Multilevel autoregressive models for planar shape

In this paper we extend the autoregressive (AR) model to the multilevel AR model with wavelet transformation, in order to get the AR coefficients at each level as a set of shape descriptors for every level. To get the multilevel AR model, we use the wavelet transformation such as Haar wavelet to a boundary data. Then real AR and complex-AR (CAR) models are adopted to the multilevel boundary data of a shape to extract the features at each level. Furthermore we present the relation of the autocorrelation coefficients between adjacent resolution levels to elucidate the relation between AR model and wavelet transformation. Some experiments are also shown for the multilevel AR and CAR models with a certain similarity measure.