We propose a new method to find the proper center of the circular harmonic filter using simulated annealing. The new method is two orders of magnitude faster than the previous method. The proper center is a chosen expansion center which ensures the maximum peak of the correlation output to be at its center, thus a truly shift and rotation invariant pattern recognition system. The proper center is to be used in a new synthesis of filters: the geometrical approach of multiple circular harmonic filters. In this approach, the distances between the correlation peaks in multiple correlation outputs are used as features for pattern recognition. This method has good discrimination capability and can be implemented for practical applications.