. The analysis of multichannel two-dimensional random signals. Green. -ig. Representation of a color image as a 3-channel 2-D random process. - 69- and within a particular region this signal is generated by the AR model F(n1;n2) =]TAt-liaF(n1 -il,n2 - i2) + W(nl5n2) () * i xi F(nl5n2) =F(n1,n2)+/x () where /x is a constant mean vector. The white noise W(nx ,n2) is described by a 3 x3 spatially invariant covariance matrix Ew = E[W{n1,n2)WT{n1,n2)} () which in general is not diagonal. A separate model of this type is formed for each ofthe image regions in which there is a differen

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. The analysis of multichannel two-dimensional random signals. Green. -ig. Representation of a color image as a 3-channel 2-D random process. - 69- and within a particular region this signal is generated by the AR model F(n1;n2) =]TAt-liaF(n1 -il,n2 - i2) + W(nl5n2) () * i xi F(nl5n2) =F(n1,n2)+/x () where /x is a constant mean vector. The white noise W(nx ,n2) is described by a 3 x3 spatially invariant covariance matrix Ew = E[W{n1,n2)WT{n1,n2)} () which in general is not diagonal. A separate model of this type is formed for each ofthe image regions in which there is a different texture. The essence of the segmentation algorithm is as follows. Using the models ()and a Gaussian white noise source, we can form a probability density function for theset of all pixels in the color image conditioned on the regions. Assume that there areQ regions Rx, R2,... , RQ . Since the texture is independent from region to region, thisdensity function can be written as Qp(F\Z1,Z2,...,RQ) = ]lp(F\Zl) () t= i where p{F\Ri) represents the joint density

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