Fourier-transformed preprocessing used in a noniteratively-trained perceptron pattern recognizer

When a digitized image is preprocessed by spatial quantizations in a polar-coordinate, the analog vectors representing the r and the θ quantizations can be treated separately in neural network trainings. If we apply a segmented Fourier transform (similar to FFT) to the θ vector and a segmented Hankel transform to the r vector in a noniterative perceptron training system, then not only the learning of the training patterns is very fast, but also the recognition of an untrained pattern is very robust. Specially the recognition is very robust when the test pattern is rotated even though all the training patterns are not rotated in space. The high robustness of recognition is due to the special preprocessing scheme and the optimum noniterative training scheme we adopted in the design. This paper concentrates at the theoretical origin and the experimental results of the robustness of this novel perceptron learning system