Applications to four symmetries are given. These are circular, linear, hyperbolic and parabolic symmetries. Experimental results are presented.