134.

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(5.46)

where u(i, j) is zero-mean white Gaussian noise. The covariance of u(i, j) is given by:

(5.47)

where σ_u denotes the variance of u.

5.4.2 Estimation the parameters of the MAR model

Three parameters of the MAR model are generally estimated and used as texture descriptors. These are the neighbourhood weighting parameter vector θ, the noise variance σ_u², and the mean value δ_y of the stationary random process y, respectively (Equation (5.46)). The estimation method employed here uses the least-squares method (Kashyap and Chellappa, 1983). Given an image x(i, j) of size M×M, the least-squares parameter estimates, based on a log transform of x(i, j), ln x(i, j)=y(i, j), are:

(5.48)

with covariance

(5.49)

and mean

(5.50)

where

(5.51)

Because of variations in texture, different images will generally show different value of mean, noise covariance and parameter θ, and so it is possible

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