Abstract
A new type of two-dimensional random field model, named the two-dimensional auto-regressive model, is introduced for stochastic representation of digital images. This model is an extension of the one-dimensional auto-regressive model for time serieses. In the model the gray level of each pixel in the image is represented as a linear weighted summation of gray levels of its neighbour pixels on all sides, added with a white noise.
Statistical properties and spectral representation of the model are discussed. Then the iterative algorithm is proposed to generate the image represented by the model with given parameters. The model identification from a given image by the maximum likelihood method is also discussed. It is shown that the least square error model fitting does not give correct parameters for the noncausal type auto-regressive models. The summation of square residuals multiplied by a correction term is to be minimized to identify the model. Finally, several random images have been generated by the proposed generation algorithm, and from these images the correct parameters have been obtained by the pronosed identification method.
