Two-Dimensional Pattern Analysis and Classification Using a Complex Orthogonal Estimation Algorithm

An orthogonal estimation algorithm is derived for the estimation of parameters associated with the complex autoregressive boundary model of two-dimensional shapes. It is shown that the coefficients of the orthogonal model and the original system parameters are invariant to rotation around the origin, to the choice of starting point in tracing the boundary and to scale and translation. The error reduction ratios derived from the estimation algorithm can be used to detect which terms should be included in the system model, and classification, based on the orthogonal parameters is shown to be less susceptible to incorrect model order specification. Classification based on orthogonal data sets is also derived and it is demonstrated that this approach can avoid some problems associated with classification based on the model parameters alone.