Simultaneous Position, Scale, and Rotation Invariant Pattern Classification Using Third-Order Neural Networks

摘要

We demonstrate a third-order neural network that distinguishes between classes of patterns regardless of their translational position, scale, and angular orientation. A significant feature of this network is that it is trained on only one view of each pattern, using a simple single-layer perception learning rule. In approximately one minute of run time on a Sun 3 computer, the network learns to distinguish between the letters T and C at any position, scale, or rotation in a 9 x 9 image field, with 100 accuracy in a noise-free background. Examples of both second-order and third-order networks illustrate that geometric invariances can be built into the network architecture using information about the relationships expected between input pixels. The invariances achieved require no learning to produce and apply to any input pattern learned by the network. Higher-order neural networks are therefore capable of efficiently performing both types of mapping required by pattern recognition problems, namely feature extraction and object classification.