A TRANSLATIONhXOTATION INVARIANT NEURAL NETWORK TRAINED VIA CONJUGATE GRADIENT OPTIMIZATION
Kimberly A. Reed, J.J. Helferty · 1989
A Neural Network (NN) model which possesses the properties of invariance to both left-right/up-down image translation and integer multiples of ninety-degree image rotation was computer simulated. This Invariance Network is comprised of two distinct subnetworks, the Preprocessor and the Adaptive Descrambler, which are themselves NNs. Although the overall structure of the network mimics that of the Widrow MADALINE Invariance NN [ 1,2,3 41, the operation of the two networks are different. Sigmoidal nonlinearities (versus hardlimiting nonlinearities in the Widrow model) are employed for the neurons in this model. Consequently, a conventional conjugate gradient optimization routine can be utilized to train the weights in the network on standard (normal reading position and centered in the field of view) input images. Once trained on the standard images only, the network is also capable of recognizing as the same image one with left-right/up-down translation or integer multiples of ninety-degree rotation. Successful simulation results were achieved for both bipolar and gray level input images.