A complex nonlinear exponential autoregressive model approach to shape recognition using neural networks

A complex nonlinear exponential autoregressive (CNEAR) process which models the boundary coordinate sequence for invariant feature extraction to recognize arbitrary shapes on a plane is presented. A neural network structure is constructed to calculate all the CNEAR coefficients synchronically. The network is simple in structure and easy to implement. The nonlinear parameter is easy to determine using the network. The coefficients are adopted to constitute the feature set. They are proven to be invariant to the transformation of a boundary such as translation, rotation, scale, and choice of the starting point in tracing the boundary. Afterwards, the feature set is used as the input to a complex multilayer perceptron (C-MLP) network for learning and classification. Experimental results show that complicated shapes can be recognized with high accuracy, even in the low-order models. It is also seen that the CNEAR model performs better than the complex autoregressive (CAR) model when shapes have random noise on the boundaries or have differentiating features at detailed levels. Finally, an extended training scheme is developed in which the network is gradually retrained sequentially with shapes containing small increments of noise to improve the robustness of the C-MLP classifier.