Two-Dimensional Markov Representations of Sampled Images

This paper shows that, under certain weak restrictions, a two-dimensional discrete Markov process can be represented either "causally" by a one-sided difference equation, or "noncausally" by a multiple-sided difference equation. The former representation is pertinent to the analysis of image coders and processors that operate sequentially on scanned image data. The latter representation is applicable to the analysis of block coders and processors. The general relation between the two representations is given and the specialized forms resulting under separable scene covariance studied.