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65(BIC(K) = 2 L IND (Y −B | θ ˆ K , K) − N )02 log(1 − R2 K) − D K log(N 0 ) (4.76)In equation 4.76, Y −Bis the image Y excluding the boundary B. K is thenumber of segments, and ˆ θ K is the vector of estimated parameters for the modelwith K segments. The 4 autoregressive coefficients are included in ˆ θ K , as well as(K − 1) mixture proportions, K mean parameters, and, for the Gaussian case, Kvariance parameters. The R 2 K value is from the autoregression described in section4.4. N 0 is the number of pixels in Y −B , and D K is the number of parameters inˆ θ K .4.4 Fitting the Raster Scan Autoregression ModelAfter performing a segmentation of the image into K segments, the estimatedsegmentation ˜Z can be used to create a mean-corrected version of the image M.This procedure is described in section 4.3. After finding M, we need to fit themodel given in equation 4.77.M i = β W +1 M i−(W +1) + β W M i−W + β W −1 M i−(W −1) + β 1 M i−1 + ɛ i (4.77)It is quite straightforward to compute this model with standard least squaresregression software. The response variable is the vector of M i values in rasterscan order, excluding the observations on the image boundary.Since the RSAmodel involves the four neighbors which precede each observation in raster scanorder, the four predictor vectors are these four lagged values for each pixel. Thepredictor vectors will each contain some of the boundary pixels. When a leastsquares regression is computed from this model, the coefficients of the 4 predictorsare exactly the four estimated β values for the RSA model. The R 2 value from this