Estimation of stochastic model for random moving image by means of noncausal model

A new method for estimating a stochastic model of a random moving image is proposed. Assuming that the spatiotemporal spectrum of a moving image is separable in space and time, a stochastic image model is obtained by combining a noncausal model in two-dimensional space and a causal AR model in time. Model estimation uses the method of minimizing whiteness for the noncausal spatial model and the method of ''sequential orthogonalization'' for the causal temporal model. The separable spectrum can be readily applied to a drifting moving model. Applying the spatial filter to a drifting moving image, the moving image is decomposed into a set of uncorrelated time series along the drifting time axis; this allows the AR models to be estimated separately. It is confirmed by computer simulation that the correct model can be estimated by this method. On the other hand, in the model estimation for a real, natural moving image, spectral separability is not always valid and, therefore, the output time series of the spatial filter is not rigorously uncorrelated. For such a real moving image, the method devised is an extended AR model which takes into account the spatially correlated data for AR model estimation. For estimating an extended AR model, the method of quasisequential orthogonalization is developed by modifying the sequential orthogonalization. It is successfully applied to processing a real moving image taken from a video recording.