This paper addresses the problem of identification of appropriate autoregressive (AR) components to describe textural regions of digital images by a general class of two-dimensional (2-D) AR models. In analogy with univariate time series, the proposed technique first selects a neighborhood set of 2-D lag variables corresponding to the significant multiple partial auto-correlation coefficients. A matrix is then suitably formed from these 2-D lag variables. Using singular value decomposition (SVD) and orthonormal with column pivoting factorization (QRcp) techniques, the prime information of this matrix corresponding to different pseudoranks is obtained. Schwarz's (1978) information criterion (SIG) is then used to obtain the optimum set of 2-D lag variables, which are the appropriate autoregressive components of the model for a given textural image. A four-class texture classification scheme is illustrated with such models and a comparison of the technique with the work of Chellappa and Chatterjee (1985) is provided.
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